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.
Game Over
Sun, Dec 7, 2008
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