Expert: Satyajit Das - 1/2/2008

Question
Is checkmate possible if I have two bishops and a king and the opponent is have only king.

Is check mate possible if I have two knights and a king  and the opponent is have only king.


Answer
Hi Babu,

Thanks for the question.

Checkmate is possible with two bishops and the king against a king. However checkmate is not possible with two knights and the king against a king.

Let me explain the two situations a bit more clearer..

1. Let's first check out the two bishops mate.

 It is not too difficult for two bishops to force checkmate, with the aid of their king. Two principles apply:

a) The bishops are best when they are near the center of the board and on adjacent diagonals. This cuts off the opposing king.
b) The king must be used aggressively, in conjunction with the bishops.

Let me give you a situation: WHITE:Kd1,Bc1,f1   BLACK:Kd4
White to move. (Here are the moves, you can try them at a chess board)
1. Ke2 Ke4 (Black tries to keep his king near the center)
2. Be3 Ke5 (forcing the king back, which is done often)
3. Kd3 Kd5
4. Bd4 Ke6
5. Ke4 Kd6 (Black tries a different approach to stay near the center)
6. Bc4 (White has a fine position. The bishops are centralized and the king is active.
6... Kc6 (Black avoids going toward the side)
7. Ke5 Kd7 (Black is trying to avoid the a8 corner)
8. Bd5 (keeping the black king off c6)
8... Kc7
9. Bc5 Kd7
10. Bd6! (an important move that forces the king to the edge of the board)
10... Ke8 (Black is still avoiding the corner)
11. Ke6 (now the black king can't get off the edge of the board)
11... Kd8
12. Bc6 (forcing the king toward the corner)
12... Kc8 (Black's king is confined to c8 and d8. The white king must cover a7 and b7)
13. Kd5 (13. Ke7? is stalemate)
13...Kd8
14. Kc5 Kc8
15. Kb6 Kd8 (Now White must allow the king to move into the corner)
16. Bc5 Kc8
17. Be7! (an important move that forces the king toward the corner)
17... Kb8
18. Bd7! (the same principle as the previous move)
18... Ka8
19. Bd8 (White must make a move that gives up a tempo. This move is one, along with Bc5, Bf8, Be6, or Ka6.)
19... Kb8
20. Bc7+ Ka8
21. Bc6#

2. Now let's try to see the two knight mate case.

It is impossible to force checkmate with a king and two knights, although checkmate possitions are possible. e.g. WHITE: Kf7,Nf6,g6   BLACK: Kh8.

Let's see a situation here where mate can be done but the opponent always has anathor move possible by which he can escape his mate.
e.g. WHITE: Kb6,Na6,b5   BLACK: Kb8
If Black plays 1... Ka8? White can checkmate with 2. Nbc7#, but Black can play 1... Kc8 and escape the threat. The defender's task is easy — he simply has to avoid moving into a position in which he can be checkmated on the next move, and he always has another move available in such situations

Satyajit Das
INDIA