(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
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
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Black would not have been able to occupy this favorable square with his Bishop, had not White withdrawn his Knight from d4.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
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
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
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.
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
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.
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
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.
+———————————————————-+ | | 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 | | +———————————————————-+
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
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.
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
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
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
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
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
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.
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.
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
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
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."
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
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 18-15Draw.
(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
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.
32 31 30+———————————————————-+| | | | | | | | | 29|———————————————————-|28 | o | | | | | | | ||———————————————————-|| | | | | | | | | 21|———————————————————-|20 | oo | | ** | | | | | ||———————————————————-|| | | | | | | | | 13|———————————————————-|12 | oo | | ** | | | | | ||———————————————————-|| | | | | | | | | 5|———————————————————-|4 | | | | | | | | |+———————————————————-+