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Chess and Checkers: The Way to Mastership

Complete instructions for the beginner [and]
valuable suggestions for the advanced player.

by

Edward Lasker





TABLE OF CONTENTS



INFORMATION ABOUT THIS E-TEXT EDITION

INTRODUCTION

     THE HISTORY OF CHESS
     THE HISTORY OF CHECKERS

PART I: THE GAME OF CHESS

     I.   THE RULES OF THE GAME

            Board and men
            The moves of the men
            Special terms
            Symbols for moves
            Chess laws

    II.   ELEMENTARY TACTICS

            Fundamental endings
            Relative value of the men
            How the different men cooperate
            Sacrificing

   III.   GENERAL PRINCIPLES OF CHESS STRATEGY

            King's Pawn openings
            Queen's Pawn openings
            The middle game

    IV.   ILLUSTRATIVE GAMES

            Game No. 1: Jackson Showalter vs. Edward Lasker,
            Lexington, Ky., 1917

            Game No. 2: Edward Lasker vs. Jose R. Capablanca,
            New York, 1915

     V.   PROBLEMS

PART II: THE GAME OF CHECKERS

     I.   THE RULES OF THE GAME

    II.   ELEMENTARY TACTICS

   III.   THE FIVE FUNDAMENTAL POSITIONS

            The first position
            The second position
            The change of the move
            The third position
            The fourth position
            The fifth position

    IV.   GENERAL PRINCIPLES AND ILLUSTRATIVE GAMES

     V.   PROBLEMS



INFORMATION ABOUT THIS E-TEXT EDITION



The following is an e-text of "Chess and Checkers: The Way
to Mastership," by Edward Lasker, copyright 1918, printed in
New York.

This e-text contains the 118 chess and checkers board game
diagrams appearing in the original book, plus an extra chess
diagram that appears on the front cover of the book, all in
the form of ASCII line drawings. The following is a key to
the diagrams:

For chess pieces,

  R  =  Rook
  Kt =  Knight
  B  =  Bishop
  Q  =  Queen
  K  =  King
  P  =  Pawn

Black pieces have a # symbol to the left of them, while
white pieces have a ^ symbol to the left of them. For example,
#B is the Black bishop, while ^B is the white bishop. #Kt is
the black knight, while ^Kt is the white knight. This will
let the reader instantly tell by sight which pieces in the
ASCII chess diagrams are black and which are white.

For Checkers pieces,

  *  =  black single piece
  o  =  white single piece

  ** =  black king
  oo =  white king

Those who find these diagrams hard to read should feel free
to set up them up on a game board using the actual pieces.



PREFACE



The present world war has given great impetus to the game of
Chess. In the prison camps, in the field hospitals, in the
training camps and even in the trenches Chess has become a
favorite occupation in hours of leisure, not only because it
offers a most fascinating pastime, but mainly because it serves
beyond any doubt to develop what is now the most interesting
study for every soldier--the grasp of the principles underlying
military strategy and the ability to conceive and to carry out
military operations on a large scale.

Frederick the Great, Napoleon and Moltke, the great scientists of
war, had a decided liking for the game of Chess and owed to it
many an inspiration which helped them in laying out their
military plans. Indeed, no other game exists which offers such
complete analogies to war.

Two armies oppose each other on the Chess board, composed of
different units which may well be compared with infantry, cavalry
and artillery.

The success of the operations on the board, which represents the
battlefield, does not depend upon any element of chance, but
solely upon the ingenuity and the skill of the players who are
the commanders-in-chief of the forces.

Although a Chess game differs from a battle in that the material
strength of the opponents is equal, the order of events is the
same in Chess as in war. The troops are first mobilized and made
ready for action with utmost speed, then important positions are
occupied which give the troops freedom of action and insure safe
lines of retreat and, finally, when the formation of the enemy is
known, the strategic plan is made which the generals try to carry
out by means of different tactical maneuvers.

Considering this similarity of Chess and war it is not surprising
that Chess has gained greatly in popularity among all those whose
work or thought is more than superficially influenced by the
present war.

No special inducement, however, would be necessary to learn the
game, were it more generally known that great advantage is to be
derived from the study of Chess, quite apart from the cultivation
of strategic ability.

The faculty which is developed by playing Chess is useful
wherever logical thinking and concentration are needed, and it
cannot be denied that these qualities are most desirable in the
every day struggle in which mental work has so largely superseded
manual labor.

The thoughtful playing of the game not only cultivates the
logical quality and imaginative power of the mind but also tends
to develop strength of character. It teaches us not to be hasty
in our decisions, but to exercise foresight at all times as we
must abide by all consequences of our actions. Moreover, we learn
from it circumspection which causes us to survey the whole scene
of action and does not allow us to lose ourselves in detail; we
also learn not to be discouraged by reverses in our affairs but
to hold out and always search for fresh resources.

Thus, Chess serves a good purpose for young and old. The boy will
find it a fascinating pastime and, unconsciously sharpening his
wits in playing the game, will acquire a fine preparation for his
calling in life, no matter what it may be. For the man, and the
woman too, Chess is well worth learning, as it will prove the
best companion in hours of leisure.

The reason why many people hesitate to learn the game and to
teach it to their children is that Chess has been misrepresented
as a game which is very difficult to master. This false
impression has been created mainly by the wrong methods of
teaching usually employed. The majority of writers on Chess deal
with a maze of variations and they expect the reader to memorize
the moves with which to parry the maneuvers of the opponent,
instead of simply developing a few common sense principles which
are easy to grasp and perfectly sufficient to make a good player
of any one.

This is really the great advantage of the game of Chess over any
other board game, that it lends itself to the application of
general principles, so that any one can grasp and enjoy it
without memorizing more than the rules according to which the men
move.

I have tried to develop these principles in a simple way so that
they are sure to be easily understood, and I have been greatly
aided in my task by Miss Helen Dvorak and Mr. Eugene Fuller, who,
without any previous knowledge of the game, have learned it in
reading through the manuscript of this book. They have given me
many valuable hints in pointing out all that did not seem readily
intelligible to the mind of the beginner.

In explaining the game of Checkers, to which the second part of
the book is devoted, I have also tried to develop general
principles of strategy, rather than to offer a mere
classification of analyzed lines of play, which the reader would
have to memorize in order to be able to compete with experts.

I was fortunate enough to secure the collaboration of the Checker
Champion, Alfred Jordan, who enthusiastically adopted the new
idea of teaching and furnished most of the material which I have
used in illustrating the vital points of the game.

EDWARD LASKER.



INTRODUCTION



The History of Chess


The game of Chess in the form in which it is played to-day is
usually assumed to be of a much older date than can be proved
with certainty by documents in our possession. The earliest
reference to the game is contained in a Persian romance written
about 600 A.D., which ascribes the origin of Chess to India. Many
of the European Chess terms used in the Middle Ages which can be
traced back to the Indian language also tend to prove that India
is the mother country of the game.

We are, therefore, fairly safe in assuming that Chess is about
1300 years old. Of course we could go farther, considering that
the Indian Chess must have been gradually developed from simpler
board games. Indeed we know from a discovery in an Egyptian tomb
built about 4000 B.C. that board games have been played as early
as 6000 years ago; but we have no way of finding out their rules.

The game of Chess spread from India to Persia, Arabia and the
other Moslem countries, and it was brought to Europe at the time
of the Moorish invasion of Spain. It also reached the far East,
and games similar to Chess still exist in Japan, China, Central
and Northern Asia, the names and rules of which prove that they
descended from the old Indian Chess.

In Europe Chess spread from Spain northward to France, Germany,
England, Scandinavia and Iceland. It became known with
extraordinary rapidity, although at first it was confined to the
upper classes, the courts of the Kings and the nobility. In the
course of time, when the dominance of the nobility declined and
the inhabitants of the cities assumed the leading role in the
life of people, the game of Chess spread to all classes of
society and soon reached a popularity which no other game has
ever equaled.

While in the early Middle Ages the game was played in Europe with
the same rules as in the Orient, some innovations were introduced
by the European players in the later Middle Ages which proved to
be so great an improvement that within a hundred years they were
generally adopted in all countries including the Orient. The
reason for the changes was that in the old form of the game it
took too long to get through the opening period. The new form,
which dates from about 1500 A.D. and the characteristic feature
of which is the enlarged power of Queen and Bishop, is our modern
Chess, the rules of which are uniform throughout the civilized
world.

In the Seventeenth Century Chess flourished mostly in Italy,
which consequently produced the strongest players. Some of them
traveled throughout Europe, challenging the best players of the
other countries and for the most part emerging victorious. At
that time Chess was in high esteem, especially at the courts of
the kings who followed the example of Philip the Second of Spain
in honoring the traveling masters and rewarding them liberally
for their exhibition matches.

Towards the beginning of the Eighteenth Century the game reached
a high stage of development in France, England and Germany. The
most famous master of the time was the Frenchman, Andre Philidor,
who for more than forty years easily maintained his supremacy
over all players with whom he came in contact, and whose fame has
since been equaled only by the American Champion, Paul Morphy,
and by the German, Emanuel Lasker.

During the Eighteenth and Nineteenth Centuries the number of
players who obtained international fame increased rapidly, and in
1851, due to the efforts of the English Champion Staunton, an
international tournament was held in London to determine the
championship of Europe. It was won by the German master
Anderssen, who maintained his leading place for the following
fifteen years, until he was beaten by the youthful Morphy. The
latter, at twenty years of age, was the first American master to
visit Europe and defeated in brilliant style all European masters
whom he met.

Morphy withdrew from the game after his return to America and did
not try to match himself with the Bohemian Steinitz, who in the
meantime had beaten Anderssen, too, and who had come to America.
Steinitz assumed the title of the World's Champion and defended
it successfully against all competitors until 1894, when he was
beaten by Emanuel Lasker, who is still World's Champion, having
never lost a match.

The next aspirant for the World's Championship is the young
Cuban, Jose Raoul Capablanca, who has proved to be superior to
all masters except Lasker. He entered the arena of international
tournaments at the age of twenty-two in San Sebastian, Spain, in
1911, and won the first prize in spite of the competition of
nearly all of Europe's masters. In the last international
tournament, which was held in Petrograd in 1914, he finished
second, Emanuel Lasker winning first prize.

The present ranking of the professional Chess masters is about
the following:

       1. Emanuel Lasker, Berlin, World's Champion.
       2. J. R. Capablanca, Havana, Pan-American Champion.
       3. A. Rubinstein, Warsaw, Russian Champion.
       4. K. Schlechter, Vienna, Austrian Champion.
       5. Frank Marshall, New York, United States Champion.
       6. R. Teichmann, Berlin.
       7. A. Aljechin, Moscow.

Other players of international fame are the Germans, Tarrasch and
Spielmann, the Austrians, Duras, Marocy and Vidmar, the Russians,
Bernstein and Niemzowitsch, the Frenchman, Janowski and the
Englishman, Burn. Up to the time of the outbreak of the war the
leading Chess Clubs of the different countries arranged, as an
annual feature, national and international tournaments, thus
bringing the Chess players of all nationalities into close
contact.

This internationalism of Chess is of great advantage to the Chess
player who happens to be traveling in a foreign country. There
are innumerable Chess Clubs spread all over the globe and the
knowledge of the game is the only introduction a man needs to be
hospitably received and to form desirable social and business
connections.

It would be going beyond the limit of this summary of the history
of Chess if I tried to give even an outline of the extremely
interesting part Chess has played in French, English and German
literature from the Middle Ages up to the present time. Suffice
it to mention that Chess literature by far exceeds that of all
other games combined. More than five thousand volumes on Chess
have been written, and weekly or monthly magazines solely devoted
to Chess are published in all countries, so that Chess has, so to
speak, become an international, universal language.


The History of Checkers


The literature on the game of Checkers (English: Draughts) is
very limited and there are no certain references to prove that
the game was known before the Sixteenth Century. Two theories are
current as to its origin; one of them claiming it to be a
simplified Chess, the other explaining it as the result of
transferring the Spanish game Alquerque de doze to the Chess
board.

H. J. R. Murray, the greatest authority on the history of games,
considers it most likely that the game has been evolved from both
Chess and Alquerque. The method of capturing men and the rule
concerning the huffing of a man unquestionably point to the
Spanish game, while the board, the diagonal move of the men and
the idea of crowning a man are taken from Chess.

In France, Germany, Italy and Spain the name of the game is still
that of the Queen of Chess (Dame, Dama) whose move in the Middle
Ages was identical with the move of the Checkermen.

Checkers has never been able to attain more than national
uniformity, and it is played with different rules in different
countries. In the United States it is more popular than in any
other country and a number of players have obtained national
fame. The best players at present are considered to be Newell
Banks and Alfred Jordan.



PART I: THE GAME OF CHESS



I



THE RULES OF THE GAME



BOARD AND MEN

The game of Chess is played by two armies who oppose each other
on a square board or battlefield of sixty-four alternate white
and black squares. Each army has sixteen men; one King, one
Queen, two Rooks (or Castles), two Bishops, two Knights and eight
Pawns. The Generals of the two armies are the two players
themselves. The men of one side are of light color and are called
White, those of the other side are of dark color and are called
Black.

The object of the game is to capture the opposing King. When this
is done the battle is ended, the side losing whose King is
captured. To understand what is meant by the capture of the King
it is first necessary to become acquainted with the laws
according to which the different men move on the board.

To start with, the board must be placed so that the players have
a white square at their right. Then the men take the positions
shown in Diagram 1.

The Rooks occupy the corner squares; next to them stand the
Knights; then the Bishops and in the center the King and the
Queen.

       +---------------------------------------+
     8 | #R | #Kt| #B | #Q | #K | #B | #K | #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P | #P | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^P | ^P | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q | ^K | ^B | ^Kt| ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 1

The white Queen must be on the white square and the black Queen
on the black square. These eight, men are commonly known as
"pieces" in distinction from the Pawns. The latter occupy the
line of squares immediately in front of the Pieces.

The lines of squares now occupied by the men and the other four
vacant horizontal lines between them are called RANKS. The
vertical lines of squares running perpendicularly to the ranks
are called FILES. The oblique lines of squares, that is, lines
which connect squares of the same color, are called DIAGONALS.

To describe the moves of the men on the board in a simple way it
is necessary to indicate every square and every man by a short
symbol. For this purpose different systems have been suggested at
different times, but only two of them have been generally
adopted. The older one, called the "descriptive notation," still
predominates in the English, French and Spanish speaking
countries, but as leading English and American writers have
lately used the newer "algebraic notation" which is much more
simple, the latter will be employed in this book. Later the
former method will be explained for the sake of completeness.

In the algebraic notation the files are lettered from a to h,
starting from the file on White's left. The ranks are numbered
from 1 to 8, starting from the rank on which White's pieces stand
at the beginning of the game. Each square is now easily indicated
by naming the file and rank at which it forms the intersection.
The Rook in Diagram 2, for instance, stands on e4, the Bishop on
C4, the Pawns on h4 and g7, the Knight on f7, the Queen on d6 and
the Kings on c1 and g3.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    | ^Kt| #P |    |
       |---------------------------------------|
     6 |    |    |    | #Q |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    | #B |    | ^R |    |    | ^P |
       |---------------------------------------|
     3 |    |    |    |    |    |    | #K |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    | ^K |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 2

As symbols for the men the first letters of their names are used.
Thus K stands for King, Q for Queen, R for Rook, B for Bishop, Kt
or N for Knight and P for Pawn.



THE MOVES OF THE MEN



Each of the six kinds of men moves in a different way. To
remember the six varieties of moves naturally requires a little
more effort than to remember just the one way of moving as in
most other board games. But it takes only very little practice to
become familiar with the various moves of the Chessmen and it is
soon revealed to the learner that the variety of the moves
enables a surprising depth and wealth of combinations which give
keener and greater pleasure to this game than to any other.


The Rook


The Rook may move forward, backward or sideways in a straight
line along a path not obstructed by a man of the same color. In
other words, he may move to any square of the rank or file on
which he stands unless another man of his own color is in the
way. If there is a hostile man in the way he may capture him by
occupying his square and removing him from the board.

In Diagram 2, for instance, the Rook could move to e5, e6, e7,
e8, e3, e2, e1, f4, g4, d4 and c4. In making the latter move he
would capture the black Bishop. The Rook may not go to h4 because
a man of his own color stands there nor may he go to b4 or e4
because he is not allowed to jump over the Bishop. He could, of
course, move to either of these squares on his next move after
capturing the Bishop.


The Bishop


The Bishop moves along an oblique line, that is, he may move to
any square of the diagonals on which he stands unless--as in
the case of the Rook--his way is obstructed by a man of his own
color. If there is a hostile man in the way he may capture him.
In Diagram 2, therefore, the Bishop may move to a2, b3, d5, e6
or, by capturing the Knight, to f7. He may not move, however, to
g8, until his next move after capturing the Knight. In the other
diagonal all squares, that is, fi, e2, d3, b5 and a6, are
accessible to him.

As the Bishop is confined to squares of the same color as the one
on which he stood at the beginning of the game he has access only
to thirty-two squares of the board, and from this it is evident
that the Rook to whom all squares of the board are accessible is
a stronger man.


The Queen


The Queen has the power of both Rook and Bishop having the choice
of moving to any square of the rank, file or diagonal on which
she stands as long as her path is clear. In Diagram 2 the squares
to which the Queen may move are, therefore, e3, b4, c5, e7, f8,
f1, b5, C7, b8, d1, d2, d3, d4, ds, d7, d8, a6, b6, c6, e6, f6,
g6 and h6. Like the Rook and Bishop she has the power of
capturing a hostile man by occupying his square.

The Queen is by far the most powerful of the pieces. Later it
will be seen that ordinarily her strength is about equal to the
strength of two Rooks.


The King


The King, like the Queen, moves and captures in any direction,
but he is much less powerful because he may move only one square
at a time. Nevertheless, he is the most important man, for, as
said at the beginning, the object of each side is the capture of
the opposing King.

To save the King from untimely death there is a rule that the
King may not move into any square which is in the direct range of
any man of his enemy. Thus, in Diagram 2 the black King may move
to f2, g2, h2, f3 and h3, but he may not move to f4 or g4 nor may
he capture the Pawn on h4, for on any of these squares he could
be captured by the white Rook.

The white King in Diagram 2 has only three squares to which he
may go, namely, b1, b2 and c2, as the squares d1 and d2, though
being in his range, are commanded by the black Queen.


The Knight


The Knight moves neither in rank nor file nor diagonal and,
therefore, usually offers a little more difficulty to the
beginner than the other pieces. The Knight's move is perhaps best
described as a leap to the next but one square of different
color.[Footnote: It may be helpful to consider the Knight's move
when completed as having described a letter "L" composed of four
squares, three in one direction and one at right angles to them.]
For instance, in Diagram 2 the Knight may move to d8, d6, e5, g5,
h6 and h8. In moving to d6 he would capture the Queen.

His move would be in no way obstructed if some of his own or his
adversary's men were occupying the squares next to the one on
which he stands. This enables the Knight as the only one of the
pieces to move at the beginning of the game before any Pawn move
has been made.

The strength of the Knight is ordinarily regarded as about equal
to that of the Bishop. The latter's range is larger but the
Knight has the advantage of being able to reach any square of the
board regardless of color.


The Pawn


It remains to describe the move of the Pawn, the only man who
captures in a different way from that in which he moves. The Pawn
moves FORWARD ONLY in the file in which he stands, and only one
square at a time with the exception of his first move on which he
may advance two squares. Thus, in Diagram 2, the white Pawn may
move only to h5 while the black Pawn may move to either g6 or g5.

The Pawn may capture only diagonally, only forward and only one
square at a time. The privilege of taking a double step on the
first move does not extend to the capture. Thus in Diagram 2, the
white Pawn could capture only a black man on g5, the black Pawn
only a man on either f6 or h6, but not on e5. If a man stood on
h5, the Pawn h4 would be blocked. Likewise would the Pawn on g7
be blocked by a man on g6.

There is one peculiar rule to be remembered in connection with
the move of the Pawn. If a Pawn uses his privilege of making a
double step to avoid capture by a hostile Pawn he can be put back
one square and captured just the same. For instance, in Diagram
2, if the white Pawn stood on h5 and Black moved his Pawn to g5,
White could put Black's Pawn back to g6 and capture him with his
Pawn. This way of capturing is called taking "en passant" (French
for "in passing") and can be done only by a Pawn, never by a
piece.

Lastly must be mentioned the power of the Pawn to become
transformed into a piece. This is done automatically whenever a
Pawn reaches the extreme opposite side of the board. That is, the
player must remove the Pawn from the board and put any piece on
his place except a King. Thus it can happen that a player may
play with three or more Rooks, Bishops, Knights or Queens. As the
Queen is the strongest Piece the Pawns are practically always
exchanged for Queens and for this reason the process of the
exchange is called "queening."

Although a Pawn has comparatively little value as measured by his
mobility--his range of movement--he is really a very valuable man
because of the possibility of his eventually queening.


Castling


Only once in a game is a player allowed to move more than one
piece at a time. This one move is called "castling" and is made
by the King together with one of the Rooks. In castling the King
moves two squares toward the Rook and the Rook is placed on the
square over which the King has passed. In the position of Diagram
3 both players may castle either side.

White, in "castling King's side" would place his King on g1 and
the King's Rook on f1; in "castling Queen's side" the King would
leap to c1 while the Queen's Rook would take his stand on d1.
Likewise Black would castle by either playing the King to g8 and
the Rook from h8 to f8, or the King to c8 and the Rook to a8 to
d8.


       +---------------------------------------+
     8 | #R |    |    |    | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P |    | #Q | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt| #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    | #B |    | #P |    | ^B |    |
       |---------------------------------------|
     4 |    |    | ^B |    | ^P |    | #B |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^Q |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                 DIAGRAM 3.


       +---------------------------------------+
     8 | #R | #Kt|    |    | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #P |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    | #P | ^P |    |    |    |
       |---------------------------------------|
     4 |    | ^B |    |    |    | ^P |    |    |
       |---------------------------------------|
     3 |    |    |    |    | #Kt| ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 4.

Castling is permitted only when neither King nor Rook concerned
has previously moved, when none of the squares between the King
and the Rook are obstructed and when none of the three squares
involved in the King's move are controlled by an adverse man.
Thus if in check (see page 17) the player may not castle. In
Diagram 4, neither White nor Black may castle.


SPECIAL TERMS


Attack and Defense


A man is said to ATTACK another man if he moves so that on his
next move he could capture the other man. Thus, in Diagram 5,
White could attack Black's Bishop by moving his Rook to d1 or to
e6.

A man is said to DEFEND or to PROTECT another man if he moves so
that in case the other man is captured by a hostile man he could
recapture the latter. Thus, in Diagram 5, Black could defend his
Bishop by moving his Knight to either e4 or e8 in case White
attacks with the Rook from d1. Should White attack from e6, then
Black would not defend the Bishop with the Knight, for on e4 as
well as on e8 the Knight is unprotected and could be captured by
the Rook without White losing anything in exchange. Black has a
much more simple way to defend the attack of the Rook from e6,
that is, by capturing the Rook with the Pawn f7. For this reason
White would not have moved the Rook to e6.


Check and Checkmate


If a man makes a move which attacks the opposing King the King is
said to be in "check." The player whose King is checked then has
to make a move which gets the King out of check

       +---------------------------------------+
     8 |    |    |    |    |    |    | #K |    |
       |---------------------------------------|
     7 |    |    |    |    |    | #P | #P |    |
       |---------------------------------------|
     6 |    |    |    | #B |    | #Kt|    | #P |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 | ^P |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^P |    |    |    |    | ^P |
       |---------------------------------------|
     2 |    |    |    |    |    |    | ^P |    |
       |---------------------------------------|
     1 |    |    |    |    | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 5.

or he forfeits the game. This is the only case in which a player
is not at liberty to make any move he likes.

Unless the attacking man can be captured there are only two ways
of getting out of check. One of these is to interpose a man
between the King and the attacking piece, and the other to move
the King out of the line of attack. In Diagram 5 Black could give
check by moving the Bishop to c5. In answer to this White has
four moves at his disposal. He may either move the King to f1 or
h1 or h2, or he may interpose his Rook on e3. The latter would be
very unwise as Black would simply take the Rook with his Bishop,
again checking White's King. The situation would then not have
changed at all except that White would have lost his Rook.
White's King could not move to f2, for this would leave him still
attacked by the Bishop.

Instead of checking on c5 Black could have attacked White's King
on h2. But in this case the King would have simply captured the
Bishop.

If it were White's move he could give check with the Rook on e8.
But Black could take the Rook with the Knight. He would naturally
do this instead of either moving out with the King to h7 or
interposing the Bishop on f8.

If a King is in Check and there is no move with which to get him
out of it he is said to be "checkmate" and the game is ended.
Diagram 6 shows an example in which either player can give
checkmate on the move.

If it were White's move he would take the Pawn on g6 with his
Queen. Now Black's King is in check as White's Queen threatens to
take him on the next move. The King cannot move to either g7 or
h7, for these two squares are also commanded by White's Queen.

       +---------------------------------------+
     8 |    |    |    | ^R |    | #Kt| #K | #R |
       |---------------------------------------|
     7 | #P | #B | #P |    |    | #P |    |    |
       |---------------------------------------|
     6 |    | #P | #Q | #B |    |    | #P |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    | ^Kt| ^Kt|    |
       |---------------------------------------|
     3 |    | ^B |    | ^Q |    |    |    | ^P |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    |    | ^P | ^K |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                 DIAGRAM 6.

Moreover, the latter cannot be taken by the Pawn on f7 as the
black King would be in check by the Bishop on b3. The Pawn is
"pinned" by the Bishop. Black's Knight cannot take White's Queen
either as he is pinned by White's Rook. Finally, there is no
piece available which may be interposed between White's Queen and
Black's King; in other words: Black is checkmate, his game is
lost.

If it were Black's move he would take the Pawn g2 with the Queen.
Now White's King is in check as Black's Queen threatens to take
him on the next move. He may not take the Queen as he would then
be captured by the Bishop b7. Neither may the Knight f4 take the
Queen as he is pinned by the Bishop d6. Moreover, the King may
not escape to g1, h1 or g3, these three squares lying in the
rangeof Black's Queen; and so there is no move on the board with
which to get White's King out of check: He is checkmate, White
loses the game.


Stalemate


If a player, without being in check, cannot make any move which
would not get his King into check, he is said to be STALEMATE. In
this case the game is considered a draw. Diagram 7 shows an
example.

White on the move, although his forces are much inferior, can
draw the game by checking with the Rook on f3. Black cannot very
well make a move with his King in reply, as then White's Rook
would take the Queen. Black, therefore, must capture the Rook
with the Queen and with this move he stalemates White, as the
latter has no move left which would not bring his King into
check.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    | #Q |    |    |    | #K |
       |---------------------------------------|
     2 |    |    |    |    |    | ^R |    |    |
       |---------------------------------------|
     1 |    |    |    |    | #R | ^Kt| ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 7.

If it were Black's move he would easily win. In fact he has two
different ways of checkmating White in three moves. One of them
would be to take the Knight with the Rook, attacking the King and
forcing White's Rook to recapture as the King has no square to go
to; then to give check with the Queen on g3 forcing White's King
to h1 and enabling the mate with the Queen on g2 or h2.

The other way would be to start with the check on g3. As White's
Knight is pinned he cannot capture the Queen.

       +---------------------------------------+
     8 |    |    |    |    |    |    | #K |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    | #P |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^Q |    |    |    |
       |---------------------------------------|
     3 |    | #Q |    |    |    |    | ^P |    |
       |---------------------------------------|
     2 | #P |    |    |    |    |    |    | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    | ^K |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 8

Interposing the Rook on g2 would not help either as the Queen
would simply take him at the same time checkmating the King.
White's only move is, therefore, to play the King into the
corner, and Black then mates by first taking the Knight and then
moving the Queen to g2 or h2.

Perpetual Check


If a player is able to check the opposing King continually and he
indicates his intention to do so the game is considered a draw.
In the following position, for instance, White on the move can
draw the game by giving a perpetual check on e8 and h5. Black
cannot help himself as he has to go back and forth with the King
on h7 and g8. Without the possibility of this perpetual check
White would be lost, for he cannot prevent the Pawn a2 from
queening and with two Queens against one Black would easily win
as will be seen later from the discussion of elementary endings.


Exchange


To exchange means to capture a hostile man when it allows a man
of the same value to be captured by the opponent.

It is rather confusing that the term "exchange" is also used for
the difference in value between a Rook and a Bishop or a Knight.
To win the exchange, in this sense, means to capture a Rook and
to lose for it only a Bishop or a Knight.

Double Pawn


Two Pawns of the same player standing in one file are called a
double Pawn. Three Pawns in one file are called a triple Pawn.


Passed Pawn


A Pawn whose advance to the eighth rank is not blocked by an
opposing Pawn in the same file and who does not have to pass one
on an adjoining file is called a passed Pawn.


Isolated Pawn


A Pawn is called isolated if there are no Pawns of the same
player on the adjoining files.


Backward Pawn


A Pawn is called backward if he cannot advance far enough to be
protected by fellow Pawns in an adjoining file.


Fork


A Pawn is said to fork two pieces if he attacks them
simultaneously.


Minor Piece


The Bishops and the Knights are called minor Pieces as compared
with the Rooks and the Queen.


Sacrifice


To sacrifice means to give up a man without obtaining for him a
man of the opponent or to give up a man for one of lesser value.


Discovered Check and Double Check


A discovered Check is an attack on the King caused by a man
moving out of the line of a piece which he was obstructing. If
the man discovering the Check also attacks the King the Check is
called a double Check.


SYMBOLS FOR MOVES


In addition to the symbols used for squares and men, as explained
on page 5, the following are used to indicate the moves:

-- means "moves to"

X means "captures"

o-o means "Castles King's side"

o-o-o means "Castles Queen's side"

+ means "check"

+/- means "checkmate"

Thus: R-f5 means the Rook moves to square f5. If either Rook
could move to f5 then the original square of the Rook to be moved
must also be shown.

Kte3xd5 means the Knight standing on e3 captures the man standing
on d5.

o-o-o means the player castles Queen's side and in so doing
gives check.

[Footnote: In the descriptive notation alluded to on page 5 every
square of the board has two different names, each player counting
the ranks from his own side. The files are named after the pieces
which stand on them at the beginning of the game. Thus, c4 would
be QB4 (Queen's Bishop's fourth) or QB5 depending on whether a
black or a white move is described. If a square is referred to
without relation to a particular move it is necessary to add from
which side of the board the square is counted. It is customary to
say in cases of this kind "White's Queen's fourth" or "Black's
Queen's fourth," etc.

Instead of naming the square on which a capture takes place, the
man captured is named, so that an additional description is
necessary in case more than one man of the same kind can be
captured.

As a matter of comparison the first ten moves of a game are
described above in both notations.]

! signifies a good move.

? signifies a bad move.

          (1) P-d4          P-d5
          (2) P-c4          P-e6
          (3) Kt-c3         P-c5
          (4) Kt-f3         Kt-c6
          (5) Pxd5          Pxd5
          (6) B-f4          Kt-f6
          (7) P-e3          B-e6
          (8) B-d3          B-e7
          (9) o-o           o-o
         (10) R-c1          Kt-h5

          (1) P-Q4          P-Q4
          (2) P-QB4         P-K3
          (3) Kt-QB3        P-QB4
          (4) Kt-B3         Kt-QB3
          (5) PxQP          KPxP
          (6) B-KB4         Kt-B3
          (7) P-K3          B-K3
          (8) B-Q3          B-K7
          (9) Castles       Castles
         (10) R-B           Kt-KR4



CHESS LAWS



If a player having the move touches one of his men he is
compelled to move him; if he touches a hostile man he must
capture him. This law is void, however, if the man so touched
cannot be legally moved or captured.

A man may be moved to any square accessible to him as long as the
hand of the player has not left him. If an illegal move has been
made it must be retracted and if possible another move must be
made with the same man. If a player has castled illegally, King
and Rook must be moved back and the King must make another move,
if there is a legal one.

If a player touches a man with the sole object of adjusting his
position, he must indicate his intention by saying "j'adoube"
(French for: I adjust) beforehand. In castling, the King must be
moved first as otherwise a doubt might arise whether castling or
a Rook's move only was intended.

A game is void if a mistake has been made in setting up board or
men or if in the course of the game the position or number of men
have been altered in a manner not in accordance with the rules of
play and the position cannot be reconstructed from the point
where the error was made.

If a player resigns his game before he is actually mated he
acknowledges that in the end mate is unavoidable, and the game is
counted as a loss to him.

If neither player has sufficient material left to enforce a mate
(compare following chapter) the game is considered a draw. A draw
may also be claimed by either player if the moves are repeated so
that the same position occurs three times with the same player on
the move, or if fifty moves have been made without the capture of
a man or the move of a Pawn.



II


ELEMENTARY TACTICS



The beginner who thinks he ought to be able to play a good game
of Chess after learning the moves of the men is like the soldier
who is confident that he could lead an army after he has learned
how to march.

He may have great strategical gifts but he will not be able to
use them to any advantage unless he is thoroughly conversant with
the tactical possibilities afforded by the cooperation of the
different units of which his army is composed and by the
topography of the ground on which the battle takes place.

The different conditions of the battle ground in war which make
some positions more easily accessible to infantry than to
artillery and vice versa have their equivalent on the Chess board
in the different ways in which the men move and which make
certain squares accessible to some of them which others cannot
reach.

The first thing, then, for the beginner to do is to acquaint
himself thoroughly with the characteristic features of each man
so that he may know exactly how much work to expect from him. The
best way to accomplish this is the study of the elementary
problems which are in end games, that is, in positions where only
a few men are left on each side.



FUNDAMENTAL ENDINGS



Considering that the object of the game is the capture of the
opposing King, it seems most important to find out whether there
are positions in which this capture can be accomplished in the
face of the best possible defense. Naturally a player must have a
certain material superiority to be able to force a mate, and the
first question which offers itself is what MINIMUM force is
required to compel the surrender of a King whose men have all
been captured during the game.

It is clear that in order to checkmate the lone King it is
necessary to attack the square on which he stands as well as all
adjacent squares to which he could escape. The most unfavorable
position for the King is, of course, a corner of the board as
there he has only three squares to go to while in the middle of
the board eight squares are accessible to him. Consequently, in
an ending in which one player has only his King left the other
player will try to drive the King into a corner where he needs
control over only three additional squares.

It can easily be seen that this can be done without difficulty
with King and Queen or with King and Rook. Supposing, for
instance, White has his King on c3 and his Queen on h3 while
Black's King stands on d6 as shown in the following diagram.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    | #K |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^K |    |    |    |    | ^Q |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 9.

How will White proceed in order to drive the King into a corner
and checkmate him there?

A direct onslaught with the Queen on e6 or d7 is clearly not
advisable as the Queen would not be protected on these squares,
so that the King could simply capture her. A long range attack
from h2, g3, d3 or h6 is not effective either as it would not
restrict the mobility of the King who could go to either d5 or e6
or e5, that is away from the corner to which he is to be driven.

The correct way of maneuvering for White will be to confine
Black's King to a smaller and smaller territory until he finally
has to back up against the side or the corner of the board. This
consideration indicates the following line of play:

(1)Q-f5, K-c6; (2)Q-e5, K-d7; (3) K-c4, K-c6; (4) Q-e7, K-b6; (5)
Q-d7, K-a6. White must now be very careful to avoid a stalemate
which would result if he deprived the King of all mobility
without attacking him at the same time. This would be the case if
he now moved Q-c7. For then Black could not move the King to b5,
as this square is controlled by White's King, and he could not go
to any of the other four squares in his range on account of
White's Queen attacking all of them. The correct move is (6) K-
c5. This leaves only the square a5 for Black's King, and White
checkmates by (7) Q-a7 or (7) Q-b5.

If, in Diagram 9, White had a Rook on h3 instead of the Queen,
the mating process would take a few more moves, but there would
be no escape for Black either.

It will again be White's aim to confine Black's King to a smaller
and smaller number of squares. The best way to start will
therefore be (1) R-e3. No matter what Black replies, he cannot
prevent White from driving him to the edge of the board in a
similar way to the one shown in the following example:

(1) ..., K-d5; (2) R-e1. This is a WAITING MOVE. Black must leave
d5, thus enabling either White's King to advance or the Rook to
occupy e5. (2) ..., K-c5; (3) R-e5; K-d6; (4) K-d4, K-c6; (5) R-
d5, K-b6; (6) R-c5, K-b7; (7) K-d5, K-b6; (8) K-d6, K-b7; (9) R-
b5, K-a6; (10) K-c6, K-a7; (11) K-c7, K-a6; (12) R-h5, K-a7; (13)
R-a5 mate.

The two examples discussed show that it is not necessary to drive
the King into the corner but that he can be mated on any square
of the edge by Queen or Rook. It will be observed that in the
mating position three of the six squares at Black's disposal are
controlled by White's King and the other three by the Rook (or
the Queen). If White had only a Bishop or a Knight in addition to
the King he could never mate Black, for neither Bishop nor Knight
can attack the King and at the same time control a square
adjacent to the King. This, however, is at least necessary to
force the mate, even in the most unfavorable position of the
King, that is, in the corner.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 | ^Kt|    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    | #P |
       |---------------------------------------|
     2 |    |    |    |    |    | ^K |    | #K |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 10.

There are possibilities of a player mating his opponent with only
King and Knight or King and Bishop, but then there must be a man
of the opponent blocking the escape of the King. Diagram 10 is an
example of such a case. White plays (1) Kt-c5, K-h1; (2) Kt-e4.
Now Black cannot continue with P-h2, as White would checkmate
with Kt-g3. Therefore, he must play (2) ..., K-h2. White then
gets the Knight in such a position as to deprive Black's King of
the escape to h2 and to keep the square g3 accessible to the
Knight: (3) Kt-d2 (not Kt-g3, which would stalemate Black's
King), K-h1; (4) Kt-f1. The only move left to Black is now P-h2,
and White mates by (5) Kt-g3.

If it were Black's move in the position of the Diagram the game
would be a draw, for after (1) ..., K-h1; (2) Kt-c5, P-h2 Black
is stalemate unless White moves his King so as to make the square
g1 accessible to Black. However, he will not do that as it would
enable Black to queen the Pawn and to win the game.

In the case of King and Bishop against King and another man a
mate can only occur through a blunder. Supposing for instance
White has the King on f3 and a Bishop on d5 and Black has the
King on h1 and a Bishop or a Pawn on h2, then White on the move
would mate by K-f2. But it is evident that Black must have made a
blunder, for on the move preceding the position of the Diagram he
must have either played his King into the corner or moved the
Bishop or Pawn to h2, both moves which were in no way forced.

To checkmate with King and two Bishops against King or with
Bishop and Knight against King offers no difficulty.

       +---------------------------------------+
     8 | #K |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 | ^K | ^B | ^B |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 11.

The only thing the player must keep in mind is that he needs his
King for the drive. The two pieces are not sufficient to confine
the opposing King to the corner. In Diagram 11 for instance, it
will be the best policy for White to advance right away with his
King in order to prevent Black's King from escaping into the
middle of the board. The following play might then ensue:

(1) K-b2, K-b7; (2) K-c3, K-c6; (3) K-d4, K-d6; (4) B-f5, K-c6;
(5) B-f4, K-b5; (6) B-e4, K-b4; (7) B-d3, K-b3; (8) B-d2, K-b2;
(9) K-c4, K-a3; (10) K-c3, K-a4; 11) K-c2 (not K-b2 which would
stalemate Black's King), K-a3; (12) B-b5, K-a2; (13) B-c1, K-a1;
(14) B-b2, K-a2; (15) B-c4 mate.

In the fight of King, Bishop and Knight against the King the mate
can be enforced only in a corner controlled by the Bishop, if the
lone King always makes the best move. Diagram 12 may serve as an
example of this ending. White has a black Bishop and so he will
have to drive Black's King to either h8 or a1 as it is not
possible to mate him in the white corner a8, unless he makes a
blunder.

After (1) B-e5 for instance, Black must of course not go into the
corner as Kt-b6 would mate him. He will play K-c8 and White will
have to prevent the flight of the black King into the middle of
the board. It is easy to see, by the way, that the Kt cannot be
placed so as to control the square c8, thereby forcing the King
into the corner, and to threaten the mate on b6 at the same time.
For he can control c8 only from a black square while he would
have to stand on a white square to be able to reach b6 in one
move.

After (1) B-e5, K-c8; (2) K-b6, K-d7; (3) Kt-f4 Black's King is
confined to the seventh and eighth ranks and it is only a
question of time when he will be forced to h8.

       +---------------------------------------+
     8 |    | #K |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 | ^K |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    | ^Kt|    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^B |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
        ---------------------------------------
         a    b    c    d    e    f    g    h

                DIAGRAM 12.

White's Bishop being only capable of commanding black squares the
Knight will have to be used to drive the King from white squares.
For instance: K-c8; (4) K-c6, K-d8; (5) Kt-g6, K-c8; (6) Kt-e7,
K-d8; (7) K-d6, K-e8; (8) K-e6, K-d8; (9) B-h2. A waiting move.
White wants to place the Bishop on c7 so as to make d8
inaccessible to Black. (9) K-e8; (10) B-c7, K-f8; (11) Kt-f5, K-
e8; (12) Kt-g7, K-f8; (13) K-f6, K-g8; (14) K-g6, K-f8; (15) B-
d6, K-g8; (16) Kt-f5, K-h8; (17)

       +---------------------------------------+
     8 |    | #K |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    | ^K |    | ^Kt|    |    |    |    |
       |---------------------------------------|
     5 |    |    | ^Kt|    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
        ---------------------------------------
         a    b    c    d    e    f    g    h

                DIAGRAM 13.

B-a3. Again a waiting move. White cannot play Kt-h6 right away as
Black would be stalemate. (17) ..., K-g8; (18) Kt-h6, K-h8; (19)
B-b2 mate.

It is not possible to force a mate with King and two Knights, for
even if a position similar to Diagram 13 is arrived at, in which
the King can be driven into the corner, the Knight who prevents
the King from escaping is never ready to give the checkmate, and
in order to prevent a stalemate the other Knight would have to
let the King out of the corner again. If Black had a spare move,
for instance if he had a Pawn left, then White would win. (1) Kt-
a6, K-a8; (2) Kt-e8, Pawn moves; (3) Kt-c7 mate.



RELATIVE VALUE OF THE MEN



From the foregoing examples it is possible to form a vague idea
of the strength of the different pieces. The Queen is apparently
the strongest piece. On account of her superior mobility she can
confine the hostile King with a few moves and force him into a
mating net. Of the other pieces the Rook is no doubt the
strongest for he is sufficient to force a mate in conjunction
with his own King, while Bishop or Knight cannot do so. Two
Bishops apparently are stronger than two Knights, while it is not
possible yet to say anything about the relative value of one
Bishop and one Knight.

The above valuation, however, holds good only on the
comparatively vacant board, where the pieces can make full use of
their mobility. It is the mobility alone which decides the value
of a man, and positions often occur in which a Knight is more
valuable than a Rook or in which a Pawn might be preferable to a
Bishop and so on. The reason is that sometimes the weaker man
occupies a commanding square while the stronger man is obstructed
somehow or other so that he cannot be made to work. Examples for
positions of this kind will be discussed in the Chapter on
combination.

Although it is impossible to indicate exactly the relative value
of the men in each position, experience enables a fair estimation
of their average strength. The Queen is about as strong as two
Rooks or as three minor pieces (Bishops or Knights). A minor
piece is about equivalent to three Pawns, and a Rook is
consequently equal to a minor piece and one to two Pawns.

The value of a Pawn is the hardest thing to grasp for the
beginner. A Pawn appears to be of so little use on account of his
limited mobility, that it seems hardly worth while to waste time
on saving a Pawn that is attacked, as so much greater things are
apparently at issue. What he overlooks is the latent value of the
Pawn which lies in the possibility of queening him later in the
game.

To realize the importance of the Pawn it is necessary to know
exactly under what conditions he CAN be queened. This knowledge
is all the more indispensable to the Chess player as the vast
majority of all games finally resolve themselves into Pawn
endings in which the advantage of one or more Pawns decides the
issue.

In most of these cases some pieces are on the board in addition
to the Pawns and sometimes it is only by their exchange that the
game can be won. The most elementary example is that shown in the
following Diagram.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 | #Q |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    | #K |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    | ^Q |    |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 14.

White is a Pawn ahead and it will be his object to Queen it. The
beginner, in his haste to advance the Pawn, will probably play P-
e5 at once and lose the Pawn, as Black can answer Q-d4 check with
simultaneous attack on the Pawn. The correct way to play for
White is (1) Q-d1+, K-a3 or b4; (2) Qxa4, Kxa4. Now that the
Queens are exchanged White need not any longer worry about any
interference with his plans to queen the Pawn except maneuvers of
the black King, which might still lead to the capture or the
blockade of the Pawn.

A rash advance of the Pawn would again be the wrong thing. The
right way of playing is indicated by a simple calculation. The
Pawn needs four moves to reach the queening square. But the black
King arrives there in the same number of moves, so that he can
capture the Pawn the moment he queens. Consequently White will
only be able to enforce the safe queening of his Pawn if he can
gain control of the queening square with his own King, thus
protecting the Pawn at the time of queening.

Now, White needs three moves to bring his King up to his Pawn on
f4. In the meantime Black will have reached the square d6 and
after White's (4) K-f5 Black will block the further advance of
White's King by K-e7. However, White can force Black to give the
way free. The maneuver by which he does this is one which occurs
in a similar form in nearly all Pawn endings and its thorough
grasp is therefore essential. Diagram 15 shows the critical
position.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    | #K |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    | ^K |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 15.

White can win the game only by playing (5) K-e5. The technical
term for this move is "going into OPPOSITION." The Kings oppose
each other in one line on squares of the same color and the one
who has to move out of opposition--in this case Black's King--is
compelled to allow the advance of the opposing King to the next
line. If Black plays K-d7, White answers (6) K-f6, and if Black
plays K-f7, (6) K-d6 would follow. Then, after Black's K-e8,
White repeats the maneuver by taking the opposition with (7) K-
e6, and again Black must back out with either K-d8 or K-f8, so
that White can advance to either f7 or d7. This clears the way
for the Pawn who now advances unimpeded to the queening square.

The important role which the opposition of the Kings play in Pawn
endings is still more strikingly illustrated by the situations
which would result if in the position of Diagram 15 White played
(5) P-e5 instead of K-e5. Black would then draw the game by
maintaining the opposition himself. He would play K-f7 and
although after (6) P-e6, K-e7; (7) K-e5 White has regained the
opposition he cannot keep it if Black continues correctly. The
move which saves the game for Black is K-e8. K-d8 or K-f8 lose,
as then White could go into opposition by K-d6 or K-f6. The play
in these three cases would be this: A: (7) ..., K-e8, (8) K-f6,
K-f8; (9) P-e7+, K-e8; (10) K-e6 and Black is stalemate, the game
is drawn. B: (7) ..., K-d8; (8) K-d6, K-e8; (9) P-e7 and Black
must move K-f7 enabling White to obtain control of the queening
square by (10) K-d7. C: (7) ..., K-f8, (8) K-f6, K-e8, etc.,
similar to the play in B.

To sum up the investigation of this Pawn ending: The deciding
factor is the opposition of the Kings on the 6th and 8th ranks.
If the weaker party succeeds in obtaining that opposition with
the Pawn on the 6th rank he draws the game.

If the Pawn is not yet advanced to the 6th rank the opposition of
the Kings is of no avail to the weaker party as the Pawn
advancing would force the opposing King out of opposition again.
Suppose, for instance, White has the King on e6 and the Pawn on
e5 while Black's King stands on e8 with White on the move. White
must get out of opposition by playing K-f6 or K-d6 and Black
keeps the opposition by K-f8 or K-d8. But then White has a move
to spare which forces Black out of opposition and thereby wins
the game. He plays P-e6 and the game ends in the way discussed
above.

The ending King and Pawn against King is one of the most
important for every Chess player to know, not only because a
great number of positions can be reduced to this ending by the
exchange of all the other men left on the board, but also because
it gives the first insight into the peculiar maneuvers of the
King which have to be carried out in connection with gaining or
giving up the opposition, and which, as will be seen later on,
constitute the essence of the most frequent pawn endings.

For the beginner, of course, the opposition maneuvers are rather
difficult to grasp and it is fortunate for him that the vast
majority of pawn endings are of a much simpler form. The winning
maneuver in these endings into which most Chess games resolve
themselves, is easily explained and after understanding it the
beginner can readily see the fundamental principle underlying
every game.

Diagram 16 shows a typical position on which the winning method
should be studied. White is a pawn ahead, but as demonstrated on
the position of Diagram 15 he cannot queen his passed Pawn
because his King is not in front of it. On the other hand, there
cannot possibly be any advantage in advancing the Pawns on the
other side of the board as there Black has the same number of
Pawns as White and consequently there is no reason why one of the
white Pawns should succeed in breaking through. It is all the
same very easy for White to win and the strategy to be employed
will be evident from the following consideration: Black's King is
considerably confined in his movements as he has to be constantly
watching White's passed Pawn.

        +---------------------------------------+
      8 |    |    |    |    |    |    |    |    |
        |---------------------------------------|
      7 |    |    |    |    |    |    |    |    |
        |---------------------------------------|
      6 |    |    |    |    |    |    |#P  |    |
        |---------------------------------------|
      5 |    |    | #K |    |    | #P |    |    |
        |---------------------------------------|
      4 |    |    |    |    |    |    |    |    |
        |---------------------------------------|
      3 |    | ^P |    |    |    | ^P |    |    |
        |---------------------------------------|
      2 |    |    | ^K |    |    |    | ^P |    |
        |---------------------------------------|
      1 |    |    |    |    |    |    |    |    |
        +---------------------------------------+
          a    b    c    d    e    f    g    h

                   DIAGRAM 16.

White's King, however, is free to go wherever he likes without
any immediate danger. There is consequently nothing to hinder him
attacking and capturing the black Pawns, for if Black's King
tries to stop White's advance, White's passed Pawn marches on and
compels the opposing King to catch him, thereby giving the way
free to his own King. According to this scheme play could proceed
like this: (1) K-d3, K-d5; (2) K-e3, K-e5; (3) P-b4, P-g5; (4) P-
b5, K-d5; (5) P-b6, K-c6; (6) K-d4, Kxb6; (7) K-e5, P-f4; (8) K-
f5, K-c6; (9) Kxg5, K-d6; (10) Kxf4, K-e6; (11) K-g5, K-f7. Now
White would win even without the Pawn g2 by playing (12) K-f5 and
so on as explained on Diagram 15.

From the foregoing it will be clear to the beginner that if a
player succeeds in winning a Pawn he can win the game if he is
able to exchange all pieces so that only the Pawns are left.
However, he will not yet see the way in which this exchange of
pieces can be forced. It is evident that the player who has lost
the Pawn will try to avoid the exchange, hoping that he may be
able to regain the Pawn with his pieces. Therefore, he will
permit his opponent an exchange only if, in avoiding it, he would
sustain an additional loss. The position of Diagram 17 offers a
simple example. White on the move will play R-e5, offering the
exchange of Rooks. If Black tried to avoid the exchange by
playing R-b6, White would capture the Pawn f5 with the Rook and
after Black's King moves out of check he would take the Pawn g4
too. Therefore Black has to make the offered exchange of Rooks,
and White then wins by advancing the c-Pawn which forces Black's
King over to the Queen's wing and leaves the Pawns of the King's
wing unprotected.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    | #P |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    | #R |    |    |    | #P |    | #K |
       |---------------------------------------|
     4 |    | ^P |    |    |    | ^K | #P | ^P |
       |---------------------------------------|
     3 |    |    | ^P |    |    |    | ^P |    |
       |---------------------------------------|
     2 |    |    |    |    | ^R |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 17.

The beginner might think that inasmuch as the loss of a Pawn in
most cases means the loss of the game on account of the final
promotion of the Pawn to the Queen, it may be advisable to
sacrifice a piece if thereby the loss of a Pawn can be avoided.
However, this idea, which is frequently met, is altogether wrong
as the additional piece will easily enable the opponent to gain
as many Pawns as he likes within the further course of the game.
The position of Diagram 18 may serve as an example.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    | #P | #K |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 | #B |    |    |    |    | ^K | ^P |    |
       |---------------------------------------|
     3 |    |    |    | ^Kt|    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    | ^B |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 18.

In the following line of play it is assumed that Black makes the
best moves, but the method employed is the same for any defensive
maneuvers which Black might try, with the only difference that
White would win still more quickly. (1) Kt-c5, B-c6; (2) B-f3,
Bxf3; (3) Kxf3, P-b6; (4) Kt-e6, P-c5; (5) P-a4. This move
retains the black Pawns so that the Knight can attack them with
better effect. (5) ..., P-c4; (6) Kt-c7, K-g7; (7) Kt-b5, P-a6;
(8) Kt-d6, K-f6; (9) Ktxc4, P-b5; (10) Pxb5, Pxb5; (n) Kt-a3, P-
b4; (12) Kt-c2, P-b3; (13) Kt-d4, etc.

Often it happens that a player can give up his additional piece
to advantage for one or two Pawns thereby enforcing an ending
which is won on account of the Pawn position. Diagram 19 is an
example.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    | #P |    |
       |---------------------------------------|
     6 |    |    |    |    | #B |    |    | #K |
       |---------------------------------------|
     5 | ^P |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    | ^Kt|    |    |    | ^K | ^P |    |
       |---------------------------------------|
     3 | ^Kt| #P |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    | #P |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 19.

Black is a piece down but his two connected passed Pawns
constitute a dangerous threat. White, therefore, does best to
sacrifice a Knight for the two Pawns, as he then remains with two
Pawns against one. Black must finally give up his Bishop for
White's a-Pawn who threatens to queen, and then White wins by
capturing Black's g-Pawn and queening his own. Play might proceed
as follows: (1) Ktxc2, Pxc2; (2) Ktxc2, B-d5; (3) Kt-b4, B-a8;
(4) P-a6, K-g6; (5) P-a7, K-f6; (6) Kt-a6, K-e7; (7) Kt-c7, B-h1;
(8) P-a8 (Queen), Bxa8; (9) Ktxa8, K-f6; (10) Kt-c7, K-g6; (11)
Kt-d5, K-h6; (12) K-f5, K-h7; (13) K-g5, K-h8; (14) K-g6, K-g8;
(15) Kt-e7+, K-h8; (16) Kt-f5, K-g8; (17) Ktxg7, K-h8; (18) K-f7,
K-h7; (19) P-g5, K-h8; (20) Kt-f5, White could not play P-g6, as
Black would have been stalemate. (20) ..., K-h7; (21) P-g6+, K-
h8; (22) P-g7+, K-h7; (23) P-g8 (Queen) mate.

The game endings discussed up to now have illustrated the method
of winning with a superior force and it is now possible for the
beginner to understand that the leading rule for all maneuvers is
to AVOID THE LOSS OF MATERIAL--no matter how small--as it will
ultimately lead to the loss of the game by one pawn or the other
queening.

The next step will be to find out under what conditions it is
possible to gain a man and when it will be possible to avoid
loss. To understand the attacking and defensive maneuvers
involved it is necessary first to become acquainted with the
different ways in which the various pieces can be made to do some
useful work, where their strength lies and where their weakness,
and how they are able to cooperate. Not before all this is clear
to the beginner--in the outlines at least--will he be in a
position to play a sensible game or even to understand the most
elementary strategic principles.

The reader is therefore urged to study carefully the next chapter
in which the characteristic features of the different men are
discussed. In this way he will much more quickly arrive at a fair
playing strength than by relying on the experience which he may
gain in playing a great number of games, trying to find out
everything for himself instead of profiting by the knowledge
which has been gathered by others in centuries of study.



HOW THE DIFFERENT MEN COOPERATE



There are two kinds of elementary attack. One when a single man
attacks two or more hostile men at the same time; the other when
more men are brought up to attack an opposing man than can be
mustered for defense. The beginner, as a rule, makes attacks with
the sole aim of driving away a hostile piece; it is clear that
these attempts will in most cases be futile as they generally
allow the attacked piece to move to another square just as or
perhaps more favorable. The advantage of attacking two men at
once is evident in that probably only one of them can be saved.
The advantage of bringing up more men for attack than can be
gathered for defense is not less obvious, but will be found more
difficult to carry out. Using both methods of attack in
conjunction is the secret of the successful cooperation of the
men.

In the following diagrams simple illustrations are shown of
elementary cases of such attacks. These positions often occur in
games of beginners on account of their placing the men on
unfavorable squares. In studying them the eye of the beginner
will become accustomed to dangerous formations of the pieces and
he will be able to foresee similar threats in his games.

       +---------------------------------------+
     8 | #R |    |    |    | #K |    | #Kt| #R |
       |---------------------------------------|
     7 | #P | #B | #P |    | #B | #P | #P | #P |
       |---------------------------------------|
     6 |    | #P | #Kt| #P |    | #Q |    |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    | ^B |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P | ^B | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 20.

This is especially true of the mating positions which are
discussed below in connection with attacks instituted by the
Queen in the middle of the game. It is these attacks to which the
beginner at an early stage of the game falls victim in ninety out
of a hundred cases when playing against an experienced opponent.

In the position of Diagram 20 White on the move wins the exchange
and thereby practically the game by playing (1) Kt-d5. With this
move he attacks the Queen and at the same time the Pawn c7.
Black, in order not to lose the Queen, must move her, but he
cannot move her so that she will protect the Pawn c7.

       +---------------------------------------+
     8 | #R | #Kt| #B |    | #K | #B |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    | #Q |    |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt|    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q | ^K | ^B | ^Kt| ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 21.

On the next move White will, therefore, take the Pawn calling
Check and at the same time attacking the Rook a8. The King must
move and the Knight takes the Rook.

Quite frequently a similar attack with the Knight is likely to
win the Queen if the opponent is not familiar with situations of
that kind. If in the position of Diagram 21 White plays (1) Kt-
d5, Black must protect the Pawn c7 by Q-d8 or Q-d6, but not by Q-
c6; for in the latter case White would continue with (2) B-b5,
Qxb5; (3) Ktxc7+ and (4) Ktxb5.

       +---------------------------------------+
     8 | #R | #Kt| #B |    | #K | #B |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    | #P | #Kt|    |    |
       |---------------------------------------|
     5 | #Q |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    | ^B | ^P |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt|    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^B |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q | ^K |    | ^Kt| ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 22.

Sometimes two pieces are involved in the double attack, the line
of one of the pieces being discovered by the other. Thus, in the
position of Diagram 22, which could be brought about by the moves
(1) P-e4, P-d5; (2) Pxd5, Qxd5; (3) Kt-c3, Q-a5; (4) P-d4, Kt-f6;
(5) B-c4, P-e6; (6) B-d2, white threatens to play (7) Kt-d5,
uncovering the Bishop d2 on Black's Queen and at the same time
attacking the Pawn c7, which Black cannot keep protected.

Threats of this kind more frequently occur in connection with a
discovered Check. As an example the following opening will serve:
(1) P-e4, P-e5; (2) Kt-f3, Kt-f6; (3) Ktxe5, Ktxe4; (4) Q-e2, Kt-
f6. Black's last move exposes his King to a discovered Check, and
White wins the Queen by playing (5) Kt-c6+.

Next to the Knight the Queen is most frequently in a position to
carry out a double attack. Two typical examples are shown in the
following diagrams.

After the opening moves (1) P-e4, P-e5; (2) P-f4, B-C5; (3)
Pxe5?? the position of Diagram 23 is reached, in which Black wins
a Rook by Q-h4+. White cannot reply (4) K-e2 on account of Qxe4
mate. His only move is (4) P-g3 and then follows Qxe4 attacking
King and Rook simultaneously.

This opening offers another opportunity to demonstrate the
dangerous mobility of the Queen. Instead of (3) Pxe5 White should
have played (3) Kt-f3. The game could then have continued as
follows: P-d6; (4) B-c4, Kt-f6; (5) Pxe5, Pxe5: Again White
cannot win the Pawn e5 for (6) Ktxe5 would be answered by Q-d4,
attacking Knight and Bishop and threatening mate on f2.

       +---------------------------------------+
     8 | #R | #Kt| #B | #Q | #K |    | #Kt| #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    | #B |    | ^P |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^P |    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q | ^K | ^B | ^Kt| ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 23.

Diagram 24 shows a typical case of a double threat with the Queen
in conjunction with other pieces. White on the move plays B-d3,
and now Black cannot castle as White would continue with Q-e4
threatening mate through Qxh7 and at the same time attacking the
Bishop e7 for the second time who is only once protected. Black
would have to defend the mate by either P-g6 or P-f5 or Q-h5 and
White would capture the Bishop.

When castling on the King side a player must always beware of an
attack by the Queen and another piece on the King's Rook's Pawn.

       +---------------------------------------+
     8 | #R |    | #B |    | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P | #B | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    | ^B | #Q |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^P |    |    | ^Q |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B |    | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 24.

In the case illustrated above it was the Bishop who assisted the
Queen. A Knight could aid in an attack on h7 from either g5 or
f6. More frequently he does so from g5 as usually the square f6
is not accessible to him on account of the Pawn g7 protecting it.
In the majority of cases the Knight goes to g5 from f3, and the
Queen attacks h7 from h5, coming from her original square d1.
Then, if Black cannot protect h7 by a Knight from f6 or by the
Bishop, from f5 for instance, or from g6, the only protection as
a rule is to advance the Pawn to h6. The position of Diagram 25
may serve as an example.

       +---------------------------------------+
     8 | #R | #Kt| #B | #Q | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P | #Kt| #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    | #B |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    | ^B | #P | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |^Kt | ^B | ^Q | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 25

Black's last move was Kt-e7, while Kt-f6, which protects the Pawn
h7 against future attacks, is generally preferable in any
opening. White can now play Kt-g5, attacking the Pawn f7 for the
second time, as it is already attacked by the Bishop c4. The
student will, at this stage of his development, not yet know why
Black should be so anxious to defend the Pawn f7, considering
that he is a Pawn ahead so that the loss of a Pawn would only
equalize the forces but would not give White a material
advantage. However, later on, when discussing the strategy of the
opening, it will become evident that in the position of the
diagram Black must, under all circumstances, defend the Pawn f7
as otherwise his game would soon become hopeless on account of
the exposed position of his King.

There are only two ways for Black to defend f7. One is to advance
the Queen's Pawn to d5, interrupting the diagonal of White's
Bishop; the other is to castle, so that the Rook procures the
second protection for the Pawn f7 which is needed. It would then
not be good for White to capture the Pawn because he would have
to give up Knight and Bishop for Rook and one Pawn, which is not
a sufficient equivalent.

Of the two ways indicated only the first one is feasible. For if
Black castles he gives White an opportunity to institute an
attack on the weak Pawn h7 with Knight and Queen against which
Black has no satisfactory defense. Play would develop as follows:

          (1) Kt-g5          o-o
          (2) Q-h5           P-h6

This is the only defense against the threat Qxh7 mate. But
White's Queen's move involved a double threat. It brought up a
third attack on the Pawn f7, and the latter now falls, forcing
Black to give up some more material.

          (3) Ktxf7          Rxf7

Black has to sacrifice the exchange. If he moved the Queen, which
is attacked by the Knight, he would expose his King to a deadly
double check, viz.: (4) Ktxh6++, K-h8 or h7; (5) Kt-f7+
(discovered), K-g8; (6) Q-h8 mate. After giving up his Rook for
the Knight on the third move Black has a lost game, for as
explained in the previous chapter White can simply exchange all
pieces and force the win in the ending with his superior
material.

Another square which after castling on the King side is often the
mark of attack for the Queen in connection with either Knight or
Bishop, is the one immediately in front of the King in the
Knight's file. Diagram 26 illustrates several possibilities of
this kind. White, on the move, can play (1) Q-g5, attacking for
the second time the Pawn g7 which is only once protected. The
threat, however, is not only to win a Pawn, but to win the game,
for in taking the Pawn with the Queen White would checkmate
Black's King.

       +---------------------------------------+
     8 | #R |    |    |    |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    | #B |    | #P |    |    |    |    |
       |---------------------------------------|
     5 |    |    | #Q |    | #P | ^Kt|    |    |
       |---------------------------------------|
     4 |    | #Kt|    |    | ^P |    |    | ^B |
       |---------------------------------------|
     3 |    | ^P |    | ^P |    |    |    |    |
       |---------------------------------------|
     2 |    | ^P | ^P | ^Q |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 26

The only defense at Black's disposal is P-g6, but this move helps
only temporarily. White can force the mate within a few moves in
different ways. One would be the following:

          (2) Kt-h6+          K-g7

If the King goes to h8 White mates by Q-f6.

          (3) Q-f6+          Kxh6
          (4) B-g5+          K-h5
          (5) P-h3

and the mate through P-g4 cannot be protected.
Another way would be:

          (2) Q-h6          Pxf5
          (3) B-f6

and the mate through Q-g7 cannot be protected.

The position of Diagram 26 enables another mating attack for
White, demonstrating the possibility of mating with Bishop and
Knight in the middle of a game, which occurs oftener than one
would be inclined to think. White can play (1) B-f6 instead of Q-
g5 as suggested above. Black cannot take the Bishop as White
would continue Q-h6 with Q-g7 mate. Neither can Black play P-g6
as then White would mate right away with Kt-h6. The latter mate
with Knight and Bishop White can force, even if Black does not
move the Pawn g7 but makes some other indifferent move, as for
instance Qxc2. White would then make the surprising move Q-h6,
allowing Black to take the Queen. In doing so, however, Black
again enables the mate Kt-h6.

The only move which Black could try in answer to (1) B-f6 is P-
h6, preventing the Queen from occupying g5. Now Qxh6 would not be
feasible as after Pxh6 White does not mate with Ktxh6, but leaves
the square h7 open to Black's King.


       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R |    | #K |
       |---------------------------------------|
     7 | #P | #P | #P | #P | ^Kt| #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    | #Kt|    |    | ^R |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^P |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B | ^Q |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 27.

However, White wins easily through (2) Ktxh6+. If Black takes the
Knight, White mates with Qxh6 and Q-g7. If Black does not take
but plays K-h7, White goes back with the Knight to f5, again
threatening Q-g5 and Qxg7. (3) ..., R-g8 is of no avail, as (4)
Q-g5 threatens mate of h5 which can only be prevented by either
P-g6 or a move with the Rook, after which White mates by either
Q-h6 or Qxg7.

It remains to show some examples of the cooperation of Rooks with
other pieces. Diagram 27 shows one of the positions in which the
beginner is frequently caught.

       +---------------------------------------+
     8 |    |    | #R |    |    |    | #K |    |
       |---------------------------------------|
     7 | ^R |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    | #P |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    | ^P |
       |---------------------------------------|
     4 |    | #B |    |    | ^Kt|    |    |    |
       |---------------------------------------|
     3 | #P |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^K |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 28.

White plays (1) Q-h5, and if Black makes an indifferent move he
mates through (2) Qxh7+, Kxh7; (3) R-h5.

Black could try to defend himself with (1) ..., P-g6. White can
then continue with (2) Q-h6 and again Black cannot make an
indifferent move such as P-d6 for instance, as White would have
another mate in two moves, namely (3) R-h5 (threatening Qxh7),
Pxh5; (4) Q-f6.

More frequent than the mate with Rook and Knight shown above is
one which usually occurs in the end game and which is illustrated
in Diagram 28.

       +---------------------------------------+
     8 |    |    | #R |    | #R |    | #K |    |
       |---------------------------------------|
     7 | #P |    |    |    |    | #P |    |    |
       |---------------------------------------|
     6 |    | #P |    |    | #P |    | #P |    |
       |---------------------------------------|
     5 | #Q |    |    | #P |    |    |    |    |
       |---------------------------------------|
     4 |    | #Kt|    |    |    | ^P |    | ^B |
       |---------------------------------------|
     3 |    | ^P |    |    | ^P | ^R |    |    |
       |---------------------------------------|
     2 | ^P |    |    |    | ^Q |    | ^P | ^P |
       |---------------------------------------|
     1 |    |    |    | ^R |    |    |    | ^K |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 29.

White plays Kt-f6+ and Black cannot go with the King into the
corner as the Rook would mate him on h7. After K-f8 White draws
the game through perpetual check; for after (2) Kt-h7+, K-e8; (3)
Kt-f6+ the King must go back to f8 as on d8 he would be mated by
R-d7. Consequently White can check the King indefinitely on h7
and f6.

An example for the cooperation of Rook and Bishop is shown in
Diagram 29. White plays B-f6, and there is no way for Black to
prevent the mate threatened through R-h3 followed by R-h8.

It is evident that the force of the Rooks will increase as the
board gets emptier through the exchange of men, for they will
then find more open lines to act in. One of the most important
lines for Rooks to occupy is--especially in the ending --the one
in which most of the attackable Pawns of the opponent are
standing, that is in the majority of cases the second or the
seventh rank respectively. If both Rooks cooperate with each
other in this rank they usually decide the victory within a short
time.

Following is an example which is taken from a master game. As far
as the material is concerned the players are about even, as the
Queen is worth as much as the two Rooks while Knight and Bishop
are an approximate equivalent of the Black Rook and the Pawn
which Black is ahead. The Pawn a4 is rather dangerous for White,
as he needs only three more moves to reach the first rank where
he can be promoted into any piece. On the other hand the Rooks
doubled in the seventh rank give White so strong an attack on the
Black King that he forces the mate before Black succeeds in
realizing the advantage of his advanced passed Pawn.

       +---------------------------------------+
     8 |    |    |    |    | #R | #K |    |    |
       |---------------------------------------|
     7 |    | #P | ^R | ^R |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 | #P |    |    |    | ^P | ^Kt|    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    | ^P | ^B |
       |---------------------------------------|
     2 | #Q |    |    |    |    | ^P |    | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                     DIAGRAM 30.

It is White's move. If Black's Queen did not protect the Pawn f7
White would be able to give a mate in five moves, thus: (I)
Rxf7+, K-g8; (2) Rxg7+, K-h8 (not K-f8 on account of Rc7-f7
mate); (3) Rxh7+, K-g8; (4) R-g7+ and Kt-g6 mate.

Therefore, White will try to interrupt the diagonal in which the
Queen defends the threat, and he can do so by (1) Kt-d5. Black
being unable to keep f7 protected, must defend g7 or h7, or he
will be mated. In the game in question Black played Q-a1+ ; (2)
K-g2, P-a3. After (3) Rxf7+, K-g8 it would not be good for White
to take g7, giving up the two Rooks for the Queen, as he would
then have no more attack while Black still has the dangerous Pawn
in the a-line. If possible he will rather interrupt again the
diagonal of Black's Queen. This suggests the move (4) Kt-f6+.
After Pxf6 White's Rooks are at last free to act unmolested in
the seventh rank, and they do it with deadly effect. White forces
the mate through (5) R-g7+, K-h8; (6) Rxh7+, K-g8; (7) Rh7-g7+,
K-h8; (8) B-f5! Now R-g4 is threatened followed by R-h7 mate, and
Black has no defense.

In the opening and in the middle game the main threat of a Rook
is the "pinning" of a hostile piece. What is meant by this is
illustrated in Diagram 31. Supposing Black, to save his Knight f6
which White has just attacked by P-e5, plays Kt-g4 and after (2)
P-h3 takes the Pawn e5 with the Knight g4, then White wins a
piece by (3) Ktxe5, Ktxe5; (4) R-e1. This move "pins" Black's
Knight to his place as the King would be exposed to White's Rook
if the Knight moved. (4) ..., P-d6 or Q-e7 is not a sufficient
defense, for White continues with (5) P-f4.

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt|    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    | #B |    | ^P |    |    |    |
       |---------------------------------------|
     4 |    |    | ^B | #P |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                     DIAGRAM 31.

Pieces that can be used for pinning a hostile man are, apart from
the Rooks, the Queen and the Bishops; in fact pinning is the main
activity of a Bishop throughout the game. Right after the first
few moves one of the Bishops, as a rule, finds an opportunity to
pin a hostile Knight. For instance: (1) P-e4, P-e5; (2) Kt-f3,
Kt-c6; (3) B-b5 and as soon as the Pawn d7 moves in order to give
an outlet to the Bishop c8, the Knight c6 is pinned. Or: (1) P-
d4, P-d5; (2) Kt-f3, Kt-f6; (3) P-c4, P-e6; (4) B-g5 and the
Knight f6 is pinned, as the Queen would be lost if the Knight
moved.

       +---------------------------------------+
     8 | #R |    |    |    |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P | #P | #B | #Q | #P | #P | #P |
       |---------------------------------------|
     6 |    | #B | #Kt|    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    | ^B |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^B | ^Kt| ^P |    | ^Kt|    | ^P |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^Q |    | ^P | ^P |    |
       |---------------------------------------|
     1 | ^R |    |    |    | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                       DIAGRAM 32.

The disadvantage arising from having a piece pinned is often that
the opponent might be able to concentrate more men to attack the
piece which is pinned than can be gathered for defense. The
position of Diagram 32 will serve as an illustration.

Two of Black's men are pinned, namely, the Knight f6 and the Pawn
e5, and of both pins White can take advantage.

The Pawn e5 is attacked twice and defended twice. White cannot
take Pawn, as he would lose Knight and Rook but would get for it
only Knight and Pawn. However, he can win the Pawn by playing (1)
P-d4. This attacks the Pawn for the third time and although Black
can defend him for the third time with R-e8, the defense is not
serviceable as Black would lose Pawn, Knight and Queen for Pawn,
Knight and Rook.

P-e4 in answer to P-d4 would not help either; for on e4 the Pawn
is twice attacked and only once protected as the Knight f6 cannot
be counted as protection on account of his being pinned by the
Bishop g5. All White needs to do is to take the Knight f6 first
and then to capture the Pawn e4.

It remains to examine whether in answer to (1) P-d4 Black can
take the Pawn with either Bishop or Knight. Apparently this is
possible as the Pawn d4 is protected only by the Knight f3 and
the Queen. Indeed, the combination would be correct if the Bishop
d7 were sufficiently protected. As it is White wins a piece in
the following way:

          (1) P-d4          Bxd4
          (2) Ktxd4         Ktxd4
          (3) Qxd4          Pxd4
          (4) Rxe7          Pxc3

Up to this move an even exchange of pieces has taken place, but
now Black loses the Bishop which is attacked by White's Rook,
because White can remove the Knight which protects the Bishop.

          (5) Bxf6          Pxf6
          (6) Rxd7, etc.

Instead of playing (1) P-d4 and taking advantage of the fact that
the Pawn e5 is pinned, White can direct his attack against the
other Black man which is pinned, namely the Knight f6. He can
play (1) Kt-d5 and thereby attack the Queen and at the same time
the Knight f6 for the second time. It will not be evident to the
beginner that White can derive any advantage from this double
attack, as Black can answer either Q-d6 or Q-d8 keeping his
Knight twice protected. Indeed, White does not gain anything on
f6, the square itself upon which the pin is effected, but he uses
the pin to force an opening into the chain of Pawns which
protects Black's King by exchanging on f6, compelling Black to
retake with the Pawn g7. The advantage resulting from this break
in Black's Pawn position will be explained later on when
discussing the strategy of the middle-game.



SACRIFICING



A player is said to SACRIFICE if he allows a certain amount of
his forces to be captured without recapturing himself an
equivalent amount of his opponent's forces. He will not, of
course, knowingly do so unless he expects to obtain some other
advantage which will at least compensate for his loss of
material. Such compensation can only be afforded by a superiority
of the position. In as much as a position can only be considered
superior if it enables the mating of the opposing King or the
obtaining of an advantage in material which will secure a win in
the ending, it is evident that in sacrificing a player really
never intends to give up more than he gets, but that on the
contrary he expects to gain more than he loses. In other words, a
sacrifice, if correct, is a sacrifice only TEMPORARILY, and very
soon yields either the same, if not more material, or an attack
on the King to which the latter falls victim.

The less evident the way is in which a player recovers the
material sacrificed or realizes an equivalent advantage the more
beautiful the sacrifice is considered. If the effect of a
sacrifice is a direct mating attack on the King, it is as a rule
not difficult to foresee as long as the typical mating positions
are known to the player, most of which have been discussed in the
previous chapter. The following diagrams illustrate examples of
such sacrifices which occur fairly often in actual games.

In Diagram 33, White on the move can play for a similar mate as
the one explained in the discussion of Diagram 29 by placing his
Rook on g3. The best protection against Rxg7 which Black has at
his disposal is P-f6. But if he does not know the mating position
illustrated in Diagram 29 he is liable to play P-g6, and then
White forces the mate by sacrificing his Queen on h7.

          (1) R-g3          P-g6
          (2) Qxh7+         Kxh7
          (3) R-h3+         K-g8
          (4) R-h8+

Black could have prolonged the agony one move by interposing his
Queen on h4 on the third move.

       +---------------------------------------+
     8 |    |    | #R |    |    |    | #K |    |
       |---------------------------------------|
     7 | #P | #P | #R |    | #Q | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt|    | #P |    |    |    |
       |---------------------------------------|
     5 |    |    |    | #P |    |    |    | ^Q |
       |---------------------------------------|
     4 |    |    |    |    |    | ^P |    |    |
       |---------------------------------------|
     3 |    | ^P |    |    | ^P | ^R |    |    |
       |---------------------------------------|
     2 | ^P | ^B | ^P |    |    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 33

In the position of Diagram 34 White institutes a mating attack by
(1) P-f6. The only move to protect the mate on g7 is P-g6. It
will then be White's desire to enter with his Queen on h6 again
threatening the checkmate on g7. He will, therefore, play either
Q-f4 or Q-g5. Black has no other way to defend himself against
White's threat than by K-h8 followed by R-g8. But after K-h8; Q-
h6, R-g8 White plays R-f3 and Black is unable to prevent White
from sacrificing his Queen on h7 and mating by R-h3.

If Black's Queen were standing on c5 instead of b5 he could avert
the mate by moving the Rook f8 and playing the Queen to f8
thereby protecting g7.

       +---------------------------------------+
     8 | #R |    |    |    |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt|    |    |    |    |    |
       |---------------------------------------|
     5 |    | #Q |    | #P | ^P | ^P |    |    |
       |---------------------------------------|
     4 |    |    | #P |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    | ^Q |    |
       |---------------------------------------|
     2 | ^P | ^P |    | ^B |    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    | ^R |    | ^K |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 34.

The mate with Rook and Knight demonstrated by the position of
Diagram 28 is liable to occur in several variations of the play
which might result from the following situation:

       +---------------------------------------+
     8 |    |    |    | #R |    | #Kt|    | #K |
       |---------------------------------------|
     7 | #P | #B | #Q |    | #R | #P | #P |    |
       |---------------------------------------|
     6 |    | #P |    |    | #P |    |    | #P |
       |---------------------------------------|
     5 |    |    | #P |    | ^P |    |    | ^Q |
       |---------------------------------------|
     4 |    |    | ^B | ^P | ^Kt|    | ^R |    |
       |---------------------------------------|
     3 |    |    | ^P | ^R |    |    |    |    |
       |---------------------------------------|
     2 | ^P |    |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 35.

White starts his mating attack with (1) Kt-f6. This threatens the
sacrifice of the Queen on h6 followed by R-g8 mate. White's
Knight move can hardly be called a sacrifice as it is quite
evident that Black cannot take the Knight on account of Qxh6+,
Kt-h7; Q-g7 mate. The only way to parry White's threat is (1)
..., Kt-g6. However, this helps only momentarily as White
continues (2) R-h3 threatening Q-g5, Rxh6+ and Qxh6 mate, a
threat against which Black has no defense. White can very nearly
force the mate by sacrificing his Queen on h6 instead of the
Rook. But after (3) Qxh6, Pxh6; (4) Rxh6+, K-g7; (5) R-h7+, K-f8;
(6) R-h8+ Black does not take the Rook as White would like him to
do to enable the mate R-g8, but he goes back to g7 with the King
and White could not do any better than draw by perpetual check on
h7 and h8.

       +---------------------------------------+
     8 | #R |    |    | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 |    | #B |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P | #Kt| #Kt|    | #P |    |    |    |
       |---------------------------------------|
     5 |    | #P | #P | #P | ^P |    |    |    |
       |---------------------------------------|
     4 |    |    |    | ^P |    | ^P |    |    |
       |---------------------------------------|
     3 |    |    | ^P | ^B |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P |    | ^Kt|    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 36.

In the position of Diagram 36 White can make an attack which will
recall somewhat the play shown in connection with Diagram 25. (1)
Kt-g5 would not lead to anything, as Black could defend himself
by P-g6 or P-h6. White has a much more direct way to attack the
black King. This is by the sacrifice (1) Bxh7+. After Kxh7; (2)
Kt-g5+, K-g8; (3) Q-h5 Black can protect the mate only by
sacrificing his Queen for White's Knight. For (3) ..., R-e8 with
the view to escape with the King to e7 via f8 if attacked by Q-h7
and Q-h8 would be rendered futile by White through (4) Qxf7+, K-
h8; (5) Q-h5+, K-g8; (6) Q-h7+, K-f8; (7) Q-h8+, K-e7; (8) Qxg7
mate. Before making the sacrifice of the Bishop White will, of
course, have to make sure that Black cannot save himself by
evading altogether the attack which is threatened through Q-h5.
Black could, indeed, avoid this variation by going with the King
to g6 on the second move instead of g8. But in this case too
White has a winning continuation. He would play (3) Q-g4
threatening to win Black's Queen by the discovered check Ktxe6.
If Black moves the Queen, then White gives the discovered check
in any case forcing the King to h7 and leading over to the
variation which was originally intended. If, on the other hand,
Black tried (3) ..., P-f5, attacking White's Queen and thereby
rendering the discovered check ineffective, White would first
take the Pawn en passant and after (4) Pxf6, Kxf6 the Queen mates
on e6.

Frequently a sacrifice is brought to maintain a pin which is
bound to yield a piece in return sooner or later. The position of
Diagram 37 is typical for cases of this kind.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt| #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    | ^B |    |
       |---------------------------------------|
     4 |    | #B | ^B |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 37.

Supposing Black plays (1) ..., P-h6; (2) B-h4, P-g5 to free
himself of the pinning Bishop. Then White can sacrifice the
Knight f3 for the two black Pawns and thereby maintain the pin
with the threat to regain the Knight immediately through Kt-d5.
The ensuing play could be the following: (3) Ktxg5, Pxg5; (4)
Bxg5, Bxc3; (5) Pxc3. Now White threatens to play P-f4 and Pxe5
opening the line of his Rook and thereby attacking the pinned
Knight for the second time. This threat cannot be effectively
countered. Black could try to unpin the Knight by (5) .... K-g7;
(6) P-f4, Q-e8. Indeed, Black saves his Knight in this way, but
the exposed position of his King leads to a speedy disaster. For
instance: (7) Pxe5, Kt-h7; (8) B-f6+, Ktxf6; (9) Pxf6+, K-h7;
(10) Q-h5+, K-g8; (11) Q-g6+, K-h8; (12) Q-g7+/-. Black could not
take White's Queen on the 11th move because the Pawn f7 was
pinned by the Bishop c4.

If Black had moved his King to g8 or g6 on the 8th move instead
of taking the Bishop f6, White would have forced the mate by
sacrificing his Rook on f5, thereby cutting off the Bishop c8 and
giving his Queen access to the square g4.

Sacrifices with the view to utilizing a pin occur in various
other versions which are essentially different from the one
illustrated above. Following are typical examples of the three
most frequent cases.

In the position of Diagram 38 Black must not take the Pawn e4
although he can protect the Knight with B-f5 in case White pins
him with R-e1.

       +---------------------------------------+
     8 | #R |    | #B |    | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P |    |    |    |    | #P | #P |
       |---------------------------------------|
     6 |    |    | #P |    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P | ^Kt|    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    | ^B |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^R |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 38.

The way in which White would obtain the advantage is this:

          (1) R-e1          B-f5
          (2) Rxe4          Bxe4
          (3) R-e1

Through sacrificing one Rook for the Knight White has freed the
square e1 for the other Rook who now pins the Black Bishop
without Black being able to protect it.

The position of Diagram 39 is somewhat related to that of Diagram
38, as far as the possibility of a sacrifice for the sake of a
pin is concerned. If White plays B-b5+ Black must not interpose
his Bishop, for White will give up his Rook for the Bishop in
order to force the Rook d8 into a pinned position and then he
will win the Rook by R-d1.

       +---------------------------------------+
     8 |    |    |    | #R | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    | #B |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    |    | ^P | ^P |
       |---------------------------------------|
     1 |    |    | ^K | ^R |    | ^B |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 39.

In the position of Diagram 40 there is also a possibility of a
sacrifice with the view to pin a piece that defends a certain
threat as long as it is mobile. White plays (1) Q-d5, and Black
dares not take White's Knight with his Queen for White would
continue (2) Qxf7+, Rxf7; (3) R-e8+/-.

What Black could try is (1) Kt-h6.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P |    | #P |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    | #P |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    | #Kt| ^Kt|    |
       |---------------------------------------|
     4 |    |    | ^B |    | ^R |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 40.

The Pawn f7 would then be three times attacked and three times
protected so that White cannot take him as now the pin of the
Rook resulting from Ktxf7, Ktxf7; Qxf7, Rxf7 does not lead to
anything, the square e8 being protected by the Queen. However,
White can force the win by (2) Ra1- e1, threatening again the
sacrifice of f7, as he now controls the square e8 twice. If Black
replies (2) ..., Q-f6, protecting f7 for the fourth time and
thereby making impossible White's sacrifice on that point, White
continues with (3) R-e8. This threatens Rxf8+, Kxf8; Ktxh7+
winning the Queen. Black cannot defend himself with Q-g6 on
account of (4) B-d3 followed by Bxh7+ and Rxf8, etc., nor can he
play (3) ..., Q-f4 on account of P-g3 followed by Qxd6, attacking
the defenseless Rook f8.

A sacrifice with the view to enabling a mating attack through the
cooperation of Rooks and Bishop somewhat similar to the examples
discussed in the previous chapter is possible in the position of
Diagram 41 which occurred in a Tournament game in London in which
the author conducted the black men.

Black's combination starts with the sacrifice of the Queen on f3.
After (1) ..., Qxf3; (2) Pxf3, B-h3+; (3) K-g1 White's King is
held in an immobile position by the Black Bishop and a check with
one of Black's Rooks in the g-file would be deadly.

However, White can, for a while, protect himself against all
mating attempts of Black. If Black continued (3 ) ..., R-e6,
White would take the Pawn d3 with the Queen thereby defending
the mate R-g6. After giving up his Queen for one of Black's Rooks
White would still have an advantage in material.

The correct way to carry on the attack is (3) ..., Ra8-e8, as
then White cannot take the Pawn d3 on account of R-e1+; Q-f1,
Rxf1+; Rxf1, R-e6 and R-g6 mate.

       +---------------------------------------+
     8 | #R |    | #B |    |    |    | #K |    |
       |---------------------------------------|
     7 | #P | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    | #Q |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    | ^P | ^P |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    | #P |    | ^Kt|    |    |
       |---------------------------------------|
     2 |    | ^P |    |    | #R | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^K |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 41.

The main threat of Black's third move is R-e6-g6 mate. Another
threat is P-d2 followed by R-e1+. The only way for White to
defend himself is (4) P-f4. If now P-d2, then (5) P-f3, R-e1+;
(6) K-f2 affords a sufficient protection. And if (4) ..., Re8-e6,
then (5) P-f5 prevents the Rook from going to g6.

However, by repeating the mating threat with (5) ..., Re6-e4,
which forces White to protect, g4 by (6) P-f3 Black opens the
second rank for a combined assault of the Rooks similar to the
one illustrated by Diagram 30. What makes matters worse for White
is that with (6) ..., R-g2+ he is forced into the line of the
Bishop h3 so that he is exposed to a discovered check. After (7)
K-f1, Rxb2 discovered check; (8) K-g1, Re4-e2 White must give up
his Queen for the Rook immediately, as otherwise Black would mate
in four moves by R-g2+, K-f1, Rxh2+, K-g1, Rb2-g2+; K-f1, Rxh1+/-.

Although White is still ahead in material after (9) Qxe2, Rxe2 he
cannot avoid the loss of the game on account of the continued
threat which Black exerts by the cooperation of his Rook and his
Bishop. The only move which would save the Rook a1 from getting
lost through R-g2+, followed by a discovered check with
simultaneous attack of the Rook by Black's Rook would be (10) R-
d1 with the idea of protecting the Rook with the King thus (10)
..., R-g2+; (11) K-f1, R-d2; (12) K-e1; but this plan fails as
Black checkmates with (12)  ..., R-e2.

A mating position which has not been discussed up to now but
which occurs frequently enough in the actual game to warrant its
special mention is one in which the King is deprived of all
mobility by his own men who surround him and in which a hostile
Knight can check the King. Diagram 42 offers an example.

       +---------------------------------------+
     8 |    |    | #Q |    | #R |    |    | #K |
       |---------------------------------------|
     7 | #P | #P |    |    |    |    | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    | #B |    |    |
       |---------------------------------------|
     5 |    |    |    | ^R |    |    | ^Kt|    |
       |---------------------------------------|
     4 |    |    | ^Q |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    | ^P |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    |    |    | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                    DIAGRAM 42.

White on the move can force the mate by (1) R-d8, a very
surprising sacrifice indeed, for not only can Black take the Rook
with either Queen or Rook but he can also take White's Queen. In
the latter case, however, he would be mated in two moves by (2)
Rxe8+, Q-g8; (3) Kt-f7. This is one example of the "throttled
mate" by the Knight. Another one, which is really the typical
one, occurs if Black takes the Rook instead of the Queen. The
mating process then is: (2) Kt-f7+, K-g8; (3) Kt-h6 double check,
K-h8; (4) Q-g8+, Rxg8; (5) Kt-f7+/-. White could not have played Q-
g8+ right on the second move because then Black would have taken
the Queen with the King, while he could not do so with White's
Knight on h6.

Sacrifices made with the view of a direct mating attack are, as a
rule, the easiest to figure out, as there is no guesswork
connected with them. In those cases the player does not face the
question as to whether the position attained after the sacrifice
will be strong enough to insure a gain of material at least
equivalent to the amount of material sacrificed, a question which
to answer correctly sometimes requires a good deal of instinct
trained by experience; all that is necessary if to ascertain
whether the opponent can be mated in a definite number of moves
or not. If the mate cannot be clearly foreseen, the sacrifice
must not be made. The possibility of a sacrifice with consequent
forced mate is always indicated if a greatly superior force is
available for attack at the part of the board where the opposing
King is located. An example is offered by the position reproduced
on the book cover.

  [E-text editor note: The position on the book cover is:

       +---------------------------------------+
     8 | #R | #Kt|    |    |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #B | #P | #P | #Q |    | #P | #P |
       |---------------------------------------|
     6 |    | #P |    |    | #P | #B |    |    |
       |---------------------------------------|
     5 |    |    |    |    | ^Kt|    |    | ^Q |
       |---------------------------------------|
     4 |    |    |    | ^P | ^Kt|    |    |    |
       |---------------------------------------|
     3 |    |    |    | ^B |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h       ]

This position occurred in a game between Sir G. A. Thomas of
London and the author. Black has just played Q-e7 in order to
protect the mate which was threatened by Ktxf6+ followed by Qxh7.
If in the position of the diagram White played Kt-f6+, Black
would retake with the Pawn, thereby protecting the Pawn h7 with
his Queen. However, White can force the mate with a neat Queen's
sacrifice which drives Black's King right into the arms of the
remaining White pieces. Play continued as follows:

          (1) Qxh7+         Kxh7
          (2) Ktxf6++       K-h6

The King cannot go to h8 on account of Kt-g6 mate. White now
continually checks Black's King in such a manner that he has only
one square to go to until he is finally driven to the first rank,
all White pieces participating in the chase.

         (3) Kte5-g4+

In answer to Ktf6-g4+ Black would play K-h5; (4) B-g6+, K-h4; (5)
P-g3+, K-h3 and there is no mate.

          (3) ...      K-g5
          (4) P-h4+    K-f4
          (5) P-g3+    K-f3
          (6) B-e2+    K-g2
          (7) R-h2+    K-g1
          (8) K-d2 mate.

White could have forced the mate in seven instead of eight moves
by playing (6) K-f1, or (6) o-o, for there was no protection
against (7) Kt-h2.



III

GENERAL PRINCIPLES OF CHESS STRATEGY



In reading the chapter on "Elementary Tactics" the beginner will
have obtained a fair idea of the value of the different pieces
and he will have gained an insight into the possibilities of
their cooperation. However, the fundamental principle of Chess
strategy, the method of developing the inherent powers of the men
so that they may be able to do all the work possible for them,
will still be a secret to him.

At the beginning of the game the Knights are the only pieces
which are able to move, and consequently the other pieces are
worthless until openings have been created for them by Pawn
moves. Now, the first thing the beginner should try to keep in
mind is that only such Pawn moves can be good as open lines for
their fellow pieces or obstruct lines of opposing men. The reason
is this:

In any hand to hand fight evidently that player will get the
better of it who has more pieces ready for action on the
battlefield. When examining the typical positions discussed in
the previous chapter the fact will strike the observant reader
that the winning player always has a decided superiority of
forces at his disposal where the actual fight is going on, so
that in some cases he can even sacrifice a great amount of them
and still have enough left for the final onslaught against the
King. The same holds good in combinations where lesser objects
than the King are fought for; the player who has more pieces
ready to take part in the struggle will emerge victorious; the
player who attacks with less pieces than the opponent has on the
spot for defense, cannot hope to succeed.

The important point, therefore, is to place the pieces so that
they will be in readiness for concentration on whatever part of
the board they are needed.

Moreover, it will be important to place the pieces on such
favorable squares in the shortest possible time--meaning with the
smallest number of moves--as wasting moves on maneuvers which do
not further the mobilization of the troops will give the opponent
an opportunity to gather a superior force somewhere on the board
and make an attack with the best chance in the world to succeed
before reinforcements can be brought up.

With this aim in mind the beginner will readily see that it is by
no means immaterial which Pawn moves are made in the opening. The
fact that a Pawn move opens an outlet for a piece is not
sufficient. If possible Pawn moves will have to be found which
enable the development of more than one piece for they will lead
to an advantage in the mobilization unless the opponent, too,
hastens the development of his pieces by equally good Pawn moves.

The only Pawn moves which fit this description are moves with the
King's or Queen's Pawns as they open lines for Queen and Bishop--
apart from an additional square for the Knight--while the other
Pawns cannot free the way for more than one piece. Whether the
move with the King's Pawn or the Queen's Pawn is better when
beginning the game is impossible to say. In neither case can it
be proved that White can obtain an advantage which is sufficient
to win the game. With correct play on both sides it can be only
White who gains an advantage, for he has the first move and so he
is one move ahead of Black in the development as long as he does
not waste any time on maneuvers which do not increase the
mobility of his pieces.

By the mobility of a piece is meant the number of squares
accessible to it. A Bishop or a Rook which stands in an
unobstructed file is obviously worth more than one whose sphere
of action is limited on account of his way being blocked. This
does not mean, however, that a Bishop or a Knight to whom, at a
certain moment, three or four squares are accessible, is more
valuable than a Rook who at the same moment can go only to one or
two squares; for a few moves later the Rook might be in
possession of his full freedom while the action of the Bishop or
the Knight might be hampered. It is, therefore, best to value the
pieces according to their latent strength, that is, the strength
which is likely to show in the ending after all temporary
obstructions have been removed. The comparative values given for
the different men on page 42 will serve as good guide in most
cases. It is not advisable though to give up a minor piece for
three Pawns or two minor pieces for a Rook and one Pawn as long
as Queens and minor pieces are on the board, as with a piece
ahead the opponent mostly succeeds in winning through a direct
attack against the King before the superiority of Pawns becomes
dangerous.

In trying to place the pieces on squares where they have as much
mobility as possible individual thought is required with each new
game as it depends altogether upon the moves of the opponent
which lines can be opened for Bishops, Rooks and Queen and where
a good field of action can be secured for the Knights. However,
it is possible to give a few rules which common sense tells us
must hold good in the majority of games if both players play
well. Of course, if a player makes bad moves in the opening, that
is, moves which do not aim at a speedy mobilization of all
pieces, then the opponent may soon have a chance to win the game
with moves which are not in accordance with those common sense
rules either but which force an immediate issue in a maneuver of
a kind that ordinarily does not occur in an opening but is
characteristic of the middle game. This is a point which the
majority of Chess players overlook. They argue that--granted the
value of general principles of strategy, which will greatly help
to build up a safe position--cases occur in which a move may win
which is not according to principles, and that, therefore,
following the trend of a certain combination which seems
profitable, is advisable even if the general principles are
violated.

Even a Chess master once said, that generalities are of no use in
Chess and that it is necessary to figure out every move in all
variations to which it may lead to make sure that the move is
good. As an example he offered the following opening: (1) P-f3,
P-e5; (2) P-g4. Now, he asks, should Black omit to give the
checkmate with Q-h4 because it is against the general principles
to bring out the Queen at an early stage of the game?

The shallowness of this argument is obvious. The reason for the
general rule that the Queen should not come out too soon is that
she is liable to be attacked by the minor pieces of the opponent
so that she has to move again and again and time is lost which
could be used for the development of other pieces. Of course, if
the opponent does not develop his pieces, the Queen may often
come out without danger and she may do a lot of harm before she
can be driven away.

In formulating general strategical principles it is, then,
assumed that both players will follow them, and it is taken for
granted that if one player deviates from these principles and
thereby weakens himself at some point, the other player is
expected to exact the full penalty for this deviation with any
means at his disposal. It will always be found that these means
are also indicated by the general principles if only their
meaning is intelligently applied to the position in question.

As was stated before, the point of greatest importance in the
opening is to develop the pieces without loss of time, that is,
to place them on squares where they have as much mobility as
possible without making any move which retards this development.
There are different ways in which the development may be
retarded, and which consequently must be avoided. For instance,
no Pawn move should be made which is not absolutely necessary to
open a line for a piece; or, no piece should move twice as long
as there are pieces which have not yet moved at all; or, no piece
should be developed to a square from which the opponent can drive
it away at the same time furthering his own development; or, the
right of castling should not be foregone by moving the King or by
any other way, as castling develops a Rook and places the King in
safety with one move while more moves are required to the same
end if castling is not possible, and so on.

The beginner who makes this great principle of development quite
clear to himself has made the most difficult step on the way to
mastership. The grasp of the far reaching influence of the
mobility of the pieces in the opening upon the further
development of the whole game is really what distinguishes the
master from the average player.

Of course, it would be too difficult for the beginner to find out
for himself what squares are the most favorable for the different
pieces; at any rate, it would take him a long time to gain that
knowledge by experience. Fortunately, the experience of the
masters of several generations is accessible to us and so it is
possible to expedite considerably the process by which the mind
of the student is adapted to the tactics required in every game
of Chess to carry out the principle of speedy development. To a
great extent these tactics, too, can be simply explained from the
point of view of giving the pieces their utmost mobility so that
they will be readily understood by the reader who has followed
the arguments given in the foregoing pages.

There is a considerable difference in the constellation of the
pieces depending on whether the game is opened with (1) P-e4, P-
e5 or (1) P-d4, P-d5. These two openings shall therefore be
treated separately. All other openings are related to one of the
above main branches and need little additional discussion.



KING'S PAWN OPENINGS



After (1) P-e4, P-e5 the only Pawn which both players have to
move to enable the development of all pieces is the Queen's Pawn,
which obstructs the Queen's Bishop. Of course, it would also be
possible to secure an outlet for the Queen's Bishop by advancing
the Queen's Knight's Pawn one step; but in the long diagonal the
Bishop is ordinarily not so well posted as the development of the
Queen's Knight to his most natural square, that is c3 or c6
respectively, would block the way of the Bishop. The Queen's
Knight is best placed in the c-file because on the edge of the
board, in the a-file, he has less mobility; less squares are
accessible to him. In order to place him in the d-file it would
be necessary to move the d-Pawn, and as this would also give an
opening to the Queen's Bishop the move of the Queen's Knight's
Pawn is superfluous.

Before moving the Queen's Pawn the players will have to make sure
that in advancing him they will not block the way of any piece.
Consequently, White will not play P-d3 on his second move. He
will first develop the King's Bishop. Of course, he will not
place him on d3, obstructing the Queen's Pawn and thereby the
Queen's Bishop. Neither will he play B-b5, as Black could drive
him away from there immediately with P-c6, opening another
diagonal for the Queen. The choice between the remaining squares,
e2 and c4, is not difficult. On e2 the Bishop would be in the way
of the Queen and his way would soon be blocked by the King's
Knight, who for similar reasons to those given for the move of
the Queen's Knight will go to f3 in preference to other squares.
Therefore, the only move to be considered in case the King's
Bishop is played at this early stage of the game, is B-c4.

White is not forced to develop this Bishop on the second move by
any means. He could either play (2) Kt-f3 or (2) Kt-c3 or (2) P-
d4. The objection to the latter move, however, is that after (2)
...., Pxd4; (3) Qxd4 the white Queen is exposed to the attack of
the Knight b8, which means loss of time. Kt-f3 or Kt-c3 are
probably preferable to B-c4 on the second move, because it is
certain that the Knights will not find any better squares on
their initial move. The Bishop, however, may have an occasion to
be used on b5 instead of on c4, and it is a good thing, generally
speaking, to keep the option of moving a piece to different
squares as long as it is compatible with the other requirements
of the position.

That the Bishop may be used to advantage on b5 will be seen from
the following variation. Supposing White plays (2) Kt-f3. Then
the Pawn e5 is attacked. The only sensible protection is (2) ...,
Kt-c6; for P-f6 does not come into consideration, as it is a Pawn
move which does not add anything to the development of the
pieces; P-d6 blocks the Bishop f8; B-d6 obstructs the Queen's
Pawn and Q-f6 or Q-e7 hinders the development of the Knight or
the Bishop respectively. Now, it can readily be seen that after
(2) ..., Kt-c6 White may want to place his King's Bishop on b5,
for with this move he repeats indirectly his attack on the King's
Pawn through the threat to remove the protecting Knight. It is
true, that this threat needs no attention as long as White's
King's Pawn is not protected (for instance: (3) ..., Kt-f6; (4)
Bxc6, Pd7xc6; (5) Ktxe5, Q-d4 attacking Knight and Pawn at the
same time and thereby regaining the Pawn) but as soon as White
has defended the Pawn--with P-d3 may be--the Bishop b5 is at work
and Black must seek additional protection for the Pawn e5.

If White, on his second move, plays B-c4, he attacks the Pawn f7.
This Pawn is protected by Black's King and so he need not be
defended any further; but Black must be on the alert against a
concentration of some more white men on f7. White could try (3)
Q-f3 or Q-h5. However, Black would then have time to defend
himself with Kt-f6 or Q-e7 respectively.

Therefore, on the second move, Black may make any developing
move; he could, of course, play (2) ..., Kt-f6, preventing
White's Queen from going to h5, but this is unnecessary, as Q-h5
would be a very bad move, placing the Queen on a square from
which she is bound to be chased away very soon. For instance: (2)
...., B-c5; (3) Q-h5, Q-e7 (not P-g6 on account of Qxe5 attacking
the King and the Rook at the same time). Now, whatever White
plays, he will have to retire again with his Queen as soon as
Black attacks her with Kt-f6, and so he loses his birth-right of
attack; for it will be Black who is a move ahead in the
development instead of White, as it ought to be.

If both players refrain from premature attack the game might
develop as follows: (2) B-c4, B-c5; (3) Kt-f3, Kt-c6; (4) P-d3,
Kt-f6; (5) Kt-c3, P-d6; (6) o-o, o-o; (7) B-g5. This move is the
first one with which White trespasses the "frontier" which may be
said to run in the openings of all games between the fourth and
fifth ranks of the board. The Bishops are the only pieces for
whom there is a field of action in the opponent's camp early in
the game. They pin a hostile Knight and thereby exert a certain
pressure on the opponent who naturally does not like to see any
of his pieces deprived of its mobility. The fact that Black can
drive White's Bishop away with P-h6 does not lead to any loss of
time for White, for the Bishop can retire to h4, still
maintaining the pin, while Black has not furthered his
development by his Pawn move; in fact, he has somewhat
compromised his position and as explained by the discussion of
the position of Diagram 37 the advance of the Pawn g7 to g5
cannot follow without the risk that White will uphold the pin
even at the cost of a piece and obtain an overwhelming attack.

That the move P-h6 creates a weakness even if it is not followed
up by P-g5 will be demonstrated later on in the discussion of the
middle game. The correct answer to White's seventh move is easily
found with the help of the principle of development. If White did
not threaten anything Black would certainly think of nothing else
than the development of his Queen's Bishop, the only minor piece
which has not yet moved. Therefore, the first thing Black should
consider in countering the threat involved in White's last move
is a protection with a move of the Queen's Bishop. White's threat
is (8) Kt-d5, attacking the Knight f6 for the second time.
Although the Knight is twice protected, Black will naturally
endeavor to prevent an accumulation of hostile pieces on the
point f6, and he can do that indeed very easily by playing (7)
...., B-e6 with a view toward capturing the Knight if he should
move to d5.

The exchange (8) Kt-d5, Bxd5; (9) Bxd5 is manifestly not
desirable for White, as it does not improve in any way the
mobility of his men. On the contrary, White loses a move, as the
result of the maneuver is only a change of location of the King's
Bishop who was already developed while the principle of speedy
development demands that no piece should be moved twice in the
opening until ALL pieces are developed.

Unless Black's move involves a threat which needs immediate
attention White should consider only such moves as will secure a
possibility of development for his Rooks, that is maneuvers which
are liable to produce an open file somewhere on the board.

       +---------------------------------------+
     8 | #R |    |    | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt| #P | #B | #Kt|    |    |
       |---------------------------------------|
     5 |    |    | #B |    | #P |    | ^B |    |
       |---------------------------------------|
     4 |    |    | ^B |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 43.

This can only be done by the exchange of a Pawn and as the only
Pawn within easy reach is the Pawn e5 the files which are liable
to be opened first are the d-file and the f-file. In the position
of the Diagram it is not easy to find a way of opening either
file mentioned without elaborate preparation. P-d4 cannot be
played before the square d4 is three times controlled by White
and if White tries to accomplish this by (8) Kt-e2, Black spoils
White's plan by Bxc4 without being bothered by the threat Kt-d5
which existed as long as the Knight was posted on c3. If, on the
other hand, White exchanges the Bishop first on e6 he helps
Black's development by opening the f-file for his Rook. To avoid
these alternatives White could withdraw the Bishop c4 to b3 and
then play Kt-e2 followed by P-c3 and P-d4. But this maneuver
involves two moves with pieces which are already developed and it
is therefore preferable to place the Rook a1, who has to be
developed, right away in the Queen's file and then to proceed as
suggested above. In other words, White does probably best to play
(8) Q-d2 and (9) Ra1-d1.

Black, in the meantime, will of course, also aim at the
development of his Rooks. In the position of the Diagram it is
even less troublesome for him than for White to prepare the
opening of the d-file, as there is no objection to his playing
immediately Kt-e7 with P-c6 and P-d5. The only reason which might
deter Black from playing Kt-e7 is the fear that White might
answer Bxf6 forcing Black to retake with the Pawn g7 and thereby
tearing a hole in the protecting chain of Pawns around the King.
However, as will be explained in the discussion of the middle
game, this maneuver need not be feared.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    | #P |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
        ---------------------------------------
         a    b    c    d    e    f    g    h

                DIAGRAM 44.

The advance of the d-Pawn, besides the possibility of opening the
d-file for the Rooks, has another very important purpose. It
invites, and often compels the opponent to take the Pawn with his
e-Pawn thereby losing control of "the center." What is meant by
center in King's Pawn openings will be understood from the
analysis of the Diagram 44 in which only the Pawn skeleton of a
King's Pawn game is given and in which it is assumed that Black
has exchanged the Pawn e5 for the Pawn d4. This Pawn formation
offers an advantage to White because the Pawn e4, White's center-
Pawn, controls the two squares d5 and f5 while the two
corresponding squares in White's camp, that is d4 and f4, are not
in the hands of Black and could be occupied by White men. It is
evident that it must be advantageous to have pieces placed in the
center of the board as there they have naturally more mobility
than towards the edge of the board where part of their radius of
action is cut off. A Knight, for instance, placed on d4 will
possibly have an opportunity later on to go to f5 from where he
helps an attack on g7. The square f4 may be useful for the Queen
in an attempt to reach the King's wing speedily, thus
accumulating on that part of the board superior forces. These and
other advantages connected with the control of the center will be
more readily understood after the discussion of the middle game
maneuvers of which the center squares form the basis. It is
necessary, however, to touch upon this matter at this time, as in
many openings the player is confronted after the very first moves
with questions in which the maintenance of the center-Pawn is the
point at issue.

Following are a few examples:

Supposing White, after (1) P-e4, P-e5, plays (2) P-d4. Then Black
is immediately threatened with the loss of his center-Pawn, which
he cannot defend with P-d6 as after (3) Pxe5, Pxe5 White would
exchange Queens and thereby deprive Black of the possibility of
bringing his Rooks quickly into cooperation through castling.

(2) ..., Kt-c6 is out of question too; not on account of (3) P-
d5, which merely helps Black in getting his Knight over to the
King's wing via e7 and allows him to maintain his center-Pawn,
but on account of (3) Pxe5, Ktxe5; (4) Pf4, which secures the
control of the center for White and does not leave Black a chance
to advance his Queen's Pawn to d5 with the view of depriving
White of his center-Pawn too.

For these reasons Black has no choice but has to play (2) ...,
Pxd4. True enough, Black gives up his center-Pawn with this
exchange, but White cannot prevent P-d5 in the long run, so that
he also loses his center-Pawn and has no advantage over Black in
that respect. The following variations are typical for the line
of play in cases of this kind. White tries to hold back Black's
Queen's Pawn as long as he can, but finally Black enforces the
advance.

       I. (3) Qxd4          Kt-c6
          (4) Q-e3

Now P-d5 is not possible because of Pxd5 check.

          (4) ...           Kt-f6
          (5) Kt-c3         B-e7
          (6) B-d2          P-d5

Threatening to win a piece by P-d4.

          (7) Pxd5          Ktxd5

Now White has no center-Pawn either; Black has
a perfectly good game.

      II. (3) Kt-f3         Kt-c6

Most players would be tempted to play P-c5 instead.  But this
must be bad as it is a Pawn move which is not necessary. Black
does not need to defend the Pawn d4 as he is a Pawn ahead; and
the development of the pieces is much more valuable than the
advantage of a Pawn. White would obtain a far superior position
with (4) P-c3, Pxc3; (5) Ktxc3, after which Black cannot
hope ever to free his game by P-d5.

          (4) Ktxd4          Kt-f6

It would be bad to exchange Knights on d4 because White's Queen
would be brought up into a dominating position from which she
could not easily be driven away.

          (5) Kt-c3          B-b4

This attacks again the Pawn e4. Relieving the pin by (6) B-d2
would be no protection as Black could exchange on c3 and then
take the Pawn. Therefore, White must defend the Pawn with another
piece. The Bishop f1, which has to be developed in any case,
offers himself naturally for this purpose, but B-d3 is not
possible as long as the Knight d4 has to be kept protected by the
Queen. Hence, it is necessary first to exchange the Knight.

          (6) Ktxc6          Pb7xc6
          (7) B-d3           P-d5!

Again Black has succeeded in advancing his Queen's Pawn against
the opposing center-Pawn, and White cannot avoid the exchange. To
advance to e5 would be against the principle that no Pawn-move
should be made in the opening which is not absolutely necessary.
How easily (8) P-e5 could get White into trouble can be seen from
the following variation: (8) ..., Kt-g4; (9) o-o, o-o; (10) Pf4
??, B-c5+; (11) K-h1, Q-h4; (12) P-h3, Q-g3; (13) Pxg4, Q-h4
mate.

     III. (3) P-c3

With this move White invites Black to lose time in winning a Pawn
or two while the White pieces are rapidly developed. If Black
accepts the Gambit [Footnote: A Gambit is an opening in which the
sacrifice of a Pawn is offered for the sake of a speedy
development of the pieces.] the continuation might be.

          (3) ...          Pxc3
          (4) B-c4         Pxb2
          (5) Bxb2

                  or

          (4) ...          Kt-c6
          (5) Kt-f3        P-d6
          (6) Ktxc3 or Q-b3 or o-o

In all of these cases White has by far the freer game and he
remains in the possession of his center-Pawn. For this reason it
is much more advisable for Black to decline the Gambit offered
and to hasten his development by immediately advancing his
Queen's Pawn, thus:

          (3) P-c3          P-d5!
          (4) Pxd5

The advance of the King's Pawn would be quite out of place, as it
would not add anything to White's development so that Black need
not mind the loss of the move either which he sustains from the
developing point of view in gaining a Pawn by Pxc3. The future
development of Black is not any longer endangered as he has a
Pawn in the center and an outlet for his Queen's Bishop.

          (4) ...          Qxd5
          (5) Pxd4         Kt-c6
          (6) Kt-f3        B-g4
          (7) Kt-c3        Q-h5

and Black has, no doubt, the initiative.

If White, instead of playing (2) P-d4 as assumed in the above
examples, advances his f-Pawn against Black's center, Black has
ample time to make all preparations necessary to maintain his
center-Pawn, for White does not threaten Pxe5 as long as he is
not protected against Q-h4+, followed by Qxe4. Black's best move
is apparently B-c5, so that he may be able to reply P-d6 to (3)
Kt-f3 without blocking the way of the Bishop. On c5 Black's
Bishop is very disagreeable for White as he prevents his
castling. The natural development of this opening would be about
this:

          (2) P-f4          B-c5
          (3) Kt-f3         P-d6
          (4) B-c4          Kt-f6

Although this move blocks the diagonal for Black's Queen, making
impossible a check on h4, it does not enable White to win a Pawn
on e5, because (5) Pxe5, Pxe5; (6) Ktxe5 would be answered by Q-
d4.

          (5) P-d3          Kt-c6
          (6) Kt-c3         B-g4

Black has one more piece developed than White on account of the
Pawn move P-f4 which is a wasted move from the point of view of
development, especially as White cannot very well castle on the
King's side and make use of the open f-file for his Rooks.

The two principles mentioned--namely the development of the
pieces without unnecessary Pawn moves or other loss of time and
the maintenance of a Pawn in the center--are a perfectly
sufficient guidance in all King's Pawn openings, as no particular
difficulty exists for any piece to be developed to a favorable
square. Even if Black tries to avoid the well-known openings
which result from the reply (1) ..., P-e5 by playing (1) ..., P-
e6 for instance, or (1) ..., P-c5;, or, in fact, any other of the
twenty possible first moves, White will find the right way to
mobilize his men if he strictly adheres to those two principles
and resists the temptation to institute an early attack. A few
examples will show how simple the application of the principle
is.

       I. (1) P-e4          P-d5

This attacks White's Pawn and White has to decide whether to
protect, advance or exchange him. The advance P-e5 and the
protection P-f3 are out of question because these moves are Pawn
moves which do not contribute to the development and are,
therefore, to be classed as mere loss of time. The protection (2)
P-d3 is not sufficient either as Black, after exchanging on e4,
would hamper White's development by exchanging Queens so that
White would lose the right of castling. The protection (2) Kt-c3
cannot be recommended as Black could deprive White of his center-
Pawn and obtain one for himself by Pxe4, (3) Ktxe4; P-e5. For all
these reasons White cannot do better than exchanges on d5.

At first sight this might seem a violation of the principles, as
Pxd5 is a Pawn move which does not further the development of the
pieces while Black, in retaking the Pawn, develops his Queen.
However, as was already pointed out on several other occasions,
the early development of the Queen is not desirable as she is
sure to be exposed to the attack of minor pieces. Indeed, White
obtains the better game through (3) Kt-c3, Q-a5; (4) P-d4 or (4)
Kt-f3, followed by P-d4. Black cannot get his King's Pawn up to
the center [(4) P-d4, P-e5; (5) Q-h5] and in addition he is bound
to lose some more moves with his Queen as soon as White has
developed his Bishop to d2 threatening a discovered attack
through a move with the Knight c3.

      II. (1) P-e4          P-e6

With this move Black switches the center from the e-file to the
d-file.

          (2) P-d4          P-d5

Now White need not hesitate to protect his King's Pawn with Kt-
c3, for Black cannot, as shown in example 1, gain control of the
center by exchanging on e4 and playing P-e5.

The advance (3) P-e5 cannot be recommended for the reason
explained in example I. Of course, White, being a move ahead
anyhow, can afford to make a Pawn move which does not exactly
advance his own development, if that Pawn move hampers the
development of the opponent to some extent. This would be the
case after (3) P-e5, as Black could not develop his King's Knight
to the most natural square, namely, f6. However, the Pawns d4 and
e5, though forming a strong center, as long as they are both in
place, are liable to become subject to disagreeable attacks which
Black can institute with P-c5 and P-f6, and if White cannot
maintain his center, then the advance to e5 is mere waste of
time.

          (3) Kt-c3          Kt-f6

Again White's King's Pawn is attacked. The first continuation for
White to think of would be (4) B-d3, developing another piece.
However, Black can then simply exchange twice on e4 and play P-
c5, so that White loses his Pawn center. P-e5 does not seem very
good either. It does not lose any time, as Black too has to lose
a move retreating with his Knight. But the latter is well posted
on d7 from where he assists the contemplated advance P-c5 against
White's center. The best continuation is apparently (4) B-g5,
which develops a piece and protects the Pawn e4 through pinning
the Knight f6. After

          (4) B-g5          B-e7

White finally has to either advance the King's Pawn or exchange
him. The latter seems preferable. The drawbacks to the advance
have been discussed before. After the exchange White can develop
his King's Bishop to d3 where he is considerably better posted
than the corresponding Black Bishop.



QUEEN'S PAWN OPENINGS



The same two leading principles apply to Queen's Pawn openings
which were discussed in connection with the King's Pawn openings;
but there is one great difference between the two kinds of
openings which is not obvious to the beginner. This is the fact
that in Queen's Pawn openings, in most cases, neither player has
a chance to open a file in the center of the board through the
exchange of one of the center-Pawns, and that, therefore, an
additional Pawn move is necessary in the opening stage to provide
for an open file in which the Rooks later on may have an
opportunity of entering the battle.

In addition, it is in most variations not easy to find a good
place for the Queen's Bishop without further Pawn moves, and it
is here where the beginner is bound to err in the plan of his
mobilization unless he has adequate instruction.

In trying to open a file for the Rooks it will be advisable--just
as in the King's Pawn openings--to aim at the same time at the
clearing away of the opponent's center-Pawn, and this can only be
done by the advance of the c-Pawn. Therefore, it would mean loss
of time if the Queen's Knight were developed into the c-file
before the c-Pawn has moved; the Knight would have to be moved
away again in order to enable the opening of the c-file. This
consideration furnishes the key for the understanding of the most
popular Queen's Pawn opening, which is

          (1) P-d4          P-d5
          (2) Kt-f3         Kt-f6
          (3) P-c4

White offers a Pawn to induce Black to give up his center-Pawn,
hence the name "Queen's Gambit." If Black could actually hold the
Pawn he would be justified in accepting the Gambit unless it can
be demonstrated that White's advantage in development yields a
winning attack. However, White can easily regain the Gambit-Pawn,
and so there is absolutely no reason why Black should give up his
Pawn-center.

The way in which White regains his Pawn in the accepted Gambit is
this: (3) ..., Pxc4; (4) P-e3, P-b5; (5) P-a4, P-c6 (if Black
takes the Pawn a4, White captures the Pawn c4 and then regains
the a-Pawn. (5) ..., P-a6, cannot be played on account of Pxb5,
opening the a-file for White's Rook so that Black cannot retake
the Pawn). (6) P-b3, Pxb3; (7) Pxb5, Pxb5; (8) Bxb5+ and Qxb3.

Now White is far ahead in the development and in addition he has
an open file for his Queen's Rook in which the black Pawn is
bound to be lost in the long run. Moreover, Black has no
compensation for White's strong Pawn-center.

For this reason the Queen's Gambit is hardly ever accepted and
the following defense played instead:

          (1) P-d4          P-d5
          (2) Kt-f3         Kt-f6
          (3) P-c4          P-e6
          (4) Kt-c3

Black has now the choice between either advancing his c-Pawn
right away or first developing the pieces of his Queen's wing. In
the latter case he cannot place the Queen's Knight on c6 as this
would block the way of the c-Pawn. He must develop him to d7.
This appears to be a bad move as it blocks the way of the Queen's
Bishop, but this Bishop will have to be developed in a different
diagonal anyway as the Pawn e6 cannot advance opening the
diagonal c8-h3.

       I. (4) ...          Ktb8-d7
          (5) B-g5

The fact that White can develop his Queen's Bishop without
difficulty while Black cannot do so has made the Queen's Gambit
one of the most popular openings.

          (5) ...          B-e7
          (6) P-e3         o-o
          (7) B-d3         P-b6
          (8) o-o          B-b7
          (9) Pxd5         Pxd5
          (10) R-c1

White is two moves ahead in the development, as Black has still
to move his c-Pawn before he can get his Queen's Rook into play.
In the meantime White can mobilize his King's Rook with Q-e2 and
Rf1-d1, with a view to opening the Queen's file by Pd4xc5.

      II. (4) ... P-c5

If White now Plays P-e3, holding his Pawn-center, a symmetrical
development follows on both sides. If, however, White takes his
opportunity to develop the Queen's Bishop, a game of entirely
different character ensues. The following variations show typical
examples of the way these two variations are liable to develop:

       A. (5) P-e3          Kt-c6
          (6) P-a3

If White played (6) P-b3 before castling he would get into
trouble because Black could pin his Queen's Knight with Pxd4 and
B-b4. For this reason the maneuver P-a3, Pxc5, P-b4 and B-b2 is
usually adopted to develop the Queen's Bishop. It is true that
this maneuver involves two Pawn moves, which mean a loss of time,
instead of only one, as for instance when playing (6) B-d3, (7)
o-o, (8) P-b3, (9) B-b2. But Black can hardly avoid a similar
loss of time. For if he plays (6) ..., B-d6, he loses two moves
with his Bishop through recapturing on c5 (after (7) Pxc5) and
going back to d6; and if he first exchanges on d4 and then
develops the Bishop to d6, White has an open diagonal for his
Queen's Bishop and need not make any more Pawn moves to develop
him while Black still must move his Queen's Knight's Pawn to get
his Queen's Bishop into play.

          (6) ...           P-a6
          (7) Pxc5          Bxc5
          (8) P-b4          B-d6
          (9) B-b2          Pxc4
         (10) Bxc4          P-b5
         (11) B-d3          B-b7

       B. (5) Pxd5          Pxd5

The idea of this exchange is to create a weak Pawn on d5 against
which later on an attack can be instituted. However, it is very
doubtful whether the Pawn on d5 is really weak. Experience has
shown that Black wins just as many games as White in this
opening; the reason is probably that White, in order to open the
Queen's file for attack on d5, has to give away his center-Pawn
so that Black has more freedom for his pieces in the center.

          (6) P-g3          Kt-c6
          (7) B-g2          B-e6
          (8) B-g5          B-e7
          (9) o-o           o-o
         (10) Pxc5          Bxc5
         (11) R-c1          B-e7
         (12) Kt-d4 or Q-a4 followed by
                R-f1-d1.

Instead of developing the King's Bishop to g2 White can just as
well play (6) B-g5 or f4, (7) P-e3 and (8) B-d3. In either case
the success depends rather on clever maneuvering in the middle-
game than on an advantage inherent to the opening.

What has been said of irregular replies which Black may try in
King's Pawn openings holds good in Queen's Pawn openings too.
There is no series of opening moves which needs to be memorized.
The principles of speedy development and of the maintenance of a
Pawn center lead the right way in all novel openings which a
player might try to avoid the well-known paths which have been
studied out by the masters of many generations.

Following are again a few examples which show the application of
the principles:

       I. (1) P-d4          P-c5
          (2) P-e3

With Pxc5 White would give away his center-Pawn, and Black would
regain the Gambit-Pawn easily after (2) ..., P-e6. White could
play (2) P-d5, thereby depriving Black's Queen's Knight of his
best developing square. But in doing so he would lose time with a
Pawn move which does not improve the mobility of his own pieces,
and consequently (2) P-e3 is preferable.

      II. (1) P-d4          Kt-f6
          (2) Kt-f3

The advance P-c4, which, as explained, is customary in Queen's
Pawn openings, serves its original purpose only if Black has a
Pawn on d5 so that White can open the c-file. Therefore, it is
better for White to wait until Black shows what intentions he has
with his Queen's Pawn.

          (2) ...           P-d6
          (3) Kt-c3

Black's last move clearly indicates that he intends playing P-e5
and not P-d5, and so White has no reason to expect that he will
be able to open the c-file for his Rooks. Consequently there is
no objection to his developing the Queen's Knight to c3, blocking
the c-Pawn.

          (3) ...           Ktb8-d7
          (4) B-f4

This prevents P-e5 for the time being, and Black has to make
rather complicated preparations, such as P-c6 and Q-c7 before he
can advance the King's Pawn two squares. In other words, White
completes his development more quickly than Black and he has
consequently the better winning chances, provided, of course, he
knows how to maintain his advantage in the middle game and in the
end game.



THE MIDDLE GAME



It is not possible to draw a distinct dividing line between the
two stages of the game which are called the OPENING and the
MIDDLE GAME. Strictly speaking the opening comprises only such
moves as are NECESSARY for the development of the pieces, and any
move which a player--without being compelled--makes with a piece
that is already developed, ought to be regarded as a Middle-game
move. To give an example: If after (1) P-e4, P-e5; (2) Kt-f3, Kt-
c6; (3) Kt-c3, Kt-f6; (4) B-b5 Black plays Kt-d4, he deviates
from the Opening and embarks on a Middle-game maneuver; for the
Queen's Knight was already developed.

This does not mean that it is bad under all circumstances to make
a Middle-game move during the opening stage of a game. But only
such moves should be considered in cases of this kind as a player
is fairly sure to make at any rate within the further course of
the game with a view to increasing the mobility of the piece in
question.

This is the main point. A second move made with a piece must
improve its position, otherwise, common sense tells us, it is
surely bad. For instance: After (1) P-e4, P-e5; (2) Kt-f3, Kt-c6;
(3) B-b5, Kt-f6; (4) o-o, B-e7 there is no objection to White's
playing (5) R-e1 as the Rook will very likely want to get into
action in the e-file in any case, as soon as the development has
progressed with P-d4, Kt-c3, B-g5, etc.

But if in an opening like (1) P-e4, P-e5; (2) Kt-f3, Kt-c6; (3)
B-c4, Kt-f6 White plays (4) Kt-g5 for instance, or (4) B-d5, it
is evident that he merely wastes time, for in the first case he
places the Knight on a square from which he is sure to be driven
away again as soon as the direct attack involved in his move has
been warded off, and in the second case he moves the Bishop to a
square which does not afford him any more mobility than the one
on which he stood before.

As a rule only Rooks or Knights are in a position, during the
opening, to add to their mobility by a second move; the Rooks by
occupying a file which is liable to be opened by an exchange of
Pawns, and the Knights by occupying a square in the center of the
board.

The Knights are really more often under the necessity of making
several moves in succession than any other piece, because they
can never pass over more than one line at a time, and they may be
required to hasten from one wing of the board to the other just
as often as the other pieces. This is the reason why the most
favorable spot for a Knight is a square in the center of the
board; there he is always ready for an excursion to either wing.

The establishment of a Knight in the center can more readily be
effected in Queen's Pawn openings than in King's Pawn openings.
This will be evident from the following consideration:

In Queen's Pawn openings the squares e5 and e4 are the ones which
are aimed at by the respective Knights. If the opponent exchanges
the Knight with either his Queen's Knight or his King's Bishop,
the Pawn which takes the place of the Knight in recapturing,
gains control of two squares in the heart of the hostile camp. To
illustrate this by a case which often occurs: If after (1) P-d4,
P-d5; (2) Kt-f3, Kt-f6; (3) P-e3, P-c5; (4) B-d3, Kt-c6; (5) o-o,
P-e6; (6) P-b3, B-d6; (7) B-b2, o-o; (8) Ktb1-d2, P-b6; (9) Kt-e5
Black plays Bxe5, White in retaking drives Black's King's Knight
away depriving the King's wing of an important protection and
also creating a weakness on d6, where White might be able at some
later stage of the game to establish his Knight.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P |    |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    | #P | #Kt| #B | #P | #Kt|    |    |
       |---------------------------------------|
     5 |    |    | #P | #P | ^Kt|    |    |    |
       |---------------------------------------|
     4 |    |    |    | ^P |    |    |    |    |
       |---------------------------------------|
     3 |    | ^P |    | ^B | ^P |    |    |    |
       |---------------------------------------|
     2 | ^P | ^B | ^P | ^Kt|    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 45.

Another advantage of the position for White is that he can get
his King's Rook into play by P-f4 and R-f3-h3, while Black's Rook
cannot get to f6 as long as White has his Pawn on e5.

In King's Pawn openings the situation is different. Here the
squares d5 and d4 respectively are the aim of the Knights which
normally are posted on c3 and c6. However, as long as the
opposing King's Knight can exchange himself for the advancing
Queen's Knight there is no advantage in occupying the center. The
position of Diagram 46 is a typical example. If White plays Kt-d5
he loses practically a move, as after Ktxd5, Pxd5 he has in no
way improved the mobility of his men while it is Black's turn to
move. In addition, White, by transferring his Pawn to d5, gives
up his Pawn-center and blocks a diagonal which his Bishop could
use, while Black, in retreating with his Knight to e7, gains a
move towards the efficient use of the Knight on the King's wing.

All the same, the advance of the Queen's Knight in the center is
one of the most important maneuvers in King's Pawn openings when
it is properly prepared, and its consequences need thorough
discussion.

The proper preparation consists in first fixing the object at
which the Knight aims. This--from White's, the attacker's point
of view--is the Knight f6. The developing move B-g5 serves this
purpose in the most natural way, and a position arises similar to
the one shown in Diagram 43 where Black prevented any further
accumulation of white forces on f6 by B-e6. In the present case
this move is of doubtful value as White, by P-d4, can force Black
to give up his center-Pawn.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt| #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    | ^B |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    | #B |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 46.

If Black is ready to admit that Kt-d5 is a disagreeable threat he
will either exchange the Knight for his Bishop b4 or he will play
Kt-e7 in order to take White's Knight should he go to d5.
Ordinarily Black plays first Bxc3 and then Kt-e7. The reason is
that this maneuver enables Black to get his Queen's Knight over
to the King's wing while White's Bishop b5 is rather out of
action, so that Black has a good chance to enter the battle on
the King's wing with one piece more than White. Of course, White
can get his Bishop into play again by placing him on c4. But he
has to spend a move in doing so, which does not add to the
completion of the development.

In the position of Diagram 46 Black would not take any steps to
prevent Kt-d5 unless a threat is involved in this move which
cannot be counteracted by the most natural continuation, which is
the development of the Bishop c8. Indeed, there seems to be no
reason why Black should not answer (1) B-g5 with B-g4 and (2) Kt-
d5 with Kt-d4; for the Knight f6, who after Kt-d5 is attacked
twice, is defended twice, and there is no possibility for White
to attack the Knight again. On the other hand, the attack on the
Bishop b4 is balanced by the attack on the Bishop b5, and if
White were to withdraw his Bishop to c4 Black could withdraw his
to c5.

However, in the position resulting after these moves (Diagram 47)
White gets the upper hand because he is one move ahead in the
attack on the opposing King's Knight. The danger of the
concentration of two pieces on this Knight lies in the fact that
Black is obliged to retake with the g-Pawn in case White
exchanges on f6 and that thereby the squares f6 and h6 lose their
natural protection.

       +---------------------------------------+
     8 | #R |    |    | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    | #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    | #B | ^Kt| #P |    | ^B |    |
       |---------------------------------------|
     4 |    |    | ^B | #Kt| ^P |    | #B |    |
       |---------------------------------------|
     3 |    |    |    | ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 47.

Thus weak points are created of which White may find an
opportunity to make use in a manner similar to the one
illustrated by the discussion of Diagrams 26 and 29. On the other
hand, Black gains an open file for his Rooks as soon as the g-
Pawn is out of the way, and the exchange on f6 should therefore
not be made until preparations for the occupation of the
resulting weak spots are completed. The following variations will
throw some light on this rather complex problem.

Supposing White wants to try the immediate exchange on f6, hoping
that somehow or other he will be able to take advantage of the
weakness resulting on f6 and h6. In exchanging he can give up
either his Knight d5 or his Bishop g5. In both cases there are
promising possibilities for attack, but Black, with correct play,
can sufficiently defend himself and even get the better.

If White plays (1) Ktxf6 he has to lose a move before he can
bring up other pieces to help in the attack, for after Pxf6 he
must first move the Bishop g5. The only good square for the
Bishop is h4 from where he maintains the pin on f6 which would
become very dangerous for Black if he could not prevent White's
Queen from entering on h6 or render the double threat on f6
ineffective in some other way. The logical continuation for Black
is to answer (2) B-h4 with K-h8 in order to occupy the g-file
with his Rook as soon as possible. Indeed, this is at the same
time the best defense against White's threat, for if White now
plays (3) Q-d2; Black replies Ktxf3+; (4) Pxf3, Bxf3; and he is
the first to take advantage of the open g-file as his King has
already made room for the Rook.

It would be dangerous for Black to play (3) ..., Bxf3 instead of
Ktxf3. For White would continue (4) Q-h6 and the only way for
Black to prevent the disaster threatened on f6 is to give back
the piece he just won: (4) ..., Kt-e2+; (5) K-h1, Bxg2+; (6)
Kxg2, R4-g8+; (7) K-h1, R-g6; or (6) ..., Kt-f4+; (7) K- h1, Kt-
g6. In either case Black's defense is very difficult.

The play outlined in the last variation suggests a better method
for White to institute the attack in the position of Diagram 47.
This is the preparatory move (1) Q-d2. (1) Bxf6 is obviously not
as good, as Black can soon drive away the Knight d5 by P-c6,
relieving f6 of all pressure.

In answer to (1) Q-d2, which threatens (2) Bxf6, (3) Q-h6, (4)
Ktxf6 and (5) Qxh7 mate, Black has three replies, namely: Bxf3 or
Ktxf3 or P-c6.

That (1) ..., Bxf3 is not sufficient can easily be seen. White
continues (2) Bxf6, Q-d7; (3) Kt-e7+/-, and Black must give up the
Queen for the Knight as (3) ..., K-h8 would be followed by (4)
Bxg7+, (5) Q-g5+  and (6) Q-f6 mate. It is interesting to note
that it is just the one move which White is ahead in the
development that gives him the win. If he tried to checkmate
Black by (3) Q-g5, P-g6; (4) Q-h6 he would be checkmated himself
by (4) ..., Kt-e2+  followed by Bxg2+ and Q-g4+, etc.

(2) ..., Pxf6 would not be of avail either. The consequence would
be: (3) Q-h6, Kt-e2+; (4) K-h1, Bxg2+; (5) Kxg2, Kt-f4+; (6)
Ktxf4, Pxf4; (7) K-h1, K-h8; (8) R-g1, R-g8; (9) Rxg8+, Qxg8;
(10) R-g1 and the mate can only be averted by the sacrifice of
the Queen for the Rook.

The second defense which Black could try is (1) ..., Ktxf3+; (2)
Pxf3, Bxf3. Now (3) Bxf6, Pxf6; (4) Q-h6 would be fatal for White
as Black plays K-h8 and there is no protection against the threat
R-g8+. But White can again make a preparatory move which secures
for him the victory. This is (3) P-h3, with the view to make room
for the Rook by K-h2. The only way to counter White's threat is
now P-c6. However, after (4) Ktxf6+, Pxf6; (5) B-h4, K-h8; (6) K-
h2, R-g8; (7) R-g1, Q-e7; (8) R-g3 Black is unable to stave off
defeat any longer. Whatever he plays, White succeeds in attacking
f6 for the second time while Black has no second protection at
his disposal. For instance, (8) ..., B-h5; (9) Q-h6, B-g6; (10)
R-f3--or (8) ..., Rxg3; (9) Pxg3 and (10) Rf1.

The most interesting line of defense is the third one mentioned,
that is (1) ..., P-c6. After (2) Ktxf6+, Pxf6; (3) B-h4 a
situation arises similar to the one discussed in the line of play
commencing with (1) Ktxf6+, but with the big difference that
White is now one move ahead in the attack. This is the move Q-d2
in answer to which Black was forced to make the move P-c6 which
does not improve the constellation of the Black pieces in any
way.

This one move is sufficient to secure for White an easy victory.
After (3) ..., Bxf3; (4) Q-h6, Kt-e2+; (5) K-h1, Bxg2+; (6) Kxg2,
Kt-f4+; (7) K-h1, Kt-g6 the position of Diagram 48 is reached in
which White can force the mate, or win Black's Queen in a most
ingenious manner. If White tried to win by (8) R-g1, threatening
mate in four moves through Rxg6, Qxg6, Q-h6 and R-g1 Black could
sufficiently defend himself with (8) ..., P-d5, unpinning the
Pawn f7 and enabling B-e7, which would supply the much needed
protection for the square f6. However, White can frustrate
Black's intention by playing (8) P-d4!! If Black takes with the
Pawn, (9) P-e5 follows forcing Pd6xe5 after which Black cannot
any more intercept the diagonal of the Bishop c4 so that there
remains no defense against (10) R-g1.

       +---------------------------------------+
     8 | #R |    |    | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P |    |    |    | #P |    | #P |
       |---------------------------------------|
     6 |    |    | #P | #P |    | #P | #Kt| ^Q |
       |---------------------------------------|
     5 |    |    | #B |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    | ^B |    | ^P |    |    | ^B |
       |---------------------------------------|
     3 |    |    |    | ^P |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P |    | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    | ^R |    | ^K |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 48.

If, on the other hand, Black takes the Pawn d4 with his Bishop,
White continues with (9) P-c3, B-c5; (10) Ra1- d1, again
preventing the interception of the Bishop c4 and threatening R-
g1. The consequence could then be: (10) ..., K-h8; (11) R-g1, Q-
e7; (12) R-d3, R-g8; (13) R-h3, Ktxh4; (14) Qxh7+ and (15) Rxh4
mate, or: (13) ..., R-g7; (14) R-f3, Ra8-g8; (15) Bxf6, Q-d7;
(16) R-h3 and the mate on h7 can only be avoided by the sacrifice
of the Queen for the Rook.

The foregoing variations show conclusively that the position of
Diagram 47 is lost for Black. The attack which White obtains
after creating a weakness on f6 by the removal of the Pawn g7
cannot be effectively countered. The question arises, whether
Black was at fault when disregarding White's threat to place his
Knight on d5 and developing his Queen's Bishop or whether he had
a chance to improve on one of the two following moves which led
to the position of Diagram 47. Indeed, it lies near to try the
same attack which White threatens to initiate by Q-d2 one move
earlier by playing Q-d7 instead of B-c5. The fact, however, that
this Bishop is not cooperating with the pieces on the King's wing
makes a big difference and the most Black can obtain is
apparently a draw. The continuation could be: (1) Ktxf6+, Pxf6;
(2) Bxf6, P-h6; (3) P-c3, Ktxf3+, (4) Pxf3, B-h5; (5) K-h1, K-h7;
(6) R-g1, R-g8; (7) R-g3. If Black's Bishop were on c5 instead of
b4, White could not play R-g3 on account of Bxf2. He would have
to make the preparatory move Q-e2 and he would be lost after R-
g6, just in the same manner which was demonstrated in one of the
above variations with attack and defense reversed. As it is Black
cannot enter on h3 with his Queen without exchanging Rooks and so
he is unable to take advantage of the weakness on f3. After (7)
..., R-g6, (8) B-h4, B-a5 or c5, (9) P-d4 and Q-d3 the game
probably ends in a draw as it is unlikely that White can realize
an advantage from the doubled Pawn which he is ahead.

To the beginner the lines of play discussed in connection with
Diagrams 47 and 48 will have appeared rather complicated. This
they are, indeed, even for the experienced player; but it is by
no means necessary to memorize any of the variations. The
important thing to realize is the fact that in a position where
both players have castled on the King's side, a dangerous
weakness is created if the g-Pawn is forced to move, and if
pressure can be brought to bear upon the two squares which
through the move of the g-Pawn have lost their protection;
moreover, that a method to create such a weakness is the pinning
of the hostile King's Knight and the advance of the Queen's
Knight in the center.

Another important point that the variations discussed will bring
out to the observant reader is the order in which the different
pieces take their turn in the battle. First come the minor
pieces, then the Queen and then the Rooks. This, of course, is
not a rule that has to be adhered to under all circumstances, but
in most games it is a good rule to follow. The reason is obvious.
The Rooks have no opportunity of making themselves useful until a
file has been opened, while the Queen often finds an occasion to
enter the battlefield on a diagonal. Only in such games can the
Rooks be made to work at a comparatively early stage of the game,
in which the players have not castled on the same sides of the
board. For then the advance of the Pawns in front of the Rooks
does not create weakness which endangers their own King.

The following middle game from a match of two masters furnishes
an example. After White's seventh move the position of Diagram 49
was reached, in which Black continued with P-b5 with the view to
playing B-g4 and Kt-d4. White replied (8) B-b3, B-g4; (9) Kt-e2.
Better would surely have been B-e3, which develops a new piece.
To allow the exchange of f3 which forces the g-Pawn out is
dangerous because Black may castle on the Queen's side and storm
with the Pawns of his King's wing.

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K |    |    | #R |
       |---------------------------------------|
     7 |    | #P | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #Kt| #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    | #B |    | #P |    |    |    |
       |---------------------------------------|
     4 | ^B |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 49.

From Black's next move, Q-d7, it is indeed apparent that he has
decided on a maneuver of this kind. The game continued: (10) P-
c3, Bxf3; (11) Pxf3, Q-h3; (12) Kt-g3, P-h5; (13) B-e3. He cannot
play R-e1 on account of Bxf2+ followed by Qxh2+ and Qxg3. (13)
..., P-h4; (14) Kt-h1, R-h6 and wins, for if White takes the
Rook, Pxh6 opens the g-file and the other Rook occupies it with
deadly effect.

In the last example it was easy for the Rooks to take an active
part in the battle because a file was open which enabled them to
bear down on the opposing King.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 |    | #P |    | #P | #Kt| #P | #B | #P |
       |---------------------------------------|
     6 | #P |    | #Kt|    | #P |    | #P |    |
       |---------------------------------------|
     5 |    |    | #P |    |    |    | ^B |    |
       |---------------------------------------|
     4 |    |    | ^B |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^Q |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 |    |    | ^K | ^R |    |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 50.

In the majority of cases no open file is available on the wing
and the attack with the Rooks is then much more difficult. There
is little use in advancing the Pawns on the wing on which the
hostile King has castled unless one of them can be exchanged so
that a line is opened which the Rooks can occupy. As a rule such
an exchange is only possible in case one of the Pawns in front of
the King has moved. In the position of Diagram 50 for instance,
White is able to open the h-file by advancing the h-Pawn and
exchanging it against Black's g-Pawn, while Black, who would like
to use his Rooks in an attack on the Queen's wing, has little
hope to open a file on that side of the board. If Black's g-Pawn
were still on his original square, the advance of White's h-Pawn
would be of no avail. Black would simply wait until the Pawn has
advanced to h6 and then he would play P-g6 so that White's own
Pawn would block the h-file for the Rook. In the above position,
which occurred in one of six simultaneous games played by the
author in a blindfold-exhibition, the attack developed as
follows:

          (1) P-h4          P-b5
          (2) B-b3          Kt-a5
          (3) P-h5          Ktxb3
          (4) Pa2xb3        Q-a5

Black has succeeded in opening a line also, but he cannot get his
Rooks working in it. His last move threatens mate in two moves by
Q-a1; Kt-b1, Bxb2; but White simply defends himself first against
this threat and then proceeds with his attack on the King's wing
which is irresistible.

          (5) K-b1          Kt-c6
          (6) Pxg6          Pf7xg6
          (7) B-h6          R-f7
          (8) Bxg7          Rxg7

With this exchange White has weakened the defense around Black's
King who has now only the Rook and himself to rely on for
protection.

          (9) Kt-g5          P-d5

Black opens the seventh rank in the hope that it will enable his
Queen's Rook or his Queen to come to assistance. But so great is
the advantage afforded White by the open h-file that he can
sacrifice his Knight to break through Black's chain of defense
and force the mate before Black has a chance to touch his Queen
or his Rook.

          (10) Ktxh7          Rxh7

If Q-c7 or Ra8-a7, White continues (11) Q-h6! Rxh7?; (12) Qxg6+,
K-h8; (13) Q-e8+, K-g7; (14) Rxh7+, Kxh7; (15) R-h1+, etc.

          (11) Rxh7          Kxh7
          (12) R-h1+         K-g7
          (13) Q-h6+         K-f7
          (14) Q-h7+         K-f6
          (15) Q-h8+         K-e7
          (16) R-h7+         K-d6
          (17) Q-f8+         K-e5
          (18) P-f4+         K-d4
          (19) Q-f6+         K-e3
          (20) R-h3+         K-d2
          (21) Q-h4

and Black resigns as there is no defense against Q-f2.

Diagram 51 shows a similar example, the only difference being
that it is not the advance of the Black Knight's Pawn but that of
the Rook's Pawn which gives White an opportunity of opening a
file for his Rooks. He will accomplish this by advancing his
Knight's Pawn to g5 and exchanging him against Black's Rook's
Pawn. If he does not want to play P-g4 on the first move, because
Black could take the Pawn with his Knight, he can prepare the
advance by R-g1. But he need not really fear the loss of the
Pawn, because in taking him Black would himself open the g-file
for White's Rook and White is sure to obtain an overwhelming
attack. It would, of course, be futile for Black to try and stop
the advance of White's g-Pawn by P-g5, as White would then simply
open the Rook's file by P-h4 and Pxg5, quite apart from the fact
that he could sacrifice his Bishop e3 for two Pawns, thereby
depriving Black's King of all protection.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #P |    | #Kt| #B | #P | #P |    |
       |---------------------------------------|
     6 |    |    | #P |    |    | #Kt|    | #P |
       |---------------------------------------|
     5 |    |    |    | #P |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    | ^P |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^Kt| ^B | ^B | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^Q |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 |    |    | ^K | ^R |    |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 51.

The play might proceed like this: (1) P-g4, P-g5; (2) Bxg5, Pxg5;
(3) Qxg5+, K-h8; (4) Q-h6+, K-g8; (5) P-g5, Kt-e4; (6) Ktxe4,
Pxe4; (7) P-g6, Pxg6; (8) Qxg6+, K-h8; (9) R-g1, etc.

Ordinarily both players castle on the same side of the board so
that neither of them can advance his Pawns in an attack against
the opposing King without weakening his own King's position. Only
if a player holds more territory and has a greater number of
pieces on the King's wing than the opponent he can embark on an
attack which involves an advance of the Pawns in front of his
King. Diagram 52 offers a typical example.

       +---------------------------------------+
     8 | #R |    |    |    |    | #R | #K |    |
       |---------------------------------------|
     7 |    |    | #Q | #B | #B | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    |    | #P |    | #Kt|    |    |
       |---------------------------------------|
     5 | #Kt|    | #P | ^P | #P |    |    |    |
       |---------------------------------------|
     4 |    | #P |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^P |    | ^B |^Kt |    | ^P |
       |---------------------------------------|
     2 | ^P | ^P | ^B |    |    | ^P | ^P |    |
       |---------------------------------------|
     1 | ^R |    |    | ^Q | ^R | ^Kt| ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 52.

Black has a preponderance on the Queen's side, while White has
more mobility for his pieces on the King's side. Considering that
Black cannot easily throw his men over to the King's wing, White
can risk to loosen his Pawns on this wing without fearing that
Black will be able to obtain a foothold on the weak points which
are necessarily created by the advance of the Pawns in White's
camp.

White will start the attack with (1) P-g4 and (2) Kt-g3. Then he
threatens to occupy the dominating square f5 with his Knight, and
Black has hardly any other move than P-g6; for if he permits Kt-
f5 with the view to exchanging the Knight with his Bishop, he
opens the g-file for White's Rooks. P-g6 on the other hand
enables White to open the h-file by advancing the h-Pawn after
the necessary preparations such as K-g2, R-h1, P-g5, etc.

In the vast majority of games files for the Rooks are not opened
on the side but in the center of the board, as was explained in
the discussion of the openings. The many advantages arising from
the control of a center-file by the Rooks will be more fully
analyzed in the illustrative games. Generally speaking it is
easier to get the two Rooks into cooperation in the center than
on the side of the board. This cooperation--usually effected by
doubling in one file--is naturally very important and it is the
main reason why it is desirable to castle as early as possible.
Between the Rooks of a player who is prevented from castling
there are, so to speak, no natural lines of communication and it
takes so long to create artificial ones that in most cases the
opponent can, in the meantime, force a victory through the
combined efforts of his Rooks. Diagram 53 gives an example.

       +---------------------------------------+
     8 |    | #Q |    |    | #K | #B |    | #R |
       |---------------------------------------|
     7 |    | #P |    | #B |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #R |    | #P |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    | ^Q |    |    | ^B | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 53.

It is White's move, and he will naturally think of a Rook's move
as all the other pieces are already developed. The best move is
probably (1) Rf1-d1. Ra1-d1 comes also into consideration but
this Rook might be needed later on the c-file while the King's
Rook certainly will have no chance to be developed in any but the
d-file as long as the White e- and f-Pawns are still on the
board. Black, in the game from which the above position is taken,
replied B-c5, and White continued with (2) Q-c3, attacking the
Bishop c5 and the Pawn g7 at the same time.

Black has only the choice between returning with the Bishop to f8
or capturing on e3. Naturally, he chooses the latter move as he
cannot improve his position by a retrogressive play which still
further retards his development. After Bxe3,(3) Qxg7, Bxf2+;(4)
Kxf2, R-c2+; (5) K-g1, R-f8; there is not much hope for Black to
bring his King's Rook in contact with the other pieces, while
White may be able to double his Rooks in the Queen's file, which
would decide the victory as Black has no possibility to counter
the threat R-d8+ in the long run. White played (6) Kt-e5 with the
intention to sacrifice the Knight on f7 in case Black should move
his Bishop. Rxf7 would then be followed by Q-g8+ and Qxb8 or Qxe6
mate. Therefore, Black had to withdraw his Rook with (6) ..., R-
c7 and White simply played (7) R-d2 threatening to double. Black
prevented this by B-a4, at the same time threatening P-f6, but
after(8) Kt-g4, R-c2; (9) R-d4, Q-c8; (10) Kt-f6+, K-e7; (11) Q-
g5 he resigned as now the square c1 is sufficiently protected
while the threat Kt-g8++ cannot be parried.

The foregoing examples show that generally several moves are
necessary in the middle game for Knights and Rooks to reach
positions favorable for an active part in the attack. With the
Bishops it is different. They can usually be developed on their
first move to the square on which they are needed in the middle
game for either attack or defense.

In King's Pawn openings as well as in Queen's Pawn openings
White's Queen's Bishop is, in the majority of cases, used for
pinning Black's King's Knight on g5 and Black's King's Bishop is
placed on e7 to relieve the pin. The pinning of the King's
Knight, however, is not advisable in positions in which the
opponent has the option of castling to the Queen's side. After
(1) P-e4, P-e5; (2) Kt-f3, Kt-c6; (3) B-c4, Kt-f6; (4) Kt-c3, B-
c5; (5) P-d3, P-d6; for instance White should wait with B-g5
until Black has castled on the King's side. If he plays (6) B-g5,
Black will answer B-e6; (7) o-o, Q-d7; and now White would only
hurt his own game by exchanging on f6 as the open g-file is bound
to aid Black, who will castle on the Queen's side, in an attack
on the King's side.

In Queen's Pawn openings the move B-g5 is always good as Black
cannot very well castle on the Queen's side on account of the
open c-file in which White would soon obtain an overwhelming
attack. Another good square for the Queen's Bishop is in Queen's
Pawn openings b2 from where the Bishop supports the advance of
the King's Knight to e5. In this case the Queen's Knight should
be developed to d2 instead of c3 so as not to obstruct the line
of the Bishop. The same holds good for the development of Black's
Queen's Bishop.

In King's Pawn openings it is dangerous for the Queen's Bishop to
leave the long diagonal in which he is originally posted as the
opponent might threaten to gain a foothold in the f-line with a
Knight, provoking a weakening move with the g-Pawn. The position
of Diagram 54, which occurred in a game between Teichmann and
Rubinstein in the Karlsbad Tournament, 1911, furnishes an
instructive example. White played (1) P-a4, trying to make use of
the advanced position of Black's b-Pawn for opening the a-file
for his Rook, and Black replied B-b7. This crosses White's plan,
as after (2) Pxb5, Pxb5; it would not be White but Black who
would gain control of the a-line.

       +---------------------------------------+
     8 | #R |    | #B | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 |    |    |    |    | #B | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #Kt| #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    | #P | #P |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    | ^P | ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^B | ^Kt|    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B | ^Q | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                  DIAGRAM 54.

However, Black should not have withdrawn the Bishop from the
King's wing, for White can now play his Queen's Knight via f1 and
g3 or e3 to f5 unless Black weakens his Pawn position by P-g6.
The proper way to answer White's first move would have been
either B-e6 or P-b4. The latter is a Pawn move, but in the
present case it cannot be considered a loss of time as White,
too, has made a Pawn move which does not further his development.

The game went on as follows: (2) Kt-f1, Q-c7; (3) Kt-g3, P-g6;
White's aim is accomplished. He has provoked a weakness which
furnishes a mark for his attack. The way to conduct the attack--
after completing the development by B-g5, will be to open the f-
file for the Rook by advancing the f-Pawn. This advance can be
prepared by P-h3 and Kt-h2. Of course, White would prefer to do
without the move of the h-Pawn; but h2 is the only favorable
square for the Knight f3, as neither from d2 nor from h4 he has
an opportunity to help the attack while from h2 he may go to g4,
bearing on both of the weak squares f6 and h6.

Black has little chance for counterattack. The only thing he can
do is occupy the Queen's file with his Rooks and opening it by P-
d5 and Pxe4. His Queen's Bishop, however, is badly placed in any
case as he has no open diagonal to work in, and he will have to
get back into play via his original square c8.

White's King's Bishop is not well placed either and is
practically condemned to play the role of a Pawn by protecting
the square d3 without, at the same time, attacking anything.
There is, of course, a chance for him to be useful in the
diagonal a2-g8. It may be said that in King's Pawn openings
White's King's Bishop comparatively seldom has an opportunity to
take an active part in the battle. He is mostly exchanged at an
early stage of the game for Black's Queen's Knight or Queen's
Bishop. In Queen's Pawn openings, however, he finds a great field
of action in the unobstructed diagonal b1-h7. In this diagonal he
can also be used in all openings starting with P-e4 in which
Black does not advance his King's pawn to e5, as White can open
the diagonal at any time by playing P-e5.

Generally speaking, Bishops should not be placed in diagonals
which are obstructed by Pawns of their own army, and Pawns moves
should be avoided which close a diagonal formerly open to a
kindred Bishop. A striking illustration of the importance of this
rule will be found in the play which developed in the position of
Diagram 55 in a game between Teichmann and Dus Chotimirski in the
Prague Tournament 1908. Black, on the move, played (1)..., Kt-e5,
disturbing the symmetry of the position to his advantage by
opening the diagonal of his Queen's Bishop without allowing White
to make a similar maneuver. After (2) Ktxe5, Bxe5; (3) Q-e2, o-o;
(4) Ra1-d1, Q-e7; White yielded the temptation to drive away the
disagreeable Bishop e5 by (5) P-f4, a move which had to be
followed up with the advance of the e-Pawn who otherwise would
have remained very weak, not being protected by another Pawn.

       +---------------------------------------+
     8 | #R |    |    | #Q | #K |    |    | #R |
       |---------------------------------------|
     7 |    | #B |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #Kt| #B | #P | #Kt|    |    |
       |---------------------------------------|
     5 |    | #P |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    | ^P |    |    |    |    |    |    |
       |---------------------------------------|
     3 | ^P |    | ^Kt| ^B | ^P | ^Kt|    |    |
       |---------------------------------------|
     2 |    | ^B |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 55.

The game went on as follows: (5) ..., B-c7; (6) P-e4, B-b6+; (7)
K-h1, Rf8-d8; (8) B-b1, Ra8-c8; (9) Rxd8+, Qxd8; (10) R-d1, Q-e7;
(11) P-e5. This opens again the diagonal of the King's Bishop,
but it closes that of the Queen's Bishop, and it is the advantage
of the work done by his Queen's Bishop in the unobstructed
diagonal which secures Black the victory, (11) ..., Kt-d5; (12)
Ktxd5, Bxd5; (13) Q-g4, Q-b7; (14) P-f5, R-c4; (15) Q-g3, R-f4!.
White cannot capture the Rook on account of Bxg2 mate. (16) P-f6,
P-g6. There is now no defense against R-f2 which attacks g2 and
b2 at the same time. (17) B-a2, R-f2; (18) Bxd5, Qxd5! and White
resigns as he loses his Bishop on account of the mating threat.

It remains to examine typical middle-game maneuvers with the
Queen and with the Pawns. Little is to be said about the Queen.
On account of her tremendous mobility she is liable at any time
to initiate a dangerous attack in conjunction with one or more of
the other pieces, and most of the examples given for the typical
Rook's, Bishop's and Knight's maneuvers have also shown the
methods by which the cooperation with the Queen can be effected.
The main field of action for the Queen is the side on which the
opponent has castled. In games, in which both players have
castled on the same side of the board, and which, as stated
previously, constitute the vast majority of cases it is dangerous
to make excursions with the Queen to distant regions away from
the King, as her retreat might be cut off, making impossible an
adequate defense against an attack which the opponent might be
able to initiate on the King's side with the help of his own
Queen.

        +---------------------------------------+
      8 |    | #R |    | #Q |    | #R | #K |    |
        |---------------------------------------|
      7 |    |    | #P |    |    | #P | #P | #P |
        |---------------------------------------|
      6 | #P |    |    | #B | #B |    |    |    |
        |---------------------------------------|
      5 |    |    | #P |    |    |    |    |    |
        |---------------------------------------|
      4 |    |    |    |    |    |    |    |    |
        |---------------------------------------|
      3 |    |    |    | ^Q |    |    |    |    |
        |---------------------------------------|
      2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
        |---------------------------------------|
      1 | ^R | ^Kt| ^B |    | ^R |    | ^K |    |
        +---------------------------------------+
          a    b    c    d    e    f    g    h

                 DIAGRAM 56.

In the position of Diagram 56 for instance, it would be very
risky for White to take the Pawn a6. Black would play P-c4,
cutting off the retreat of White's Queen, and then start a
violent attack with his Queen in conjunction with the two
Bishops. Another example is the position of Diagram 57 which
occurred in a game between Capablanca and Bernstein in the San
Sebastian Tournament 1911. White played (1) Kt-e2 and Black, in
view of the threatening accumulation of white pieces on the
King's wing, should not have risked to capture the Pawn a2,
getting his Queen quite out of play.

       +---------------------------------------+
     8 |    |    |    |    | #R | #R |    |    |
       |---------------------------------------|
     7 | #P |    | #P | #B |    | #P | #P | #K |
       |---------------------------------------|
     6 |    |    | #P | #P | #Kt|    |    | #P |
       |---------------------------------------|
     5 | #Q |    |    |    |    | ^Kt|    |    |
       |---------------------------------------|
     4 |    |    |    | ^Kt| ^P |    | ^P |    |
       |---------------------------------------|
     3 |    | ^P |    |    | ^Q | ^P |    |    |
       |---------------------------------------|
     2 | ^P |    | ^P |    |    |    |    | ^P |
       |---------------------------------------|
     1 |    |    |    | ^R | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 57

He underestimated the danger and lost the game very quickly. The
attack developed as follows: (1) ..., Qxa2; (2) Kte2-g3, Qxc2. In
taking the second Pawn Black loses another move. He might have
tried Q-a5, threatening to exchange Queens with Q-b6. But it is
doubtful whether he would have been able to save the game. White
would, of course, have avoided the exchange by playing his King
into the corner. (3) R-c1, Q-b2; (4) Kt-h5; this prevents the
Queen from getting back into play via f6. The threat is now R-c3,
cutting Black's Queen off from g7, and then Kth5xg7 and Qxh6.
Black defends himself against this threat by (4) ..., R-h8 with
the intention to answer R-c3 with K-g8; but White's position
involves so many threats that Black cannot provide a satisfactory
protection. (5) R-e2, Q-e5; (6) P-f4, Q-b5; (7) Ktf5xg7 ! and
wins, as Ktxg7 is followed by (8) Kt-f6+, (9) Ktxd7 and (10) P-f5
or P-e5 with overwhelming attack.

The most difficult problem in the conduct of the middle-game is
the timely maneuvering with the Pawns. Although it is impossible
to give a general rule which will apply to all cases it is a good
principle to avoid Pawn moves in the middle- game just as
carefully as in the opening, at least in the early stages of the
middle-game. In the opening the argument against Pawn moves was
the time loss connected with them from the point of view of
development. In the middle-game it is mainly the weakness created
by the Pawn move on the squares which were protected by the Pawn
before he advanced. A square may be termed "weak" if it can be
safely occupied by men which help the opponent in his attack, and
this is generally possible if the square in question cannot any
longer be defended by a Pawn. The great danger involved in the
occupation by hostile pieces of such weak squares is evident if
they are situated near the King, and examples of how the attack
develops in cases of this kind have been discussed in connection
with Diagrams 48, 49, 50 and 52. It is less apparent why a Pawn
move should create a weakness if a center-Pawn or a Pawn on the
Queen's wing is concerned. In the latter case, the possibility of
deriving an advantage during the middle-game is rare, indeed; but
the weakness produced by the Pawn moves invariably shows itself
in the ending. In the position of Diagram 58 for instance, White
wins on account of the weakness of the squares a6, c6, d5 and b5
from which his King can attack the Black Pawns as soon as the
Queen and the Rook are exchanged. The following play may ensue:
(1) R-e8, Rxe8; (2) Qxe8, Q-f8; (3) Qxf8 , Kxf8; (4) K-d3, K-e7;
(5) K-c4, K-d7; (6) K-b5, K-c7; (7) K-a6, K-b8; (8) P-a4, K-a8;
(9) P-a5, Pxa5; (10) Kxa5 and wins the c-Pawn. Or: (5) ..., P-a6;
(6) K-d5, K-d7.

       +---------------------------------------+
     8 |    |    |    | #R |    |    | #K |    |
       |---------------------------------------|
     7 | #P |    |    |    |    | #P | #Q | #P |
       |---------------------------------------|
     6 |    | #P |    |    |    |    | #P |    |
       |---------------------------------------|
     5 |    |    | #P |    | ^R |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 | ^P |    |    |    | ^Q |    |    |    |
       |---------------------------------------|
     2 |    | ^P | ^P |    | ^K | ^P | ^P | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM  58.

For the time being Black has the opposition so that White's King
cannot advance any further; but White has so many more Pawn moves
at his disposal than Black that the latter is soon forced to move
his King allowing White to break in with his King at one or the
other side. For instance: (7) P-a4, P-a5; (8) P-f4, P-f6; (9) P-
g4, P-h6; (10) P-h3, P-g5; (11) P-f5; King moves, and White wins
either the f-Pawn or the b-Pawn.

This example brings out another reason why it is advantageous to
keep the Pawns of the wings back. In the ending positions
frequently arise in which it is important to have some moves to
spare in order to be able to maintain the opposition of Kings;
and the player whose Pawns are farther back naturally has more
spare moves.

A disadvantage which is liable to make itself felt in the middle
game as well as in Rooks' endings as a consequence of Pawn moves
on the wing is the opening of an adjoining file for a hostile
Rook, as illustrated by the play in the positions of Diagrams 50,
51 and 54. In the middle-game this is also true of certain Pawns,
as for instance in the following position which arises after the
opening moves (1) P-e4, P-e5; (2) Kt-f3, Kt-c6; (3) P-d4, Pxd4;
(4) B-c4, Kt-f6; (5) o-o, B-e7. The proper continuation is (6) R-
e1, protecting the center-Pawn. The advance of this Pawn is
entirely uncalled for. Not only does it enable Black to open the
f-file for his Rook by advancing his f-Pawn, but it gives up the
greatest advantage connected with the possession of a center-
Pawn, that is the control of two center-squares. As long as White
has his Pawn on e4, the two squares f5 and d5 are inaccessible to
black pieces; as soon as the Pawn advances, however, he does not
do Black any further harm, as the two squares which he controls
after the advance are firmly in Black's hands on account of the
two Pawns f7 and d7.

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P | #B | #P | #P | #P |
       |---------------------------------------|
     6 |    |    | #Kt|    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    | ^B | #P | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM  59.

A game played with this opening proceeded as follows: (6) P-e5,
Kt-e4; (7) B-d5, Kt-c5; (8) Ktxd4, Ktxd4; (9) Qxd4, o-o; (10) Kt-
c3, P-d6; (11) B-e3, P-c6; (12) B-b3, P-d5; (13) Ra1-d1, K-h8;
(14) Q-f4, P-f6. This decides the middle-game in Black's favor.
Not only will he have superior mobility with his Rooks, but his
two Bishops are much stronger than White's two minor pieces,
especially as White's Bishop is shut in.

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K | #B | #Kt| #R |
       |---------------------------------------|
     7 | #P | #P | #P | #P |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    | ^Q | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B |    | ^K | ^B |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM  60.

Moreover, Black has the better chances even in the ending, as he
has a majority of Pawns on the Queen's wing. After all pieces
have been exchanged, these Pawns would finally result in a passed
Pawn, which White would have to stop with his King while Black
can leisurely attack the Pawns of the King's side.

A disadvantage due to Pawn moves which up to now has not yet been
discussed is the weakness of so-called "backward Pawns." A
backward Pawn is one whose adjoining kindred Pawns have advanced
while he is unable himself to advance far enough to obtain their
protection from a frontal or diagonal attack. In the position of
Diagram 60, for instance, Black would make his Queen's Pawn
backward if he played P-c5; for if White handles the game right
Black will never be able to advance the Queen's Pawn beyond d6,
making him an easy mark for an attack in the d-file or in the
diagonal h2-b8, and also hampering the mobility of Black's pieces
in the center. The correct way for White to arrange his men would
be to play P-c4 and after the development of the minor pieces to
double the Rooks in the d-file. White's Queen's Bishop will be
placed best on f4 from where he helps pressing on d6.

Diagram 61 shows a position which occurred in one of the match
games played between Emanuel Lasker and S. Tarrasch for the
World's Championship in 1908, and which furnishes a good
illustration of the difficulties arising from a backward Pawn.
The game proceeded as follows: (1) Ktxd6, Pxd6; (2) Ra1-d1, Q-f6;
(3) P-c4, Rf8-e8; (4) Q-g4 (threatening Q-d7) B-c6; (5) R-e2; R-
e4; (6) Q-g3, Q-e6 (threatening R-g4); (7) P-h3, R-d8. Black
cannot protect the Pawn d6 as many times as White can attack him.
It looks as if he could have taken the Pawn c4 with his Queen,
but he was probably afraid of the weakness White would have
provoked with B-h6, (8) Re2-d2, Re4-e5; (9) B-h6 ! Black cannot
take the Bishop on account of Qxe5. (9) ..., Q-g6; (10) B-f4 and
wins, as the Pawn d6 as well as the Pawn c5 are doomed.

       +---------------------------------------+
     8 | #R |    |    | #Q |    | #R | #K |    |
       |---------------------------------------|
     7 | #P | #B | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    | #B |    |    |    |    |
       |---------------------------------------|
     5 |    |    | #P |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^Kt|    |    |    |
       |---------------------------------------|
     3 |    |    |    |    | ^B |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    | ^Q | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM  61.

In a position like that of Diagram 45 on White could play P-f4
without making his King's Pawn backward, as neither a frontal nor
a diagonal attack on e3 is possible. Of course, he would have to
see that the possibility of such an attack does not arise later
on. For instance, he would not be in a position to take the Pawn
c5 with the Pawn d4, as this would enable Black to use the
diagonal a7-g1 for operations against e3.

The player who endeavors to adhere in all positions to the
principles of Chess Strategy outlined in this chapter will
rapidly improve his strength and acquire within a short time a
much more intimate grasp of the game than others who have had
years of practice without making clear to themselves the general
laws which govern the outcome of every combination on the
Chessboard.

The illustrative games analyzed in the following chapter do not
teach anything new. They are merely examples of the application
of the general principles to the continuous series of
combinations which constitute a game of Chess. The author has
chosen games from his own tournament practice as this naturally
enabled a more thorough annotation than would have been possible
to offer for games of other players.



IV ILLUSTRATIVE GAMES



GAME NO. 1


Played in the Championship Tournament of the Western States,
1917, at Lexington, Ky.

           White            Black
     Jackson Showalter.  Edward Lasker

          (1) P-e4          P-e5
          (2) Kt-f3         Kt-c6
          (3) B-b5          P-a6

As explained previously this move cannot be regarded as loss of
time as White has to either retreat with the Bishop, adding
nothing to his development, or exchange on c6, helping Black's
development by opening a line for the Bishop c8.

          (4) B-a4          Kt-f6

The move B-c5 which Black might consider instead of Kt-f6 is not
to be recommended as White would reply P-c3 and then force the
exchange of Black's center-Pawn by P-d4. The complete control of
the center which White would gain in the further course of the
game would soon give him an overwhelming attack. For instance:
(4) ..., B-c5; (5) P-c3, Kt-f6; (6) o-o, o-o;

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K | #B |    | #R |
       |---------------------------------------|
     7 |    | #P | #P | #P |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #Kt|    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     4 | ^B |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P | ^P |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 62.

(7) P-d4, Pxd4; (8) Pxd4, B-b6; (9) P-e5, Kt-e8; (10) P-d5, Kt-
e7; (11) P-d6, Pxd6; (12) Pxd6, Kt-g6; (13) B-g5, etc.

           (5) P-d3

It is customary for White to castle at this point. P-d3 is
certainly a good move as it enables the development of the
Queen's Bishop, but o-o is very likely better as it reserves the
option of advancing the Queen's Pawn either one or two squares.
When advancing the Pawn two squares White has to avoid the
following trap: (5) o-o, B-e7; (6) P-d4, P-b5; (7) B-b3, Pxd4
(not Ktxd4 on account of (8) Bxf7  and (9) Ktxe5 +); (8) Ktxd4
??, Ktxd4; (9) Qxd4, P-c5 followed by P-c4 winning the Bishop.
What White can try in this variation is the Pawn sacrifice (8) P-
c3, Pxc3, through which he obtains a considerable advantage in
the development of the pieces.

After (5) o-o White threatens to win the Pawn e5 by (6) Bxc6 and
(7) Ktxe5, as now Q-d4; (8) Kt-f3, Qxe4 is not possible on
account of (9) R-e1. Black has various ways to counter this
threat. He can either defend the Pawn by P-d6 or play B-e7 with
the view to capture the Pawn e4 in case White should take the
Pawn e5, or, finally, he can capture the Pawn e4 at once.

All of these three variations are playable for Black although it
appears that White obtains a slight advantage however Black
continues. This opening is consequently a great favorite in
modern Tournament play.



[Footnote: Following are the two main variations which have been
adopted in the practice of the Masters:

A. (5) o-o, B-e7; (6) R-e1 (protecting the Pawn e4 so that
Black has to defend himself against Bxc6 and Ktxe5), P-b5; (7) B-
b3, P-d6; (8) P-c3 (preserving the Bishop against the exchange
threatened with Kt-a5), Kt-a5; (9) B-c2, P-c5; (10) P-d4, Q-c7.
Now the Pawn e5 is sufficiently protected and Black threatens to
exert pressure on d4 by playing B-g4 and Kt-c6. It might seem
that White can ignore this threat and as soon as d4 attacked
either exchange the Pawn on e5 or advance him to d5. However, the
former maneuver would open the d-file for Black's Rooks and the
latter would not be very good either before Black has castled;
for the advance of the d-pawn closes the center-files permanently
for the Rooks so that Black's King is safe in the center while
White may have to face an attack on the King's wing which Black
might initiate by storming with the h and g Pawns.

For all these reasons White is justified in making the waiting
move (11) P-h3, which safeguards the square d4 against the
indirect attack B-g4 and at the same time prepares an attack
along the lines of the one discussed in connection with Diagram
52. After (11) ..., Kt-c6; (12) B-e3, o-o; White can safely
advance the Queen's Pawn and then launch the attack referred to
above.

B. The second variation arising from the position of Diagram 62
is (5) o-o, Ktxe4. It seems rather dangerous for Black to take
the Pawn as long as his King is in the e-file which White can
occupy with his Rook; but after (6) R-e1, Kt-c5; (7) Ktxe5,
Ktxe5; (8) Rxe5 +, Kt-e6, White has not much attack and for this
reason the opening is generally treated in a different way. As
the strongest move is considered (6) P-d4. Black can hardly take
this Pawn as R-e1 and Ktxd4 would follow threatening to win a
piece; but he may try to maintain his Knight on the dominating
square e4 by (6) ..., P-b5; (7) B-b3, P-d5. After (8) Pxe5, B-e6;
(9) P-c3 (again providing a retreat for the Bishop), B-e7; (10)
Ktb1-d2, Black's best continuation is probably Ktxd2; (11) Qxd2
(not Bxd2 on account of B-g4); Kt-a5 or o-o. The maneuver (10)
..., Kt-c5; (11) B-c2, P-d4, which was tried in several recent
tournaments, is of doubtful value as Black loses control of the
important center-square e4. White can use this square for an
attack on the weak point c6 as follows: (12) Kt-e4, Pxc3; (13)
Ktxc5, Bxc5; (14) B-e4, Q-d7; (15) Q-c2, B-d5 (in order to answer
R-d1 with Bxe4); (16) B-g5, and Black does not seem to have a
satisfactory defense. For instance (16) ..., B-b6; (17) Ra1-d1,
Bxe4; (18) Qxe4, Q-e6; (19) R-d6 or (16) ..., Bxe4; (17) Qxe4,
Pxb2; (18) Ra1-d1, P-b1 (Q); (19) Rxb1 followed by R-c1.]



           (5) ...      P-b5

The simplest and probably best way to defend the Pawn e5 against
the threat Bxc6 and Ktxe5 is P-d6 without P-b5.

           (6) B-b3     P-d6

The alternative was B-c5. White could then not have captured the
Pawn e5 by (7) B-d5, o-o; (8) Bxc6, Pxc6; (9) Ktxe5 on account of
Q-d4, threatening mate on f2 and attacking the Knight.

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K | #B |    | #R |
       |---------------------------------------|
     7 |    |    | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #Kt| #P |    | #Kt|    |    |
       |---------------------------------------|
     5 |    | #P |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     3 |    | ^B |    | ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 63.

          (7) Kt-g5

This attack with two pieces in the early stage of the opening is
contrary to the general principles of strategy. White wins a Pawn
but this cannot be considered an adequate equivalent for the time
he loses in doing so. He neglects his development and he is bound
to suffer for that sooner than he can make the weight of his
extra-Pawn felt.

          (7) ...           P-d5
          (8) Pxd5

Black cannot recapture the Pawn as this would give White an
occasion to initiate a violent attack starting with the sacrifice
of the Knight on f7, thus: (8) ..., Ktxd5; (9) Ktxf7, Kxf7; (10)
Q-f3+, K-e6 (the Knight d5 has to be protected); (11) Kt-c3,
Ktc6-e7; (12) o-o, followed by R-e1, P-d4, etc. The exposed
position of Black's King is well worth the piece which White has
sacrificed.

       +---------------------------------------+
     8 | #R |    | #B | #Q | #K | #B |    | #R |
       |---------------------------------------|
     7 |    |    | #P |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    | #Kt|    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    | #P |    | ^P | #P |    | ^Kt|    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^B |    | ^P |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 64.

          (8) ...           Kt-d4

With this move Black crosses White's plans by exchanging the
Bishop who was to play the main part in the attack, and, as a
consequence, the Knight g5 does not have a chance to do any
useful work either.

         (9) P-d6

Opening again the diagonal of the Bishop and getting rid of the
advanced Pawn by exchange before Black has an occasion to capture
him.

          (9) ...           Ktxb3
          (10) Pxc7         Qxc7


       +---------------------------------------+
     8 | #R |    | #B |    | #K | #B |    | #R |
       |---------------------------------------|
     7 |    |    | #Q |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    |    |    |    | #Kt|    |    |
       |---------------------------------------|
     5 |    | #P |    |    | #P |    | ^Kt|    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | #Kt|    | ^P |    |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P | ^P |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R | ^Kt| ^B | ^Q | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 65.

Black could regain his Pawn by Q-d5; (11) Pa2xb3, Qxg2; (12) Q-
f3, Qxf3; (13) Ktxf3, B-b7; (14) K-e2, B-d6 and Bxc7; but in
doing so he would give up his advantage in development, which, as
the further course of the game proves, is much more valuable.

          (11) Pa2xb3        B-b7
          (12) o-o           P-h6!

If Black proceeded to develop his pieces indiscriminately, his
advantage would soon vanish. White needs only two moves--R-e1 and
Kt-e4--to paralyze the effect of Black's powerful Queen's Bishop
and to regain control of the center where at present Black has
the upper hand on account of his center-Pawn.

          (13) Kt-f3          B-d6
          (14) R-e1           o-o
          (15) Ktb1-d2        Ra8-d8
          (16) P-c3

White does not risk Kt-e4 as Black, after Ktxe4; (17) Pxe4, can
uncover the Rook by B-b4 attacking White's Queen and Rook at the
same time. White's only defense would be (18) B-d2 or Kt-d2, but
he would pin himself badly in either case and Black would obtain
an overwhelming attack by P-f5, which enables his King's Rook to
join the fray.

With P-c3 White protects himself against B-b4 and now actually
threatens to interrupt the diagonal of Black's Queen's Bishop.
Black will naturally try to prevent this and the first move which
presents itself for the purpose is P-e4, opening a line for the
Bishop d6 and the Queen at the same time. At first sight the move
does not seem playable as on e4 the Pawn is three times attacked
and only twice defended; but White cannot withdraw both the
Knight d2 and the Pawn d3 from the Queen's file on account of the
threat Bxh2+ winning the Queen for Rook and Bishop. Black can,
therefore, safely advance the Pawn.

       +---------------------------------------+
     8 |    |    |    | #R |    | #R | #K |    |
       |---------------------------------------|
     7 |    | #B | #Q |    |    | #P | #P |    |
       |---------------------------------------|
     6 | #P |    |    | #B |    | #Kt|    | #P |
       |---------------------------------------|
     5 |    | #P |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^P | ^P | ^P |    | ^Kt|    |    |
       |---------------------------------------|
     2 |    | ^P |    | ^Kt|    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B | ^Q | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 66.

          (16) ...           P-e4
          (17) Pxe4          Ktxe4
          (18) Q-c2

Now that the Queen has left the d-file, unpinning the Knight,
something must be done for the Knight e4 who is twice attacked
and only once protected. Two moves come into consideration. One
is P-f5 which maintains the Knight in the dominating center-
position, as White cannot take him without opening the f-file for
Black's Rook and losing the Pawn h2 who needs the protection of
the Knight f3. The other is Ktxd2, winning the Pawn h2 right away
no matter whether White retakes with the Bishop or with the
Knight. Which of the two moves is the better is difficult to say
and is more or less a matter of temperament. A player who prefers
a slow and sure advance will choose P-f5. A player who likes a
faster pace will start the hand-to-hand fight without delay by
Ktxd2. It is the latter move on which Black decides.

           (18) ... Ktxd2

White now faces the dilemma whether to recapture with the Bishop
or with the Knight. If he takes with the Bishop Black exchanges
on f3, breaking up White's chain of Pawns, and he regains his
Pawn by Bxh2. If he takes with the Knight, Black also wins the
Pawn h2, but the other Pawns in front of the King remain intact.
The drawback to the latter continuation is, however, that White's
development is delayed for another two moves, as the Queen's
Bishop is shut in. For this reason White decides on Bxd2,
probably also hoping that he will be compensated for the broken
Pawn position by an attack in the g- or h-file which Black's
maneuver opens.

       +---------------------------------------+
     8 |    |    |    | #R |    | #R | #K |    |
       |---------------------------------------|
     7 |    | #B | #Q |    |    | #P | #P |    |
       |---------------------------------------|
     6 | #P |    |    | #B |    |    |    | #P |
       |---------------------------------------|
     5 |    | #P |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^P | ^P |    |    | ^Kt|    |    |
       |---------------------------------------|
     2 |    | ^P | ^Q | #Kt|    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^B |    | ^R |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 67.


          (19) Bxd2          Bxf3

The fact that Black has to exchange his well placed Queen's
Bishop in order to win the Pawn h2 was very likely another reason
which induced White to retake with the Bishop.

          (20) Pxf3          Bxh2+
          (21) K-g2

       +---------------------------------------+
     8 |    |    |    | #R |    | #R | #K |    |
       |---------------------------------------|
     7 |    |    | #Q |    |    | #P | #P |    |
       |---------------------------------------|
     6 | #P |    |    |    |    |    |    | #P |
       |---------------------------------------|
     5 |    | #P |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^P | ^P |    |    | ^P |    |    |
       |---------------------------------------|
     2 |    | ^P | ^Q | ^B |    | ^P | ^K | ^B |
       |---------------------------------------|
     1 | ^R |    |    |    | ^R |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 68.

A general survey of the position shows clearly that Black has the
advantage. His Rook d8 is ready to take part in the battle while
White has to make several preparatory moves with his Rooks before
he can make use of them on the King's wing, the only part of the
board where they have a chance to be effective. In the e-line
which White's Rook controls at present, there is no tangible
object for an attack.

Moreover, White's King is rather exposed while Black's King is
safely entrenched behind his Pawns.

A good continuation for Black, which presents itself at first
thought, is R-d6, enabling the doubling of the Rooks in the d-
line or the participation of the Rook d6 in a fight on the King's
wing.

          (21) ...           R-d6
          (22) R-e4

White cannot take the Bishop h2 as Rxd2 would win the Queen. (22)
P-f4 would not be good either as Black would reply Q-d7,
threatening Rxd2 as well as Q-g4+; Kxh2, R-g6 and mate in two
moves.

With R-e4 White attempts to protect his King by R-g4 against
attacks in the g-file, and Black naturally tries to foil this
attempt.

          (22) ...           P-f5
          (23) R-h4

Black has now to decide whether he should withdraw his Bishop to
e5 or counterattack White's Bishop by Q-d7 or Q-d8 or Rf8-d8. The
counterattack looks better as it threatens to force an entrance
for the Rooks in the second rank, displacing White's Queen and
attacking the King from the flank. The withdrawal of the Bishop
would give White time to play his Queen's Rook over to the King's
wing.

The most forcible of the three moves available for the
counterattack is Q-d8, which attacks the Rook h4 too, thereby
depriving White of the possibility to save his Bishop by flight.

          (23) ...           Q-d8
          (24) Rxh2          Rxd2
          (25) Q-c1

White's Queen has now hardly any mobility and in addition she
shuts off the Queen's Rook from the King's wing. Black, on the
other hand, can easily get his Rooks to cooperate by doubling
them either in the d-file or in the second rank. He decides on
the former alternative because the control of the Queen's file
keeps White's troops separated in two parts which have little or
no communication with each other, while Black's pieces are ready
for concentration on the King's wing at any moment.

          (25) ...           Q-g5+
          (26) K-h1          Rf8-d8
          (27) Q-e1

With the intention to play Q-e6+, thereby gaining time to swing
over the Queen's Rook to the King's wing.

          (27) ...           K-h7
          (28) Q-c1

       +---------------------------------------+
     8 |    |    |    | #R |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    | #P | #K |
       |---------------------------------------|
     6 | #P |    |    |    |    |    |    | #P |
       |---------------------------------------|
     5 |    | #P |    |    |    | #P | #Q |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^P | ^P |    |    | ^P |    |    |
       |---------------------------------------|
     2 |    | ^P |    | #R |    | ^P |    | ^R |
       |---------------------------------------|
     1 | ^R |    | ^Q |    |    |    |    | ^K |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 69.

The Queen cannot leave the first rank on account of the threat R-
d1+. It lies near for Black to try to force her out by attacking
the square d1 once more with the Queen, thereby threatening to
win the Queen for a Rook by the check on d1. He can accomplish
this by playing the  Queen into the  d-file  behind the Rooks.

          (28) ...           R-d6
          (29) P-c4

Apparently White does not recognize Black's intention, or he
would have played (29) Q-f1 in order to answer Q-d8 with (30) R-
e1, R-dl; (31) K-g2. But Black would then also have had an easy
win by playing (29) ..., Rxb2 and doubling the Rooks in the
second rank.

          (29) ...           Q-d8
          (30) Q-c3

The only alternative to save the Queen was K-g2, but then R-d1
would have won a clear Rook.

Black now enforces a mate in ten moves: R-d1+; (31) Rxd1, Rxd1+;
(32) K-g2, Q-g5+; (33) K-h3, R-g1; (34) Q-d4, Q-h5+; (35) Q-h4,
Qxf3+; (36) Q-g3, Rxg3+; (37) Pxg3, P-f4; (38) K-h4, Qxg3+; (39)
K-h5, Q-g5 mate. This instructive game was not lost through a
faulty combination but on account of loss of time in the opening
which could not be regained.


GAME  NO. 2


Played in the New York Masters' Tournament 1915

          White             Black
          Edward Lasker     Jose Raoul Capablanca

          (1) P-d4          P-d5
          (2) Kt-f3         Kt-f6
          (3) P-c4          P-e6
          (4) Kt-c3         Ktb8-d7
          (5) B-g5          B-b4

Ordinarily the Bishop is developed to e7 as on b4 he is out of
place as soon as White has castled.

          (6) P-e3          P-c5

With this move Black threatens Q-a5, attacking the Knight c3 for
the second time and unpinning the Knight f6 who is then free to
cooperate with the Bishop b4 and the Queen by advancing to e4. In
trying to counter Black's threat White will seek to do as much as
he can for the development of his pieces so as to combine the
attack with defense. The King's Bishop is not yet developed, and
his most natural developing move happens to cover the square at
which Black is aiming with his Knight.

          (7) B-d3           Q-a5
          (8) Q-b3

       +---------------------------------------+
     8 | #R |    | #B |    | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P |    | #Kt|    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    | #P | #Kt|    |    |
       |---------------------------------------|
     5 | #Q |    | #P | #P |    |    | ^B |    |
       |---------------------------------------|
     4 |    | #B | ^P | ^P |    |    |    |    |
       |---------------------------------------|
     3 |    | ^Q | ^Kt| ^B | ^P | ^Kt|    |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    | ^K |    |    | ^R |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 70.

White has to be very careful on account of the various exchanges
possible in the center. Black threatens for instance to exchange
first on d4 and then to play Kt-e4 so that the Bishop g5 is
attacked by the Queen in case White takes the Knight with his
Bishop, allowing the Pawn d5 to clear the fifth rank. Or he might
play Kt-e4 first and then exchange on d4. Considering that all
these threats are based on the fact that the Knight c3 is pinned
as long as White has not yet castled it lies near for White to
try (8) o-o. It is true that Black can then win a Pawn by taking
twice on c3; however, in doing so he would retard his development
and White is bound to obtain a strong attack by getting all of
his pieces quickly into action, while Black's Queen is separated
from the rest of her troops.

White's eighth move, Q-b3, has several drawbacks. First of all
Black could play P-b5! winning a piece for three Pawns as White
cannot do better than play (9) Pxb5 or Pxd5 allowing P-C4.
Secondly, Black can make the combination indicated above which
tends to open the fifth rank so that the Queen attacks g5. The
same combination would be possible if White played (8) Q-C2.

          (8) ...            Kt-e4
          (9) o-o

Offering the Pawn sacrifice Ktxc3; (10) Pxc3, Bxc3 with the view
to attacking by (11) R-c1, etc., as previously indicated. Black
prefers to direct his attack against g5.

          (9) ...             Ktxg5
          (10) Ktxg5          Pxd4
          (11) Kt-b5

(11) Pxd4 would lose a piece on account of Pxc4, attacking the
Bishop on d3 and the Knight on g5. Black could now win a Pawn by
taking on d3, but this would be very dangerous as it would open
the f-file for White's Rook.

          (11) ...            Kt-c5

       +---------------------------------------+
     8 | #R |    | #B |    | #K |    |    | #R |
       |---------------------------------------|
     7 | #P | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     5 | #Q | ^Kt| #Kt| #P |    |    | ^Kt|    |
       |---------------------------------------|
     4 |    | #B | ^P | #P |    |    |    |    |
       |---------------------------------------|
     3 |    | ^Q |    | ^B | ^P |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 71.

The position is getting very complicated indeed. The first
possibility which White will consider is (12) Kt-d6+; but after
K-e7 there seems to be no satisfactory continuation. For
instance: (13) Q-C2, Ktxd3; (14) Ktd6xf7, R-f8 winning two
Knights for the Rook. Or: (14) Ktxc8+ ?, Ra8xc8; (15) Qxd3, Pxc4
winning a piece. Therefore, White has no alternative but to
retire the Queen.

          (12) Q-c2           Ktxd3
          (13) Qxd3           P-a6

       +---------------------------------------+
     8 | #R |    | #B |    | #K |    |    | #R |
       |---------------------------------------|
     7 |    | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 | #P |    |    |    | #P |    |    |    |
       |---------------------------------------|
     5 | #Q | ^Kt|    | #P |    |    | ^Kt|    |
       |---------------------------------------|
     4 |    | #B | ^P | #P |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    | ^Q | ^P |    |    |    |
       |---------------------------------------|
     2 | ^P | ^P |    |    |    | ^P | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    |    |    |    | ^R | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 72.

It is not easy for Black to retain tide Pawn which he has won. If
he plays (13) ..., B-e7; (14) Kt-f3, Pxe3; White can continue
(15) Pxd5 with good attacking chances on account of the open
files in the center of the board, of which Black cannot yet make
any use as he has not yet castled.

By P-a6 Black opens again the fifth rank in order to operate
against the Knight g5.

          (14) Ktxd4           Pxc4
          (15) Qxc4            B-d7
          (16) Kt-b3

A very bad move, as it violates the general principles of
strategy. In withdrawing the Knight from the dominating center
square White decreases his mobility instead of increasing it.
The logical continuation would have been Rf1-d1 or Ra1-c1,
developing one of the Rooks.

          (16) ...          Qxg5
          (17) Qxb4         B-c6

Black would not have been able to occupy this favorable square
with his Bishop, had not White withdrawn his Knight from d4.

          (18) P-e4          P-a5

This forces the Queen out of the diagonal a3-f8 as the Pawn e4
has to be kept protected.

          (19) Q-d2          Qxd2

Black demonstrates in a very simple manner that the exchange of
Queens is disadvantageous for White, a fact that White should
have foreseen as the unprotected Knight on d2 enables Black to
gain control of the d-file by castling on the Queen's side.

          (20) Ktxd2          o-o-o
          (21) Kt-c4

White cannot play R-d1 on account of R-d4, threatening Rh8-d8.

          (21) ...            Bxe4
          (22) Rf1-c1

This merely drives the Black King to a safe place. Ktxa5 was
indicated. R-d2 could then have been answered by (23) R-c1+ and
(24) R-C4.

          (22) ...            K-b8
          (23) P-f3

Again a move which helps the opponent as it drives the Bishop
where he wants to go.

          (23)...            B-d5
          (24) Ktxa5         R-c8
          (25) P-b3

This situation furnishes an instructive example of the importance
of the rules governing Pawn formations as previously discussed.
By attacking the Knight with the King Black can force the
exchange of the Bishop for the Knight on c4.

       +---------------------------------------+
     8 |    | #K | #R |    |    |    |    | #R |
       |---------------------------------------|
     7 |    | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     5 | ^Kt|    |    | #B |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    | ^P |    |    |    | ^P |    |    |
       |---------------------------------------|
     2 | ^P |    |    |    |    |    | ^P | ^P |
       |---------------------------------------|
     1 | ^R |    | ^R |    |    |    | ^K |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 73.

This leaves White with a Pawn on c4 who is weak on account of his
advanced position. Black can attack him with the King and White's
King is consequently compelled to stay on the Queen's wing
guarding the Pawn, while Black is at leisure to secure a passed
Pawn on the King's wing. These maneuvers are, of course, possible
only with the Rooks off the board. That is why Black tries to
force their exchange and why White should endeavor to prevent it.

          (25) ...            Rxc1+
          (26) Rxc1           R-c8
          (27) Rxc8+

In view of the hopeless Pawn ending it would have been best to
give up a Pawn by (27) R-d1, P-b6; (28) Kt-c4, Bxc4; (29) Pxc4,
Rxc4; (30) R-d2 in order to keep a Rook on the board, thus
obtaining a drawing chance.

          (27) ...            Kxc8
          (28) K-f2           K-c7
          (29) K-e3           K-b6
          (30) Kt-c4+         Bxc4
          (31) Pxc4           K-c5
          (32) K-d3           P-e5

Black's strategy in this ending is clearly indicated. He will
play P-f5 and advance the e-Pawn as soon as White plays K-c3.
Instead of the latter move White could play P-a3 which would also
keep Black's King from b4; but he would soon run out of spare
moves with his Pawns necessitating a King's move. For instance,
(32) P-a3, P-f5; (33) P-g4, P-g6; (34) P-h3, P-h6; (35) P-h4, P-
h5; (36) P-g5, P-b6!; (37) K-c3, P-e4; (38) P-f4, P-e3; (39) K-
d3, P-e2; (40) Kxe2, Kxc4; (41) K-e3, P-b5.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    | #P |    |    |    | #P | #P | #P |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    | #K |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    | ^P |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    | ^K |    | ^P |    |    |
       |---------------------------------------|
     2 | ^P |    |    |    |    |    | ^P | ^P |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 74.

Black needs now only six moves to queen the Pawn b5 while White
in the meantime cannot do more than capture the g- and h-Pawns,
and Black's Queen can naturally stop the White passed Pawns
without difficulty. The game proceeded as follows:

          (33) P-g4           P-f6
          (34) P-h4           P-g6
          (35) K-e4           K-d6

Black could just as well have captured the Pawn c4 and permitted
(36) P-g5, Pxg5; (37) Pxg5.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    | #P |    |    |    |    |    | #P |
       |---------------------------------------|
     6 |    |    |    | #K |    | #P | #P |    |
       |---------------------------------------|
     5 |    |    |    |    | #P |    |    |    |
       |---------------------------------------|
     4 |    |    | ^P |    | ^K |    | ^P |^P  |
       |---------------------------------------|
     3 |    |    |    |    |    | ^P |    |    |
       |---------------------------------------|
     2 | ^P |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 75.

He would then have had a Queen in another eight moves while White
could not get farther with his Pawn than to g7, so that Black
easily wins.

To march  against the  Pawn b7  instead of the Pawns on the
King's side would not help White either, as he does not get back
to the King's wing in time to protect his f- and g-Pawn.

          (36) P-f4           Pxf4
          (37) Kxf4           K-c5
          (38) P-h5           Kxc4
          (39) K-e4           P-b5
          (40) P-a3           K-c5
          (41) Resigns.



V

PROBLEMS



To offer an exhaustive treatise on the manifold varieties of
Chess problems is not within the scope of this book. The
intention of the author is merely to make it quite clear to the
reader that the Chess problem, apart from the moves of the men,
has no relation to the game and to illustrate the vast difference
between PROBLEM combinations and positions and GAME combinations
and positions by a few typical examples from the works of master
composers.

The mating methods and mating positions in the actual game very
rarely embody an element of surprise. They are all known from
previous experience and the question is merely whether the player
concerned is familiar with them. With the problem it is
altogether different. Here the mate must be accomplished in a
certain number of moves from a given position in some ingenious
way which is not known from game practice, or, if the mating
METHOD is not extraordinary, the mating POSITION must be
surprising and unlooked for.

Moreover, a number of laws must be obeyed in problem composition,
which by the general consent of problemists, or rather by natural
evolution of a more refined taste, have become the standards by
which the merits of a problem are judged.

There is first of all the law of economy in material which
demands that the idea of the problem should be expressed with the
least possible number of men, and that no pieces should be added
for the mere sake of increasing the number of variations. Then,
of course, a problem should have only one solution. A position
which has more than one key move is not considered a problem,
because the main point at issue in a problem is not the NUMBER of
moves in which the mate is accomplished but the METHOD in which
it is accomplished, and of two possible solutions one will always
be prettier so that the existence of the other must necessarily
appear a blemish.

A very important law is that the first move of White (who by
general consent has always the attack) must not deprive the black
King of a flight square, as this would be too brutal, too obvious
a procedure. The more possibilities of defense are left to Black
the more surprising is the solution and the finer is the problem.

Many problem solvers are under the false impression that the
first move in a problem must not be a check. This argument is
valid only when by the check the number of defensive moves is
limited, but this is not necessarily the case, as can be seen for
instance in problem No. 2, in which Black has to move his King
anyway, there being no other black piece on the board.

The position of Diagram 76 is an example of how a problem should
NOT be constructed. There is a tremendous number of pieces on the
board which have nothing to do with the idea of the problem. The
latter is one of the most primitive ideas used in problem
composition and has been expressed by many composers in charming
forms, so that there was no need for the above monstrous addition
to the problem literature. The key move is Q-h7 so as to pin the
Rook f5 in case Black plays K-d3 and to enable the mate (2) Rxf3.
However, if Black replies (1) ..., P-d3 or Bxe1, neither the
Queen nor the Rook f4 are necessary, but the mate is accomplished
by some of the other white pieces which are lavishly distributed
over the board.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    | ^Q |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 | ^Kt|    |    |    | #P |    |    |    |
       |---------------------------------------|
     5 |    |    | ^P |    | ^P | #R |    |    |
       |---------------------------------------|
     4 | ^B |    | #P | #P |    | ^R |    |    |
       |---------------------------------------|
     3 | #P |    | #K |    |    | #P | ^Kt|    |
       |---------------------------------------|
     2 | ^P |    |    | #B |    | ^P |    |    |
       |---------------------------------------|
     1 | ^K | #Kt|    | ^R | ^B |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 76.--Mate in Two Moves

A striking contrast will be found in the following problem which
is based on the same idea but in which all unnecessary material
is dispensed with.

The key move is B-c1, in order to mate with the Queen on b3 in
case Black takes the Rook a3. If Black moves the Rook, White
mates by Qxb6, and if the Pawn b6 advances (2) Qxe7 is mate.

       +---------------------------------------+
     8 |    | ^K |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    | #P | ^B |    |    |
       |---------------------------------------|
     6 |    | #P |    |    | #Q |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    | ^P |    |    |    |
       |---------------------------------------|
     4 |    | #K |    |    |    |    |    |    |
       |---------------------------------------|
     3 | ^R |    |    |    | ^B |    |    |    |
       |---------------------------------------|
     2 |    | #R |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 77.--Problem No. 1.

                    Mate In Two Moves.

In problem No. 2 the mating maneuver does not involve a special
trick; the idea of the composer was merely to arrive at an
extraordinary mating position, and he added considerably to the
value of the problem by producing the same mating position in
several variations. The key move is B-b3+. Black has three moves
in reply. If K-e4, White mates by (2) Q-f2, K-d3; (3) Q-f3. If K-
c6, the mate is accomplished by (2) B-b4, K-b5; (3) Q-b7; and if
K-d6, White answers (2) B-c4, K-c6; (3) Q-c7 mate.

       +---------------------------------------+
     8 |    |    |    | ^K |    |    |    |    |
       |---------------------------------------|
     7 | ^Q |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    | #K |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    | ^B |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    | ^B |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 78.--Problem No. 2.

                 Mate In Three Moves.

A favorite trick with composers is to provide a stalemate which
they relieve by obstructing the way of one of the pieces involved
in the stalemate. The move which is thereby allowed Black's King
exposes him to a discovered mate. The key move of problem No.3 is
P-g8 (becomes Knight). After P-b5 Black is stalemate, but White
relieves the stalemate by (2) Kt-e7, allowing Black to take the
Knight on b4, and then mates by Kt-c6.

In trying to solve a problem it is a good method to examine
Black's moves first. Often it will be found that whatever Black
moves White can mate in reply so that all that is necessary is to
find a first move for White, which leaves the position unchanged
as far as the different mating threats are concerned. If Black
has one or more moves at his disposal in reply to which there is
no mate, the way is indicated in which to provide for these
defenses.

       +---------------------------------------+
     8 |    |    |    |    |    | ^B |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    | ^P |    |
       |---------------------------------------|
     6 |    | #P |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    | ^Kt|    |    |    |    |    |    |
       |---------------------------------------|
     3 | #K | ^P |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    | ^K |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 79.--Problem No. 3.

                   Mate In Three Moves.

In problem No. 4 for instance, it is evident that Black has to
keep the two squares b8 and b4 guarded on which the Knight a6
threatens mate. Of course, Black can take the Bishop f5,
relieving the mating threat but White can move the Bishop to some
other square in the diagonal h3-c8. Still, Black would have the
defense Q-f8. This suggests as White's first move B-c8,
interrupting the line from f8 to b8.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 | ^K | ^Kt|    |    |    |    |    |    |
       |---------------------------------------|
     6 | ^Kt| ^P | #K |    |    |    |    |    |
       |---------------------------------------|
     5 |    | #P |    | #P |    | ^B |    |    |
       |---------------------------------------|
     4 |    | #P |    |    |    | #Q |    |    |
       |---------------------------------------|
     3 |    | ^P |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 80.--Problem No. 4.

                    Mate In Two Moves

The only square for Black's Queen from which to guard both b4 and
b8 is then d6; but there the Queen blocks a flight square of the
King, freeing the Knight b7 and enabling the mate Kt-a5.

The most difficult problems, of course, are those in which no
mate is threatened in the initial position and in which Black can
apparently foil all attempts to build a mating net. An example is
the following position which illustrates the so-called "Roman
idea."

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    | ^Kt|    |    | #B |    |    |    |
       |---------------------------------------|
     6 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     5 |    | ^B |    |    |    |    |    |    |
       |---------------------------------------|
     4 | ^K |    |    | ^P |    |    |    |    |
       |---------------------------------------|
     3 |    |    | #K |    | ^P |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    | ^Q |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

                DIAGRAM 81.--Problem No. 5.

                   Mate In Four Moves.

Black's King is stalemate so that any check with the Knight would
settle him. However, Black's Bishop guards the squares c5 and d6
from which the Knight could threaten a mate, and if White makes a
waiting move with the Queen in the second rank to force Black's
Bishop from his defensive position, Black replies B-g5 and takes
the Pawn e3 on the following move, relieving the stalemate. The
same maneuver would foil White's attempt to checkmate by (1) Q-
e2, (2) B-d3 and (3) Q-c2, and the position really does not
betray any other mating possibility.

The key of this exceptionally fine and difficult problem is (1)
Kt-d6, forcing Bxd6. The idea of this sacrifice is to change the
line of defense of the black Bishop from the diagonal h4-d8 to
the diagonal h2-b8, so that he is compelled to defend the threat
Q-e2, etc., indicated above by moving to f4, that is to a square
on which he can be taken. After (2) Q-e2, B-f4; (3) Pxf4 the
stalemate is relieved and Black can take the Pawn d4. But a most
surprising mate is now possible, which could not possibly have
been foreseen in the original position, namely: (4) Q-e5.

Problems in which no definite number of moves are stipulated for
the mate are usually called STUDIES or ENDINGS. They are nothing
but game positions in which a maneuver forces the win that is so
well hidden that it would probably not be found by a player in an
actual game. The following two positions are examples of this
class of compositions.

The first move is evident. White must play (1) P-c7, as otherwise
Black retreats with the Rook in the d-file and occupies the c-
file so that he can be sacrificed at any time for White's
dangerous Pawn.

       +---------------------------------------+
     8 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     6 |    | ^K | ^P |    |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    | #R |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 | #K |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

           DIAGRAM 82.--WHITE TO PLAY AND WIN.

After (1) ..., R-d6+ White can neither go to b7 on account of R-
d7 nor can he play K-c6 or c5 on account of R-d1 followed by R-c1
whereby Black would draw. The only way to win is: (2) K-b5, R-
d5+; (3) K-b4, R-d4+; (4) K-b3, R-d3+; (5) K-c2. At last White
has succeeded in guarding his rear, and it seems as if Black
could not any longer prevent the Pawn from Queening. However,
Black plays (5) ..., R-d4 and if White queens the Pawn he gives
check on C4 forcing Qxc4 which would stalemate the King.

       +---------------------------------------+
     8 |    |    |    |    |    |    | ^K |    |
       |---------------------------------------|
     7 |    |    |    |    |    |    | ^P |    |
       |---------------------------------------|
     6 |    |    | #B | ^B |    |    |    |    |
       |---------------------------------------|
     5 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     2 |    |    | ^Kt|    |    | #P |    | #P |
       |---------------------------------------|
     1 |    |    |    | #K |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

          DIAGRAM 83.--White to Move and Draw.

This is the point where the problem-trick enters the game. White
does not promote the Pawn to a Queen but to a Rook, avoiding the
stalemate and threatening mate on a8. Black's only defense is R-
a4 and now White wins by (7) K-b3 attacking the Rook and
threatening mate on c1 at the same time.

In the position of Diagram 83 Black threatens to queen either of
his Pawns. White can play (1) Kt-e3+ K-e2; (2) Bxh2, but after
Kxe3 there seems to be no way of stopping the Pawn f2.

       +---------------------------------------+
     8 | #K | #B |    | ^Q |    |    |    |    |
       |---------------------------------------|
     7 |    | #P |    |    |    |    |    |    |
       |---------------------------------------|
     6 | #P | ^P |    |    |    |    |    |    |
       |---------------------------------------|
     5 | ^P |    | ^Kt|    |    |    |    |    |
       |---------------------------------------|
     4 |    | ^P |    | ^Kt|    |    |    |    |
       |---------------------------------------|
     3 |    |    |    |    | #K |    |    |    |
       |---------------------------------------|
     2 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
     1 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
         a    b    c    d    e    f    g    h

           DIAGRAM 84.--Sui-Mate in Six Moves

Again an ingenious trick is available which leads to an
unexpected finish. White plays (3) K-h8 threatening to Queen his
Pawn and forcing B-d5. Then he gives up his Pawn by (4) P-g8
(Queen) and after Bxg8 he saves the game by (5) B-g1 !! If Black
takes the Bishop promoting the Pawn to a Queen or a Rook White is
stalemate. Otherwise the draw is forced by either Kxg8 or Bxf2.

It remains to explain the meaning of the so- called sui-mates. A
sui-mate is a problem in which White has to play so as to force
Black to checkmate him (White) in a certain number of moves. One
of the most beautiful examples in the literature is the above six
mover, the solution of which runs as follows: (1) Kt-b5, Pxb5;
(2) Kt-a6, Pxa6. One should not think that White can force Black
to checkmate in four more moves; but: (3) K-d4, K-b7; (4) Q-d5+,
K-c8; (5) P-b7+, K-c7; (6) K-c5 and Black has no other move
except B-a7, checkmating White.



PART II



THE GAME OF CHECKERS



I

THE RULES OF THE GAME



The game of Checkers (English: Draughts) is played on the 32
black or white squares of the Chess board by two opponents, each
of whom has twelve men of the same kind. The object of the game
is to capture all opposing men or to block them so that they
cannot move.

The original position of board and men is shown in Diagram 85. It
will be seen that the board is placed in such a way that the
players have a vacant square at their lower right hand corner.
This corner is called the DOUBLE CORNER because two men are
located in its immediate neighborhood while the left hand corner,
the SINGLE CORNER, is occupied by only one man.

The squares of the Checker board are usually described by numbers
as shown in Diagram 86. This is a rather crude method when
compared with the simple notation by means of a system of
coordinates as used in Chess, but as it is universally employed
in Checker books and Checker columns in daily papers it will be
adhered to in the following explanation of the game.

The black men are placed on the squares 1 to 12, the white men on
the squares 21 to 32. The first move must invariably be made by
the player of the black men.

             32        31        30
       +---------------------------------------+
       |    |  o |    |  o |    |  o |    |  o | 29
       |---------------------------------------|
    28 |  o |    |  o |    |  o |    |  o |    |
       |---------------------------------------|
       |    |  o |    |  o |    |  o |    |  o | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |  * |    |  * |    |  * |    |  * |    |
       |---------------------------------------|
       |    |  * |    |  * |    |  * |    |  * | 5
       |---------------------------------------|
     4 |  * |    |  * |    |  * |    |  * |    |
       +---------------------------------------+
                    3         2        1

                        DIAGRAM 85.

The move of the Checker men is a diagonal step forward, one
square at a time. If a hostile man is in his way and if the
square beyond the hostile man is vacant, he must capture him by
jumping over him on to the vacant square, and he must continue
capturing from the square on which he lands as long as this is
possible according to the above rule. Captured men are removed
from the board.

                        WHITE

       +---------------------------------------+
       |    | 32 |    | 31 |    | 30 |    | 29 |
       |---------------------------------------|
       | 28 |    | 27 |    | 26 |    | 25 |    |
       |---------------------------------------|
       |    | 24 |    | 23 |    | 22 |    | 21 |
       |---------------------------------------|
       | 20 |    | 19 |    | 18 |    | 17 |    |
       |---------------------------------------|
       |    | 16 |    | 15 |    | 14 |    | 13 |
       |---------------------------------------|
       | 12 |    | 11 |    | 10 |    |  9 |    |
       |---------------------------------------|
       |    | 8  |    | 7  |    | 6  |    | 5  |
       |---------------------------------------|
       | 4  |    | 3  |    |  2 |    | 1  |    |
       +---------------------------------------+

                        BLACK

                     DIAGRAM 86.

If a man reaches the opposite edge of the board he automatically
becomes a King and must be "crowned" by the opponent, who must
place another man on top of him. A King may move and capture
backward as well as forward. A man, who reaches the "King row" in
capturing, cannot, however, continue capturing on the same move
with the newly made King.

The position of Diagram 87 may serve to illustrate the above
rules. White, on the move, plays 14-9. Black must capture this
man with the man on 5 who jumps on to 14.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    | o  |    |    | 29
       |---------------------------------------|
    28 | *  |    |    |    |  o |    |    |    |
       |---------------------------------------|
       |    |    |    |  o |    |  o |    | *  | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | *  |    | o  |    | o  | 13
       |---------------------------------------|
    12 |    |    | *  |    |    |    |    |    |
       |---------------------------------------|
       |    | *  |    | *  |    |    |    | *  | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+

                    3         2        1

                     DIAGRAM 87.

White then sacrifices another man by 23-18 forcing Black to reply
14-23. Now White captures the three men on 23, 15 and 7 with his
man on 26, and Black, before making his next move, must crown
White's man who has just reached the King's row. He will
naturally move his man 8, as otherwise White would capture him
with the King on 3.

If a player overlooks the possibility of a capture his opponent
has the right to remove the man who should have made the capture,
from the board. This procedure is called "huffing" and does not
constitute a play. Instead of huffing a player may ask the
opponent to retract his move and to make the capture.

When neither player can force a win the game is considered a
draw. When one side appears to be stronger and refuses to accept
a draw offered the player of the weaker side can require the win
to be demonstrated within 40 moves; otherwise the game is drawn.



II

ELEMENTARY TACTICS



The first thing a Checker player has to know is what superiority
in material or position is required to FORCE a win in the ending.
The most elementary case is the one shown in Diagram 88, in which
White wins by playing 32-27. With this move White takes the
opposition or as most Checker players call it, White has the
"move." Whatever Black replies he is forced to the edge of the
board and finally he is obliged to let White capture his King.
Supposing Black plays (2) 26-22, in order to reach the double
corner, where he would be safe as he could indefinitely move from
5 to 1 and from 1 to 5, then White continues with (2) ...,27-23,
preventing (3) 22-18 which would gain the road to the double
corner. After (3) 22-17, 23-l8; Black has to retreat to the edge
by 17-13 or 17-21, and White, by playing 18-14, or 18-22 pins the
black King so that he cannot move without being captured. If it
had been Black's move in the position of the diagram, he would
have gained the opposition by 26-31 and White would have been
compelled to retire to the double corner and to draw by 32-28,
28-32, etc.

              32        31        30
       +---------------------------------------+
       |    | oo |    |    |    |    |    |    |29
       |---------------------------------------|
    28 |    |    |    |    | ** |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    |21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    |13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    |5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 88.

With one King entrenched in the double corner it takes two Kings
to force the win. In the position of Diagram 89 for instance
White would win as follows:

          Black          White

          (1) ...        19-24
          (2) 32-28      23-19
          (3) 28-32      24-28
          (4) 32-27      28-32
          (5) 27-31      19-15
          (6) 31-26      15-18
          (7) 26-31      18-22

In the ending THREE KINGS AGAINST TWO KINGS the most favorable
spots for the weaker player are the two double corners; but the
three Kings will always win when handled right.

              32        31        30
       +---------------------------------------+
       |    | ** |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | oo |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 89.

The method which has to be employed will be evident from the play
in Diagram 90. In order to win Black must exchange one King; the
position is then reduced to that of Diagram 89.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    |29
       |---------------------------------------|
    28 |    |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    |21
       |---------------------------------------|
    20 |    |    | ** |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | ** |    |    |    |    |13
       |---------------------------------------|
    12 |    |    |    |    | ** |    | oo |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    |5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 90.

If it were White's move, Black would easily win; for after (1)
..., 27-32; (2) 19-24, 9-5; (3) 10-6, White cannot avoid the
exchange. For instance: (3) ..., 5-1; (4) 24-19. The problem
reduces itself therefore to changing the move from Black to
White. This is accomplished by:

          Black              White

          (1) 15-18          27-32
          (2) 19-24           9-5
          (3) 10-14

Threatening 24-27. White can only reply

          (3) ...           32-28
          (4) 24-27          5-1
          (5) 14-9, etc., as above.

If the weaker side does not control both double corners the
exchange can be forced much more easily, as an experiment will
quickly show.

              32        31        30
       +---------------------------------------+
       |    | oo |    |    |    |    |    |    |29
       |---------------------------------------|
    28 | ** |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    |21
       |---------------------------------------|
    20 | ** |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | ** |    |    |    |    |    |    |13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 91.

Sometimes the stronger side has an occasion to give up two Kings
for one thereby forcing a position similar to that of Diagram 88.
Diagram 91 offers an example:

Black on the move wins in 5 moves, thus:

          (1) 16-19          27-31
          (2) 20-24          32-27
          (3) 28-32          27x20
          (4) 19-24          20x27
          (5) 32x23

and White is pinned.

With three Kings against four a player can sometimes offer
prolonged resistance. But finally the stronger player will always
be able to force an exchange which secures the victory. In the
position of Diagram 92 for instance Black will proceed as
follows:

          (1) 18-15          19-24

It would not help to play 27-24, as Black would reply 14-17 and
exchange on the next move by 10-14.

          (2) 11-16

limiting White's mobility.

          (2) ...            23-26

In answer to 24-20 Black would play 15-19.

          (3) 16-19          24-28
          (4) 14-18          26-30
          (5) 19-23          28-32
          (6) 15-19          27-31


              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | oo |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    | oo |    | ** |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    | ** |    |    | 13
       |---------------------------------------|
    12 |    |    | ** |    | ** |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+

                    3         2        1

                    DIAGRAM 92.

Not 30-25 on account of 18-22.

          (7) 10-14          31-26
          (8) 14-17          26-31
          (9) 17-22          31-27
         (10) 19-16          27-24
         (11) 16-19 and wins.

If, on the 10th move, White played 27-31 instead of 27-24, the
game might proceed as follows:

          (11) 18-15          32-28
          (12) 15-19          28-32
          (13) 22-26          31x22
          (14) 23-27          32x23
          (15) 19x17

These possibilities of exchanging "two for two" should always be
looked for as they often occur, enabling a win within a few
moves.



III

THE FIVE FUNDAMENTAL POSITIONS



While in the examples of elementary endings given in the previous
chapter, the correct method of play was comparatively easy to
find, positions with few men often occur which look very simple
but which require considerable thought to be handled in the right
way. The knowledge of these positions, of which there are five
distinctly different types, is essential for any one who desires
to become a fair player and they are, therefore, thoroughly
explained in the following five characteristic examples.


THE FIRST POSITION


It does not make any difference in the method of play whether the
Black man is located as shown in Diagram 93 or on 3, 4, 7, 8, 10,
11 16, 20 or 24. The essential point is that he must not be able
to march to the King row without being intercepted by White.

The winning maneuver is this: White turns the Black King out of
the double corner in the manner shown in the play from the
position of Diagram 89 and thereby compels the Black man to
advance, finally forcing an exchange which secures the
opposition.

          32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 | ** |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | oo |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 | ** |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

           DIAGRAM 93.--White to Move and Win.

This maneuver, as will be evident from a careful study of the
position, is possible only in case White has the move. If Black
has the move the ending is a draw.

          Black              White

          (1) ...            23-27
          (2) 28-32          19-23
          (3) 32-28

Black cannot play 12-16, as 27-24 would win a piece.

          (3) ...            27-32
          (4) 28-24

Again 12-16 is not possible on account of 32-27 winning a piece
in three moves.

          (4) ...            23-18

              32        31        30
       +---------------------------------------+
       |    | oo |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | ** |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    | oo |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |  * |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 94.

White played 32-28 Black would exchange by five 24-19 and draw
the game.

In the position of the Diagram Black has the choice between 24-
20, 12-16, 24-19 or 24-28, but he loses, no matter what move he
makes as demonstrated below.

(A)       (5) 24-20          32-27
          (6) 20-16          18-15
          (7) 16-20          15-18
          (8) 12-16          18-15

(B)       (5) 12-16          18-15

Now Black cannot play (6) 16-19 because of the exchange 32-27;
(6) 16-20 would also lose quickly through 15-18, (7) 24-19, 32-
28, (8) 19-16, 18-23. The best try is (6) 24-28.

Against 15-18 Black would now draw by (7) 16-19, 32-27; (8) 19-
23.

The only way to win is

          (6) ...            15-11

after which Black can do no better than

          (7) 16-19          32-27
          (8) 28-32          27-31
          (9) 32-28          11-16
         (10) 19-24          16-19, etc.

(C)       (5) 24-19          32-28
          (6) 12-16          28-32
          (7) 19-24          18-15

and White continues as shown before.

(D)       (5) 24-28          18-15
          (6) 28-24          32-28
          (7) 24-27          15-18
          (8) 12-16          28-32
          (9) 27-24          18-15

and wins as before by 15-18 in reply to (10) 16-20 or 15-11 in
reply to 24-28.


THE SECOND POSITION (See Diagram 95)


White's advantage is that he can crown his two men while Black
remains with only one King and two men. The reason why Black
cannot use his two men to advantage is that they are pinned on
the side of the board while White's men are located in the center
where they have much more mobility. All the same White must have
the move in order to win, just as in first position.

          Black              White

          (1)   ...          30-26
          (2)  9-14          26-23
          (3) 14-10          23-18


              32        31        30
       +---------------------------------------+
       |    |    |    |    |    | o  |    |    | 29
       |---------------------------------------|
    28 |    |    | o  |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    | oo |    | *  | 21
       |---------------------------------------|
    20 | *  |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    | ** |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

            DIAGRAM 95.--White to Move and Win.

          (4) 10-6           18-14
          (5)  6-1           14-9
          (6)  1-5            9-6
          (7)  5-9            6-2
          (8)  9-5            2-6
          (9)  5-1            6-9
          (10) 1-5            9-14
          (11) 5-1           14-18
          (12) 1-6           18-15
          (13) 6-9           15-19
          (14) 9-14          27-23
          (15) 14-10          23-18
          (16) 10-6           18-14
          (17)  6-1           14-9
          (18)  1-5            9-6
          (19)  5-9            6-2
          (20)  9-5            2-6
          (21)  5-1            6-9
          (22)  1-5            9-14
          (23)  5-1           14-18
          (24)  1-6           18-23
          (25)  6-10          23-27
          (26) 10-14          19-23
          (27) 14-10          23-18
          (28) 10-6           18-14
          (29)  6-1           14-9
          (30)  1-5           22-17

At last White has a position in which he can reduce the ending to
one of the fundamental cases by exchange.

          (31)  5-14          17-10
          (32)  21-25

It will be noticed that through the exchange Black gained to
move. White regains it by a second exchange.

          (32) ...            10-15
          (33) 25-30          15-19
          (34) 30-26          27-32
          (35) 26-22          19-24
          (36) 20-27          32-23

           and wins.

Second position as a rule results from a "Bridge position" like
the following: Black men on 20, 21, 23, Black King on 26. White
men on 30 and 32, White Kings on 15 and 19. Black to move:

          (1) 26-31          19-26
          (2) 31-22          32-27

and White wins by "second position."


THE CHANGE OF THE MOVE


By the exchanges of men in the foregoing example the move was
altered in each case. However, exchanges of pieces often occur
which do NOT change the move, and as win or loss in a great
number of endings depends upon which player has the move, it is
necessary for the beginner to obtain a clear insight into the
questions involved. An exchange always alters the move if the
capturing piece is recaptured in turn. If a different piece is
recaptured, it depends upon the relative position of the captured
pieces, whether the move has remained with the same player or
gone over to his opponent. For the purpose of calculating the
move and its changes it is useful to imagine the Checker board as
being composed of two "systems of squares"--the Black system
containing the ranks starting with the squares 1, 9, 17 and 25,
and the White system containing the other four ranks. If each of
the two systems contains an EVEN number of men, the player whose
turn to play it is, loses the opposition, that is: his opponent
has the move. If the number of men in each system is ODD, the
player whose turn to play it is, gains the opposition, that is,
he has the move. As the calculation of the move enters only into
such positions in which both players have the same number of
pieces, it is sufficient to correct the number of men in one of
the systems to obtain the desired information. Diagram 96
furnishes an example.

Counting the men of a system, the Black one, for instance, shows
their number to be odd. Therefore, the player whose turn it is to
play, has the move, which in the present instance

              32        31        30
       +---------------------------------------+
       |    |    |    | o  |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | o  |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    | o  |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |  * |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |  * |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |  * |    |    |    |
       +---------------------------------------+

                    3         2        1

                    DIAGRAM 96.

secures the win for White and a draw for Black, thus

          (A) Black to move

          Black              White

          (1)  8-11

This is apparently Black's best move; if he plays 2-7, White
replies 19-15, obtaining a very strong position.

          (1)  ...            31-26
          (2)  2-6            26-22
          (3)  6-10           22-18
          (4)  11-16           18-15
                       Draw.

         (B) White to move

          Black               White

          (1)  ...            31-26
          (2)  2-6            26-22
          (3)  8-11           24-20
          (4)  6-10           22-19
          Block.

              32        31        30
       +---------------------------------------+
       |    | o  |    |    |    |    |    |  o | 29
       |---------------------------------------|
    28 | * |     |  o |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    | *  | 5
       |---------------------------------------|
     4 | *  |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 97.

From the above explanation it is evident that in the case of an
exchange the move remains unaltered if the captured pieces were
located in the same system, and that the move changes if the
captured pieces belonged to different systems.

Exceptions to the rule sometimes occur due to a piece having no
mobility, as for instance in the position of Diagram 97 where
Black, on the move, loses because his man on 28 is blocked.


THE THIRD POSITION


              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |  o |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 | oo |    | ** |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 | oo |    | ** |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+

                    3         2        1

           DIAGRAM 98.--White to Move and Win.

White being a man ahead appears to have an easy win; but owing to
the difficulty of getting the man crowned he has a hard task
before him.

If the Kings on 11 and 12 were removed White would not be able to
win at all, as the Black King would go back and forth between 19
and 23. It is, therefore, clear that in forcing a win from the
position of the diagram the King on 12 must cooperate.

Another point to be borne in mind is that the following position
would be a draw with White to move.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |  o |    | oo |    | oo |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |    |    | ** |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    | ** |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 99.

White is unable to make any headway because he cannot threaten an
exchange. The method in which White threatens the exchange of the
King on 19 in the example of third position given in Diagram 98
is the following:

          Black               White
          (1)  ...            20-24
          (2) 11-15           24-27

12-8 would be of no use as 19-23 would force 8-12 again.

          (3) 15-11

If 15-18 White wins by 27-31

          (3)  ...            27-32

27-31 would admit of a draw by (4) 19-23, 28-24; (5) 23-27, 24-
20; (6) 27-23, 12-16; (7) 11-15, etc.

          (4) 11-15           12-8
          (5) 15-18           32-27
          (6) 18-15           27-31
          (7) 15-18            8-11
          (8) 18-23           11-7
          (9) 19-15

This is better than allowing the Kings to get together.

           (9)  ...            28-24
           (10) 23-27          24-20
           (11) 27-23           7-2
           (12) 15-11           2-6
           (13) 23-19           6-10

If he moved the other King, Black would draw by 19-16.

           (14) 19-23          10-14
           (15) 23-19

Black would lose easily if he allowed the man to advance

           (15) ...            14-18

Threatening to exchange

           (16) 19-24

The only move to avoid the exchange.

           (16) ...            18-23
           (17) 24-28          23-19
           (18) 28-32          31-26
           (19) 32-28          26-23
           (20) 28-32          23-18
           (21) 32-28          19-15
           (22) 11-8           20-16

and White cannot be prevented from getting another King.

An earlier setting of third position is shown in Diagram 100.

              32        31        30
       +---------------------------------------+
       |    |  o |    |    |    |  o |    |    | 29
       |---------------------------------------|
    28 |    |    |  * |    |  * |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 100.

White wins by

          (1)  ...            19-24
          (2) 27-31           32-28
          (3) 23-27           30-23
          (4) 27-32           23-18
          (5) 32-27           24-20
          (6) 27-23           19-15, etc.


THE FOURTH POSITION


Although White is a piece ahead he has great difficulties in
winning on account of the weak position of the man on 12. Black's
man on 3 holds

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    | oo |    |    | 13
       |---------------------------------------|
    12 |  o |    | oo |    | oo |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |  * |    | ** |    | ** |    |
       +---------------------------------------+
                    3         2        1

          DIAGRAM 101.--White to Move and Win.

him in check without being impaired in his effectiveness towards
the center of the board. If Black had the move, White could not
win at all, as he would be unable to dislodge Black's Kings. As
it is, he wins by means of a sacrifice which often occurs in
endings with 4 Kings against 3.

          Black               White

          (1)  ...            14-9
          (2)  1-5             9-13
          (3)  5-1            11-15
          (4)  2-6            10-14
          (5)  1-5            15-18
          (6)  5-1

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    | oo |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    | oo |    | oo | 13
       |---------------------------------------|
    12 |  o |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    | ** |    |    | 5
       |---------------------------------------|
     4 |    |    |  * |    |    |    | ** |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 102.

It would not help Black to play 6-2 on account of 13-9; (7) 5-1,
9-5; (8) 2-6, 14-17; (9) 6-2, 17-13; (10) 2-6, 18-15; (11) 6-2,
15-10, etc.

          (6)  ...           14-9
          (7)  6-2            9-5
          (8)  2-6          18-15
          (9)  6-2          15-10

This is the important move, which forces the win.

         (10)  2-6

If 2-7, White exchanges by 13-9

         (10)  ...         10-7

Only with this pretty sacrifice can White win the game. After
(11) 3-10 White plays 5-9 and should Black answer (12) 6-2, White
would get "two for one" by 9-6. Therefore, Black can do no better
than play (12) 10-15, 9-2; (13) 15-19, etc., and get a King in
each double corner. White then wins as explained in the chapter
on elementary endings.

Fourth position results in a draw only when the man is held on 12
or 21, according to whether the weaker side is Black or White. In
third position it is useless to hold the man on the above
squares, but sometimes a draw is obtained by holding him on 20 or
13.

In defending a game with two Kings against two Kings and a man,
the weaker side must have the move in the system in which the man
is pinned. The following position for instance is drawn with
White on the move.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    | oo |    |
       |---------------------------------------|
       |    |    |    |    |    | oo |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    | ** |    |  * | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    | ** |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 103.

Black, on the move, would win by (1) 13-17, 22-13; (2) 14-9.

In Diagram 104 the drawing move is 27-31. The game ought to run
like this:

          (2) 20-24          23-27
          (3) 24-28          27-32
          (4) 30-26          31-27
          (5) 22-18          27-24

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    | ** |    |    | 29
       |---------------------------------------|
    28 |    |    | oo |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | oo |    | ** |    |    | 21
       |---------------------------------------|
    20 |  * |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 104.--WHITE TO MOVE.

          (6) 26-23          24-20

and White moves back and forth between 24 and 20. In the position
of Diagram 105 White draws by:

          (1) ...            23-19
          (2) 28-32          19-24
          (3)  7-2           24-19
          (4)  2-6           19-24
          (5)  6-9           24-19
          (6)  9-14          19-24
          (7) 14-17          15-19

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 | ** |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | oo |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | oo |    |    |    |    | 13
       |---------------------------------------|
    12 |  * |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | ** |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 105.--WHITE TO MOVE.

Changing the guard

           (8) 17-22          19-23

and Black can make no progress.


THE FIFTH POSITION


White is on the move, and it is evident that he loses if he moves
the man on 27 permitting black to reply 11-15. The only way to
save the game is to sacrifice the man on 20 by 20-16. The
following play would ensue.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |  o |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |  o |    |  o | 21
       |---------------------------------------|
    20 |  o |    |  o |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |  * |    |  * | 13
       |---------------------------------------|
    12 |  * |    |  * |    |  * |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                DIAGRAM 106.

          (2) 11-2O          27-23
          (3) 20-24          22-18
          (4) 24-27          18-9
          (5) 10-14

Preventing 23-18

          (5)  ...            9-6
          (6) 27-31           6-2K
          (7) 31-27           2-6

White cannot save the piece and so he runs his opponent.

          (8) 27-18           6-9
          (9) 13-17           19-15
         (10) 18-11           9-18
         (11) 17-22           18-25
         (12) 11-15           25-22

Drawn. White would lose by 21-17, as after (13) 15-18, 17-13;
(14) 18-14, 25-22; (15) 12-16 he cannot gain the double corner.

The following has been suggested as a suitable problem to be
called SIXTH POSITION.

             32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | oo |    |    |    |    |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | o  |    | ** |    |    |    |    | 13
       |---------------------------------------|
    12 |  o |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | ** |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |  * |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

       DIAGRAM 107.--BLACK TO MOVE AND WHITE TO DRAW.

Black plays

         (1) 7-2

threatening (2) 3-7 and (3) 15-11.   White can prevent this only
by

         (1) ...          24-20

Now 3-7 would only draw on account of 16-11.

         (2) 2-6          20-24
         (3) 6-10         24-20

Again 3-7 had to be prevented.

         (4) 10-14        20-24
         (5) 14-17        24-27

This time 24-20 would have lost, as Black would have replied (6)
17-13, 20-24; (7) 3-7, 12-8; (8) 15-11.

         (6) 17-13        27-32

Avoiding 27-24 which would lose by (7) 3-7

         (7) 13-9         32-27
         (8) 9-14         27-24
         (9) 14-18        24-27

Drawn. White has to watch 3-7 and to take care to play 24-20 at
the right time so as to exchange 16-11 if 3-7 is played. At the
same time he must beware of playing 24-20 when the Black Kings
are on squares 15 and 5 or 15 and 13, as otherwise Black would
reply 5-9, 20-24; 3-7, 12-8; 15-11.



IV

GENERAL PRINCIPLES AND ILLUSTRATIVE GAMES



It is possible to apply general strategic principles to the game
of Checkers, just as well as the game of Chess, even though there
is not the scope in Checkers for strategic maneuvers on the grand
scale on which they can be carried out in Chess.

Again it is naturally the principle of greatest mobility which
should govern the plan of mobilization in any opening, and it is
consequently more desirable to have the men work in the center of
the board, than on the edge, where part of their range is cut
off.

The advantage of center squares over side squares is not so
marked in Checkers as it is in Chess. There is no doubt that a
piece has more mobility in the center, where there are two or
four moves to choose from, than on the side where only one or two
moves are possible; but a man on the side has an advantage in so
far as he is backed up by the edge of the board so that he is
safe from being captured until he moves. However, a player who
keeps his men in massed formation in the center will in almost
all cases be able to make them protect each other and to win the
upper hand against an opponent whose army is divided into two
parts, one on the left and the other on the right side of the
board.

When playing with the white men, it is advisable to occupy such
squares as 14, 18, 19, 30, 31 and 32, and it is not advisable to
occupy 5 and 12 whenever the opponent has a man on 1 or 3
respectively, as in that case the men have a tendency to act as
supports for the enemy instead of helping their own side. In the
position: Black 1, 7 and 9; White 5, 14, 18 and 22; for instance,
White's man on 5 supports Black's man on 9 and White, on the
move, has to surrender a piece by 22-17, to which Black replies
9-13.

It is naturally a good thing not to touch the men of the back row
mentioned above, as they will prevent the opponent from getting
Kings. White's man 29 and Black's man 4, however, are better off
in the middle of the board, as the squares 25 and 8 are
adequately guarded by 30 and 3 respectively. Moreover, there is
danger of the first position arising from openings in which a
player keeps his man in the single corner.

A formation which very often occurs in the middle game is the so-
called "elbow." It consists of three men arranged like the white
pieces in Diagram 108.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    | o  |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    | o  |    |    |    |    | 21
       |---------------------------------------|
    20 | *  |    |  o |    |    |    |    |    |
       |---------------------------------------|
       |    |  * |    |    |    |    |    |    | 13
       |---------------------------------------|
    12 | *  |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 108.

When adequately supported an elbow forms a solid position which
cannot easily be attacked. An example of a strong elbow will be
found in the following game:

              32        31        30
       +---------------------------------------+
       |    |  o |    |    |    |  o |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |  o |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |  o | 21
       |---------------------------------------|
    20 |    |    |  o |    |    |    |  o |    |
       |---------------------------------------|
       |    |    |    |    |    |  * |    |  o | 13
       |---------------------------------------|
    12 |  * |    |  * |    |  * |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |  * |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    | *  |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 109.

          Black               White

          (1) 10-15           23-19
          (2) 6-10            22-17
          (3) 1-6             25-22
          (4) 11-16           17-13
          (5) 16-23           26-19
          (6) 7-11            29-25
          (7) 11-16           22-17
          (8) 16-23           27-11
          (9) 8-15            24-19
         (10) 15-24           28-19
         (11) 4-8             25-22
         (12) 8-11            31-26
         (13) 3-7             22-18
         (14) 9-14            18-9
         (15) 5-14

The men on 6, 10, 13, 14, 17 and 21 form the elbow, the strength
of which becomes apparent on the 19th move.

         (15) ...             26-23
         (16) 11-15           32-28
         (17) 15-24           28-19
         (18) 7-11            30-26
         (19) 2-7             19-16
         (20) 12-19           23-16
         (21) 11-20           26-23
         (22) 7-11 and wins.

The danger involved in an elbow, which is not sufficiently backed
up, is shown in the following game.

          Black               White

          (1) 10-15           23-19
          (2) 7-10            22-17
          (3) 3-7             25-22
          (4) 9-14            29-25
          (5) 5-9             17-13
          (6) 1-5             22-17
          (7) 11-16           26-22
          (8) 16-23           27-11
          (9) 7-l6            31-26
         (10) 8-11            24-19
         (11) 16-23           26-19
         (12) 11-15           30-26

and White wins through the threat to get two for one by 19-15
after the exchange. Black cannot help the loss of a man.

The reader, who has thoroughly acquainted himself with the
fundamental endings, will have no difficulty in playing a good
game of checkers, if he follows at every move the general
principles discussed in this chapter. When playing over the
countless variations, which are offered in the majority of
checker books, he would find that they are merely illustrations
of the application of those principles to the various openings.

Following are two examples from master play, the careful study of
which will do more good to the student than the perusal of a
great number of games that lack adequate annotation.

          Black               White

         (1)  9-14

The best opening move is probably 11-15, as this enables a speedy
development of the man on 4, who, as previously explained, should
not be kept in the back row. The variations resulting from 11-15
have been so thoroughly analyzed that it is practically
impossible to defeat a player who chooses this opening and knows
the possible variations by heart. It has, therefore, been found
necessary to restrict the players in matches and tournaments by
balloting the first move of Black and White, in order to avoid
too many draws. This is a serious drawback, as it curtails the
freedom of decision, to which a player should be entitled in any
game.

          (1) ...             22-17
          (2) 11-15

It is hard to tell whether this move of 11-16 or 5-9 is the best.
6-9 and 10-15 are considered weak.

          (2) ...             25-22

More aggressive than 23-19, which can safely be played.

          (3) 15-19

8-11 or 17-13 or 23-19 are also good moves.

          Black               White

         (3) ...              24-15
         (4) 10-19            23-16
         (5) 12-19            17-1O
         (6) 6-15             21-17
         (7) 5-9              29-25
         (8) 8-12             25-21
         (9) 7-10             17-13
        (10) 1-6


              32        31        30
       +---------------------------------------+
       |    |  o |    |  o |    |  o |    |    | 29
       |---------------------------------------|
    28 |  o |    |  o |    |  o |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |  o |    |  o | 21
       |---------------------------------------|
    20 |    |    |  * |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |    |    |  o | 13
       |---------------------------------------|
    12 |  * |    |    |    |  * |    |  * |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |  * |    |  * |    |  * |    |  * |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 110.

At first sight, it might seem unwise to break up the King row,
when 9-14 could be played; but the advantage of holding the man
on 13, instead of allowing him to complicate matters by 13-9,
more than counterbalances the disadvantage of moving a back man.
Black could also play (10) 2-6, but this admits of the following
strong attack: (10) 2-6, 27-23; (11) 4-8, 23-16; (12) 12-19, 32-
27; (13) 9-14, 27-24; (14) 3-7 (8-12 would lose), 22-17; (15) 14-
18 (again 8-12 would lose), 17-14; (16) 10-17, 21-14; (17) 1-5,
31-27; (18) 6-10, 24-20; (19) 10-17, 26-22; (20) 18-25, 30-14;
(21) 7-11 (Probably the only move to draw--8-12 would lose on
account of 20-16).

          Black               White

          (10) ...            27-24
          (11) 4-8            32-27

22-18 could also be played.

          (12) 9-14           27-23

or 22-17 or 24-20.

          (13) 3-7            23-16
          (14) 12-19          22-17
          (15) 7-11           26-23

31-27 would lose through (16) 8-12, 26-22; (17) 11-16, 24-20;
(18) 19-24, 20-11; (19) 24-31, 11-8; (20) 14-18.

              32        31        30
       +---------------------------------------+
       |    |    |    |  o |    |  o |    |    | 29
       |---------------------------------------|
    28 |  o |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |  o |    |  o |    |    |    |  o | 21
       |---------------------------------------|
    20 |    |    |  * |    |    |    |  o |    |
       |---------------------------------------|
       |    |    |    |  * |    |  * |    |  o | 13
       |---------------------------------------|
    12 |    |    |  * |    |  * |    |    |    |
       |---------------------------------------|
       |    |  * |    |    |    |  * |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |  * |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 111.

          (16) 19-26          30-23
          (17)  8-12          24-20
          (18) 15-18          23-19

20-16 cannot be played on account of (19) 20-27, 16-7; (20) 2-11,
31-24; (21) 12-16.

           (19) 11-15          20-16

White can, of course, draw here by 31-26; but 20-16 also draws in
spite of Black's seemingly invincible elbow.

           Black              White

          (20) 15-24          28-19
          (21) 2-7            31-26
          (22) 18-23

If 18-22, White draws by 19-15; (23) 12-19, 13-9.

          (22) ...            26-22


              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |  o |    |  o | 21
       |---------------------------------------|
    20 |    |    |  o |    |    |    |  o |    |
       |---------------------------------------|
       |    |  o |    |    |    |  * |    |  o | 13
       |---------------------------------------|
    12 |  * |    |    |    |  * |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |  * |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 112.

Playing for a brilliant finish. He could also draw by 16-11; (23)
7-16, 26-22; (24) 14-18, 22-15; (25) 23-26, 17-14.

          Black               White

          (23) 23-27          16-11
          (24) 7-23           22-18

Drawing, although two men down.

The following game illustrates first position:

          Black               White

          (1) 11-15           22-18

This move is not considered as strong as 23-19.

          (2) 15-22           25-18
          (3) 8-11

12-16 can also be played.

          (3) ...             29-25
          (4) 4-8             25-22

24-20 is another good move.

          (5) 12-16

If 10-15, White obtains a strong game by 23-19.

          (5) ...             24-20

Considered best. 24-19 or 22-17 are also playable.

          (6) 8-12

He could lay a trap by (6) 10-15. If White replies 27-24 or 28-
24, Black wins by (7) 15-19. 24-15; (8) 16-19, 23-16; (9) 9-14.

          Black               White

          (6) ...             27-24
          (7) 10-14           24-19

              32        31        30
       +---------------------------------------+
       |    |    |    |  o |    |  o |    |    | 29
       |---------------------------------------|
    28 |  o |    |    |    |  o |    |    |    |
       |---------------------------------------|
       |    |  o |    |  o |    |    |    |  o | 21
       |---------------------------------------|
    20 |  o |    |  o |    |  o |    |    |    |
       |---------------------------------------|
       |    |  * |    |    |    |  * |    |  * | 13
       |---------------------------------------|
    12 |  * |    |  * |    |  * |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |  * |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |  * |    |  * |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 113.

In answer to 31-27, Black would win by (8) 7-10, 24-19; (9) 9-13,
18-9; (10) 5-14, 28-24; (11) 13-17, 22-13; (12) 3-7 or (10) ...,
27-24; (11) 1-5, 22-18; (12) 3-7.

         (8) 7-10             28-24

32-27 or 19-15 are considered stronger.

         (9) 3-7              32-28

This loses. The only drawing move is 30-25.

         Black               White

         (10) 9-13           18-9
         (11) 5-14           22-18


              32        31        30
       +---------------------------------------+
       |    |    |    |  o |    |  o |    |    | 29
       |---------------------------------------|
    28 |  o |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |  o |    |  o |    |  o |    |    | 21
       |---------------------------------------|
    20 |  o |    |  o |    |    |    |  * |    |
       |---------------------------------------|
       |    |  * |    |    |    |    |    |  * | 13
       |---------------------------------------|
    12 |  * |    |  * |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |  * |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |  * |    |  * |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 114.

Four variations are possible here. If 31-27 or 30-25, Black wins
by (12) 13-17, 22-13; (13) 14-18, etc. (11) ..., 22-17 loses on
account of (12) 13-22, 26-17; (13) 14-18. The sacrifice (11) ...,
21-17; (12) 14-21, 22-18 is met by (13) 10-14, 18-9; (14) 1-5,
26-22; (15) 5-14, 31-26; (16) 13-17.

          Black               White

          (12) 13-17          18-9
          (13)  6-13          21-14
          (14) 10-17          26-22

In answer to 30-25 Black wins by (15) 7-10, 25-22; (16) 2-6; but
with 31-27 White can offer prolonged resistance, thus:

              32        31        30
       +---------------------------------------+
       |    |  o |    |  o |    |  o |    |    | 29
       |---------------------------------------|
    28 |  o |    |    |    |  o |    |    |    |
       |---------------------------------------|
       |    |    |    |  o |    |  o |    |  o | 21
       |---------------------------------------|
    20 |  o |    |  o |    |  o |    |    |    |
       |---------------------------------------|
       |    |  * |    |    |    |  * |    |    | 13
       |---------------------------------------|
    12 |  * |    |  * |    |    |    |  * |    |
       |---------------------------------------|
       |    |    |    |  * |    |  * |    |  * | 5
       |---------------------------------------|
     4 |    |    |  * |    |  * |    |  * |    |
       +---------------------------------------+
                    3         2         1

                    DIAGRAM 115.

(14) ..., 31-27; (15) 17-22, 26-17; (16) 13-22, 19-15; (17) 11-
18, 23-14; (18) 1-6, 20-11; (19) 7-16, 27-23; (20) 16-19, 23-16;
(21) 12-19, 24-15; (22) 6-10, 15-6; (23) 2-18, 28-24; (24) 18-23,
24-19; (25) 23-27, 19-15; (26) 27-32. 15-10; (27) 32-27, 10-6;
(28) 27-23, 6-1; (29) 22-26, 1-6; (30) 26-31, 6-9; (31) 30-26, 9-
13; (32) 26-22, 13-9; (33) 23-18. Black has now received first
position and wins.

          Black               White

          (15) 17-26          31-22
          (16) 7-10           30-25
          (17) 2-6            25-21
          (18) 6-9            22-18
          (19) 1-5            18-15

White must give up a piece to get through, and Black can then
exchange at his leisure and win without difficulty.

          (20) 11-27, etc.



V

PROBLEMS



Checker problems, unlike the Chess problems, are intimately
related to the game itself and do not enable combinations
different in kind from those which occur in the actual fight over
the board.

         PROBLEM No. 1. WHITE TO MOVE AND DRAW.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    |    | 29
       |---------------------------------------|
    28 |    |    | o  |    |    |    |    |    |
       |---------------------------------------|
       |    | o  |    |    |    |    |    | o  | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | *  |    |    |    |    |    |  * | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    |    | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 116.

They usually represent an end game and are distinguished from
ordinary endings only by an unexpected initial move, mostly
embodying a sacrifice of several men. Diagrams 116, 117 and 118
furnish some examples:

         PROBLEM No. 2. WHITE TO MOVE AND WIN.

              32        31        30
       +---------------------------------------+
       |    |    |    |    |    |    |    | ** | 29
       |---------------------------------------|
    28 |    |    |    |    |    |    |    |    |
       |---------------------------------------|
       |    | oo |    |  o |    | o  |    |    | 21
       |---------------------------------------|
    20 |    |    |    |    |    |    | o  |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    | *  | 13
       |---------------------------------------|
    12 |    |    |    |    |    |    | *  |    |
       |---------------------------------------|
       |    |    |    |    |    |    |    | *  | 5
       |---------------------------------------|
     4 |    |    |    |    |    |    |    |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 117.

If, in Diagram 116, White tried to reach the King row with his
man 27, Black would win by first position thus: (1) . . ., 27-23,
(2) 16-20, 24-19; (3) 20-24, 19-15; (4) 24-27, 23-19; (5) 27-24,
19-16; (6) 24-19, etc. The only way to draw is to sacrifice first
the man on 21 by 21-17; and then to continue as above. This
enables White to play 23-18, instead of 19-15, exchanging the
King for a man.

The first move in Diagram 117 is 24-28, to which Black must reply
(2) 29-25. White then sacrifices his three men by 17-14 and after
(3) 25-27 (or 9-27) plays 28-32. Black must take the third man,
and White recaptures two men by 32-14, pinning both of the
remaining black men.

         PROBLEM No. 3. BLACK TO PLAY AND WIN.

              32        31        30
       +---------------------------------------+
       |    | o  |    |    |    | o  |    |  o | 29
       |---------------------------------------|
    28 |  o |    | o  |    |  o |    |    |    |
       |---------------------------------------|
       |    |    |    | o  |    | o  |    | *  | 21
       |---------------------------------------|
    20 | *  |    |    |    | o  |    | *  |    |
       |---------------------------------------|
       |    | *  |    | o  |    |    |    | o  | 13
       |---------------------------------------|
    12 |  o |    | *  |    |    |    | *  |    |
       |---------------------------------------|
       |    | *  |    |    |    | *  |    | *  | 5
       |---------------------------------------|
     4 |    |    |  * |    |  * |    | *  |    |
       +---------------------------------------+
                    3         2        1

                    DIAGRAM 118.

This is the longest stroke known to have occurred in actual play.
The game from which the above position arose went as follows:

              Black         White

          (1) 12-16         21-17
          (2) 16-20         17-13
          (3) 10-14         23-19
          (4) 14-17         19-16
          (5) 17-21         16-12
          (6) 11-16         22-18
          (7) 8-11          25-22
          (8) 7-10          26-23
          (9) 10-14         24-19
         (10) 14-17         31-26
         (11) 4-8           19-15

Now the position of the diagram is reached, in which Black wins
by

         (12) 21-25         30-14
         (13) 16-19         23-7
         (14) 3-19          12-3
         (15) 19-24         28-19
         (16) 2-7           3-10
         (17) 6-31          13-6
         (18) 1-17          22-13
         (19) 31-15

Completing a stroke, which removes 18 pieces from the board.

         (19)  ...          32-27
         (20) 15-10         29-25
         (21) 5-9

To get the move

         (21)  ...          13-6
         (22) 10-1          25-22
         (23) 1-6           22-18
         (24) 6-10          27-23
         (25) 20-24         23-19
         (26) 24-27         18-15
         (27) 10-7          19-16
         (28) 27-31         15-11
         (29) 7-3           16-2
         (30) 31-27         11-8
         (31) 27-24         8-4
         (32) 24-19         4-8
         (33) 19-15         8-4
         (34) 15-11 and wins.