Chess and Checkers : the Way to Mastership

by Edward Lasker

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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8 | | | | | | | | |
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7 | | | | | | | | |
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6 | | | | | | | | |
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5 | | | | | | | | |
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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 | |
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3 | ^Kt| #P | | | | | | |
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2 | | | #P | | | | | |
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1 | | | | | | | | |
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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.