Bishop and knight checkmate

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This article uses algebraic notation to describe chess moves.

The bishop and knight checkmate in chess is the checkmate of a lone king which can be forced by a bishop, knight, and king. With perfect play, checkmate can be forced in at most thirty-three moves from any starting position where the defender cannot immediately win one of the pieces (Müller & Lamprecht 2001:19), and the position is not in the "stalemate trap" (see below). Although this is classified as one of the four "basic checkmates" (the others being king and queen; king and rook; or king and two bishops against a lone king), it only occurs in practice approximately once in every 5000 games (Müller & Lamprecht 2001).

Contents 1 Technique 2 Example of "W manoeuvre" from a game 3 Example from grandmaster game 4 A stalemate trap 5 Quotations 6 See also 7 Notes 8 References 9 External links

[edit] Technique

Since checkmate can only be forced in the corner of the same colour as the squares on which the bishop moves, 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. Thus there are three phases in the checkmating process (Müller & Lamprecht 2001:18):

1. Driving the opposing king to the edge of the board by using all three pieces.
2. Forcing the king out of the "wrong" corner to the "right" corner, if necessary.
3. Delivering the checkmate.

The position on the right is one that typically arises after the first phase has been completed and the defender has headed to a corner of opposite colour to that of the bishop. The following method to push the king to the "right" corner is commonly given (Müller & Lamprecht 2001:18, Dvoretsky 2006:279):

1.Nf7+

First White forces the king to leave the corner. The white bishop is positioned so that the next two moves, gaining control of g8, are possible.

1...Kg8 2.Bf5

A waiting move, forcing Black's king to move so White can play 3.Bh7, taking away g8 from the king.

2...Kf8 3.Bh7 Ke8 4.Ne5

The key to the standard winning method is the Nf7-e5-d7-c5-b7 movement of the knight, forming a "W" shape. Now there are two possible defenses:

A: 4...Kf8 Black clings to the "safe" corner, but loses more quickly.

5.Nd7+ Ke8 6.Ke6 Kd8 7.Kd6 Ke8 8.Bg6+ Kd8 9.Bf7 Kc8 10.Nc5 (continuing the knight's manoeuvre) 10...Kd8 11.Nb7+ Kc8 12.Kc6 Kb8 13.Kb6 (now the king is in the right position, a knight's move from the mating corner) 13...Kc8 14.Be6+ Kb8 15.Bd7 (now the defending king is confined to the right corner, and checkmate can be given) 15...Ka8 16.Nc5 Kb8 17.Na6+ Ka8 18.Bc6#

B: 4...Kd8 Here, the defending king tries to break out from the edge. This holds out longer.

5.Ke6 Kc7 6.Nd7! White continues the knight's "W" manoeuvre, even though Black's king has temporarily left the back rank. 6...Kc6 7.Bd3!

Black'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. 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).

7...Kc7

At this point two ways of continuing are possible. One is to continue the "W" manoeuvre of the knight, by bringing it to c5 and b7. Müller & Lamprecht (2001:19) give 8.Be4 Kd8 9.Kd6 Ke8 10.Bg6+ Kd8 11.Bf7 Kc8 12.Nc5 Kd8 13.Nb7+ Kc8 14.Kc6 Kb8 15.Kb6 Kc8 16.Be6+ Kb8 17.Nc5 Ka8 18.Bd7 Kb8 19.Na6+ Ka8 20.Bc6#.

Alternatively, Dvoretsky (2006:279) gives 8.Bb5 Kd8 9.Nf6 Kc7 10.Nd5+ Kd8, reaching the following position:

This bishop and knight configuration (right) is a very important position, and can also be reached if the defender's king does not head for the "wrong" corner from the attacker's point of view.

11.Kf7 Kc8 12.Ke7 Kb7 (12...Kb8 13.Ba6! Ka7 14.Bc8 Kb8 15.Kd7 as in the main variation) 13.Kd7 Kb8 (13...Ka7 14.Kc7 Ka8 15.Ne7 Ka7 16.Nc8+ Ka8 17.Bc6#; 13...Ka8 14.Kc8 Ka7 15.Kc7 is just a move slower) 14.Ba6 Ka7 15.Bc8 Kb8 16.Kd8 Ka8 (16...Ka7 17.Kc7 Ka8 18.Ne7 Ka7 19.Nc6+ Ka8 20.Bb7#)17.Kc7 Ka7 18.Ne7 Ka8 19.Bb7+ Ka7 20.Nc6#.

[edit] Example of "W manoeuvre" from a game

This game between Mika Karttunen and Vitezslav Rasik ^[1]shows the knight's "W manoeuvre". The game continued:

84. Bc5 Kb7 85. Nd5 Kb8 86. Kc6 Ka8 87. Nc7+ Kb8 88. Bd4 Kc8 89. Ba7 Kd8 90. Nd5 Ke8 91. Kd6 Kf7 92. Ne7 Kf6 93. Be3 Kf7 94. Bd4 Ke8 95. Ke6 Kd8 96. Bb6+ Ke8 97. Nf5 Kf8 98. Bc7 Ke8 99. Ng7+ Kf8 100. Kf6 Kg8 101. Bd6 Kh7 102. Nf5 Kg8 103. Kg6 Kh8 104. Bc5 1-0 (Müller & Pajeken 2008:106-7).

Checkmate follows after 104... Kg8, 105. Nh6+ Kh8 106. Bd4#, the position at the top of the article.

[edit] Example from grandmaster game

This position is from the blindfold game between Ljubomir Ljubojević and Judit Polgár, Monaco Amber 1994.^[2] Polgár did not use the standard method, but nevertheless coordinated the pieces effectively. Play continued: 84.Kd6 Kf6 85.Kc5 Ke5 86.Kc4 Bd5+ 87.Kd3 Nf4+ 88.Ke3 (White can resist about seven moves longer by 88. Kc3) Be4 89.Kd2 Kd4 90.Kc1 Kc3 91.Kd1 Bc2+ 92.Ke1 Kd3 93.Kf2 Ke4 94.Kg3 Bd1 95.Kf2 Nd3+ 96.Kg3 Ke3 97.Kh4 Kf4 98.Kh3 Ne1 99.Kh4 Ng2+ 100.Kh3 Kf3 101.Kh2 Kf2 102.Kh3 Be2 103.Kh2 Bg4 104.Kh1 Ne3 105.Kh2 Nf1+ 106.Kh1 Bf3# 0-1

[edit] A stalemate trap

A surprising stalemate trap, not mentioned in endgame treatises, was used 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. This stalemate occurs at the climax of a study by A. H. Branton, second prize, New Statesman, 1966 (Roycroft 1972:246), though it may have been known even earlier. The position at right would also be drawn if the knight were at a7 or e7 instead. Also, 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 (see Two knights endgame). Rhine later used this discovery as the basis for a "White to play and draw" composition.

Instead of 1...Nb6+??, Black would win quickly by means of the quadrant trap by playing 1...Ne3, e.g. 2.Kd8 Bb5 3.Kc8 Nd5.

[edit] Quotations

• "... I have seen how many chessplayers, including very strong ones, either missed learning this technique at an appropriate time or had already forgotten it." – Mark Dvoretsky (Dvoretsky 2006:279)

• "Bishop and knight [checkmate] might never occur in your whole chess lifetime and is far too difficult to waste your precious study time on." – Jeremy Silman (Silman 2007:33)

[edit] See also

• Checkmate
• Pawnless chess endgames

[edit] Notes

[edit] References

• Dvoretsky, Mark (2006), Dvoretsky's Endgame Manual (second ed.), Russell Enterprises, ISBN 1-888690-28-3 
• Müller, Karsten & Lamprecht, Frank (2001), Fundamental Chess Endings, Gambit Publications, ISBN 1-901983-53-6 
• Müller, Karsten & Pajeken, Wolfgang (2008), How to Play Chess Endings, Gambit Publications, ISBN 978-1-904600-86-2 
• Roycroft, John (1972), Test Tube Chess, London: Faber and Faber, ISBN 0-571-09573-9 
• Silman, Jeremy (2007), Silman's Complete Endgame Course: From Beginner to Master, Siles Press, ISBN 1-890085-10-3 

[edit] External links

• Video explaining the bishop and knight checkmate
• Interactive bishop and knight checkmate practice