From Wikipedia, the free encyclopedia
- This article uses algebraic notation to describe chess moves.
In chess, the bishop and knight checkmate is a procedure to checkmate a lone king with a bishop, knight, and king. It can only be forced in the corner of the same square as the bishop. An opponent who is aware of this will try to stay first in the center of the board, and then in the wrong-colored corner. The basic technique is in three parts:
- Limit the opposing king to one section of the board.
- Force the king out of the wrong-colored corner without losing containment.
- Deliver the checkmate.
But to do this, the attacking side needs to have a good grasp about how the pieces work together.
[edit] How the pieces work together
[edit] How the enemy king can be forced back (two examples)
- Left: The kings are in opposition, and the bishop is between them (the knight's position makes no difference).
- Right The kings are in opposition, and the bishop and knight control the squares to the side of the defending king.
In both cases, if the enemy king is to move, it must retreat. If the attacking side is to move, then it should make a waiting move to force the enemy king to move and thus retreat.
[edit] How minor pieces can form a barrier
- Left: When the bishop and knight are on the same colored squares, they complement each other and control the maximum number of squares and make a barrier against the enemy king (marked by X).
- Right A position sometimes known as the Quadrant Trap, where the bishop and knight confine the defending king to a few squares around the mating corner, even without their king. See below for the continuation, where mate follows on move ten at the latest once the king arrives.
[edit] Attacking side's first ideal position in the centre
The attacking side should head for a position like the diagram (or variants based on symmetry), and with the bishop and knight are on the same colored squares, Note the barrier against the enemy king (marked by X). The defender is already restricted to moving away from the center.
If Black is to play, one line is:
- ...Bd3 (often if the attacker's pieces are placed optimally, the best continuation is to "lose a move" with the bishop, using zugzwang to force the defending king to retreat)
- Kf6 Kd5
- Kf7 (the defending king must retreat still further towards the edge, and should head towards the "safe" corner, of the opposite color to square the bishop controls. Here Kg5 Ke5 and the defender is being pushed into the mating corner.) Ke5
- Kg7 Ke6 (now the king must retire to the back rank)
- Kh8 Kf6
- Kg8 Ne5
- Kh8 (now the defending king is in the "safe" corner. Note how none of the attacker's moves were check. The next section explains how to drive the king out of his safe corner.
[edit] Driving the king from the "safe" corner to the mating corner
Step two is the difficult part.
Assuming a starting position with the king in the wrong-colored corner, as below:
Black to move.
- ... Nf7+
- Kg8 Bf5 (Again a "tempo move" or "losing a move" to force White to move again. .. Be4 or c2 are just as good)
- Kf8 Bh7
- Ke8 Ne5
Now there are two possible defenses:
[edit] "Passive defense"
- Kf8 (diagram right; clinging to the "safe" corner, but loses more quickly. In the winning manoeuver, there is a sequence of two moves with the knight, two moves with the king, then two moves with the bishop; and the knight and bishop move like the letter "W".) Nd7+
- Ke8 (the knight has moved twice, so now it is the king's turn) Ke6
- Kd8 (The white king is forced to the mating corner) Kd6 (equally good is heading for the Quadrant Trap by ...Bd3 4. Ke8 Bb5 5. Kd8 Nf6-d5)
- Ke8 (now it is the bishop's turn to make two moves, and note the "W" pattern) Bg6+
- Kd8 Bf7
- Kc8 (Now it is the knight's turn, and continues the W pattern) Nc5
- Kd8 Nb7+
- Kc8 Kc6 (king's turn)
- Kb8 Kb6 (now the king is in the right position, a knight's move from the mating corner)
- Kc8 Be6+ (bishop's turn)
- Kb8 Bd7 (now the defending king is confined, and it is time to move in for the checkmate)
[edit] Finishing off in the "passive defence"
- Ka8 Nc5
- Kb8 Na6+
- Ka8 Bc6#
[edit] "Active defense"
Here, the defending king tries to break out from the edge. This holds out longer.
- Kd8 Ke6
- Kc7 Nd7!
- This is the key move. The common mistake is to try to keep opponent's king on the back rank; the Black player is often afraid that allowing opponent's king off the back rank is letting him loose. But in fact it's impossible to confine opponent to the back rank with just bishop and knight; you have to let him "out". But you only let him out into a restricted area that you create with your next move.
- Kc6
3... Bd3!
-
- This gives the goal position:
White's king is now restricted to the correct-colored corner. The perimeter is bounded by a6, b6, b5, c5, d5, d6, d7, e7, f7, f8 as shown at right. Black's subsequent moves tighten this area further. Bb5 closes off c6; redeploying the knight to f6 and then to d5 closes off d7 (and e8 by the bishop).
- Kc7 Bb5
- Kd8 Nf6
- If White instead moved to b7, Black immediately closes off c7 by Kd6. But the remaining play will be similar.
- Kc7 Nd5+
- Kd8
[edit] Quadrant trap
This bishop and knight configuration (right) is a very important position, sometimes called the quadrant trap (see also above). Once the king arrives, mate should follow on the ninth or tenth move at the latest.
- ... Kf7
- Kc8 Ke7
- Kb7 (Kb8 then ... Ba6! 4 Ka7 Bc8 5. Kb8 Kd7/d8 as in the main variation) Kd7
- Kb8 (Ka7 loses faster to ... Kc7 5. Ka8 Ne7 6. Ka7 Nc8+ 7. Ka8 Bc6#; 4. Ka8 Kc8 5. Ka7 Kc7 is just a move slower) Ba6! (confining the king even further)
- Ka7 Bc8
- Kb8 Kd8
- Ka8 (Ka7 Kc7 8. Ka8 Ne7 9. Ka7 Nc6+ 10. Ka8 Bb7#) Kc7
- Ka7 Ne7 and mate in two moves.
[edit] Finishing off quadrant trap
- 9. Ka8 Bb7+
- 10. Ka7 Nc6#
[edit] A stalemate trap
|
|
| Draw! Note that the position would also be drawn if the knight were at a7 or e7 and/or if a second knight were added at (for example) c5. |
A surprising stalemate trap, not mentioned in endgame treatises, was discovered by the American master Frederick Rhine in 2000. In the position at left, after 1...Nb6+?? 2.Kb7?? Nd5, Black would be well on his way to setting up the quadrant trap. However, White draws instantly with 2.Kd8! (position at right), when the only way for Black to save his bishop is to move it, resulting in stalemate. The position at right would also be drawn if the knight were at a7 or e7 instead. Incredibly, if in any of these positions a second knight was added on any square where it does not already guard the bishop (c5, for example), Black still could not win, since if he sacrificed the bishop the two knights would be insufficient to force checkmate. Rhine later used this discovery as the basis for a "White to play and draw" composition.
