Books: Chess and Checkers: The Way to Mastership
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Edward Lasker >> Chess and Checkers: The Way to Mastership
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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.
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6 | ^Kt| | | | | | | |
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4 | | | | | | | | |
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3 | | | | | | | | #P |
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2 | | | | | | ^K | | #K |
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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.
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8 | #K | | | | | | | |
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4 | | | | | | | | |
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3 | | | | | | | | |
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2 | | | | | | | | |
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1 | ^K | ^B | ^B | | | | | |
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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.
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8 | | #K | | | | | | |
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7 | | | | | | | | |
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6 | ^K | | | | | | | |
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5 | | | | ^Kt| | | | |
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4 | | | | | | | | |
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3 | | | ^B | | | | | |
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2 | | | | | | | | |
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1 | | | | | | | | |
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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)
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8 | | #K | | | | | | |
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7 | | | | | | | | |
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6 | | ^K | | ^Kt| | | | |
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5 | | | ^Kt| | | | | |
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4 | | | | | | | | |
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3 | | | | | | | | |
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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.
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4 | #Q | | | | ^P | | | |
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3 | | #K | | | | | | |
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2 | | | | | | | | |
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1 | | | ^Q | | | | ^K | |
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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.
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8 | | | | | | | | |
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7 | | | | | #K | | | |
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6 | | | | | | | | |
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5 | | | | | | ^K | | |
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4 | | | | | ^P | | | |
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3 | | | | | | | | |
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2 | | | | | | | | |
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1 | | | | | | | | |
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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.
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8 | | | | | | | | |
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7 | | | | | | | | |
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6 | | | | | | |#P | |
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5 | | | #K | | | #P | | |
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4 | | | | | | | | |
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3 | | ^P | | | | ^P | | |
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2 | | | ^K | | | | ^P | |
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1 | | | | | | | | |
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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.
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8 | | | | | | | | |
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7 | | #P | | | | | | |
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6 | | | | | | | | |
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5 | | #R | | | | #P | | #K |
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4 | | ^P | | | | ^K | #P | ^P |
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3 | | | ^P | | | | ^P | |
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2 | | | | | ^R | | | |
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1 | | | | | | | | |
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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.
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8 | | | | | | | | |
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7 | #P | #P | #P | | | | | |
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6 | | | | | | | #P | #K |
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5 | | | | | | | | |
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4 | #B | | | | | ^K | ^P | |
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3 | | | | ^Kt| | | | |
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2 | ^P | ^P | | | ^B | | | |
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1 | | | | | | | | |
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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.
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8 | | | | | | | | |
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7 | | | | | | | #P | |
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6 | | | | | #B | | | #K |
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5 | ^P | | | | | | | |
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4 | | ^Kt| | | | ^K | ^P | |
|---------------------------------------|
3 | ^Kt| #P | | | | | | |
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2 | | | #P | | | | | |
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1 | | | | | | | | |
+---------------------------------------+
a b c d e f g h
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