Fundamental Endings
Considering that the object of the game is to capture the opposing King, it seems most important to find out whether there are positions in which this capture can be accomplished in spite of the best possible defense. Naturally, a player must have a material superiority to be able to force a mate, and the first question is what minimum force is required to force the surrender of a King whose men have all been captured during the game.
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 a corner of the board because there he has only three squares to go to while in the middle of the board he can move to eight squares. 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.
This can be done easily with the King and Queen, or with the King and Rook. Suppose White has his King on c3 and his Queen on h3 while Black's King stands on d6 as shown in the following diagram.
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 not advisable since the Queen would not be protected on these squares and the King could simply capture her. A long range attack from h2, g3, d3 or h6 is not effective either because it would not restrict the mobility of the King who could go to either d5, 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. Look at 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 that 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. Then Black could not move the King to b5 since this square is controlled by White's King, and he could not go to any of the other four squares in his range because 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 the above diagram, 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 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 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#
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. 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, because 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.
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. The following diagram is an example of such a case.
White plays 1. N-c5 K-h1 2. N-e4. Now Black can not continue with h2 since White would checkmate with N-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. N-d2 (not N-g3, which would stalemate Black's King), K-h1 4. N-f1. The only move left for Black is now h2, and White mates by 5. N-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. N-c5 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. Suppose 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 is not difficult.
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 the above diagram, 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
K-b2 instead of K-c2 would stalemate Black's King
11. ... K-a3
12. B-b5 K-a2
13. B-c1 K-a1
14. B-b2 K-a2
15. B-c4#
In the ending 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. The following diagram will 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 not go into the corner since N-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 that the Knight can not be placed so it controls the square c8, forcing the King into the corner, and to threaten the mate on b6 at the same time. He can only control c8 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. N-f4
Black's King is confined to the seventh and eighth ranks and it is only a matter of time before he will be forced to h8. Because White's Bishop is only capable of commanding black squares, the Knight will have to be used to drive the King from white squares. For instance:
3. ... K-c8
4. K-c6 K-d8
5. N-g6 K-c8
6. N-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 to make d8 inaccessible to Black.
9. ... K-e8
10. B-c7 K-f8
11. N-f5 K-e8
12. N-g7 K-f8
13. K-f6 K-g8
14. K-g6 K-f8
15. B-d6 K-g8
16. N-f5 K-h8
17. B-a3
Again a waiting move. White can not play N-h6 right away because Black would be stalemate.
17. ... K-g8
18. N-h6 K-h8
19. B-b2#
It is not possible to force a mate with King and two Knights because even if a position similar to the above 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. N-a6 K-a8
2. N-e8 pawn moves
3. N-c7#
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