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The bishop and knight checkmate in chess
Chess

Chess is a recreational and competitive game played between two Player . Sometimes called Western chess or international chess to distinguish it from History of chess and other chess variants, the current form of the game emerged in Southern Europe during the second half of the 15th century after evolving from similar, much older...
 is the checkmate
Checkmate

Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured....
 of a lone
Bare king

In chess and related games, a bare king is a situation in which one player has only the king left on the board, while the fifteen other pieces and pawns have been captured....
 king
King (chess)

In chess, the King is the most important chess piece. The object of the game is to trap the opponent's king so that he would not be able to avoid capture ....
 which can be forced by a bishop
Bishop

A bishop is an ordination or consecration member of the Clergy#Christian clergy who is generally entrusted with a position of authority and oversight....
, knight
Knight

File:Gothic armor 2.jpgKnight is the term for a social position originating in the Middle Ages. In the Commonwealth of Nations, knighthood is a non-heritable form of gentry....
, and king.






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The bishop and knight checkmate in chess
Chess

Chess is a recreational and competitive game played between two Player . Sometimes called Western chess or international chess to distinguish it from History of chess and other chess variants, the current form of the game emerged in Southern Europe during the second half of the 15th century after evolving from similar, much older...
 is the checkmate
Checkmate

Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured....
 of a lone
Bare king

In chess and related games, a bare king is a situation in which one player has only the king left on the board, while the fifteen other pieces and pawns have been captured....
 king
King (chess)

In chess, the King is the most important chess piece. The object of the game is to trap the opponent's king so that he would not be able to avoid capture ....
 which can be forced by a bishop
Bishop

A bishop is an ordination or consecration member of the Clergy#Christian clergy who is generally entrusted with a position of authority and oversight....
, knight
Knight

File:Gothic armor 2.jpgKnight is the term for a social position originating in the Middle Ages. In the Commonwealth of Nations, knighthood is a non-heritable form of gentry....
, 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 , 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
Queen (chess)

The queen is the most powerful chess piece in the game of chess. Each player starts the game with one queen, placed in the middle of their first rank next to their King ....
; king and rook
Rook (chess)

A rook is a chess piece in the strategy board game of chess. In the past the piece was called the castle, tower, marquess, rector, and comes , and non-players still often call it a "castle"....
; or king and two bishops against a lone king), it only occurs in practice approximately once in every 5000 games .

A method for checkmate using the "W" method was given by Philidor
François-André Danican Philidor

Fran?ois-Andr? Danican Philidor was a France chess player and composer. He was regarded as the best single chess player of his age , although the title of World Chess Champion was not yet in existence....
 in famous 1749 treatise. Another method is known as Deletang's Method or Deletang's Triangles , involving confining the lone king in a series of three shrinking isosceles right-angled triangles, with the "right" corner at the right angle. It was published by Daniel Deletang in 1923. His method takes five to ten moves longer than Philidor's but there are fewer rules. His "second triangle" or "middle triangle" comes up in the more standard methods (see below).

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 :

  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 ():

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. 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#.

Deletang's second triangle


Alternatively, 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 (aka Deletang's second triangle).

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! (or, Deletang's third triangle) 14...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#.

Example of "W manoeuvre" from a game


This game between Mika Karttunen and Vitezslav Rasik 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 .
Checkmate follows after 104... Kg8, 105. Nh6+ Kh8 106. Bd4#, the position at the top of the article.

Example from grandmaster game


This position is from the blindfold
Blindfold chess

Blindfold chess is a way to play chess, whereby play is conducted without the players having sight of the positions of the pieces, or any physical contact with them....
 game between Ljubomir Ljubojevic
Ljubomir Ljubojevic

Ljubomir Ljubojevic is a Grandmaster of chess. He was born on November 2 1950 in U?ice, Yugoslavia, now Serbia. He was awarded the International Master title in 1970 and the GM title in 1971....
 and Judit Polgár
Judit Polgár

Judit Polg?r is a Hungary chess Grandmaster . She is by far the strongest female chessplayer in history. In 1991, she achieved the title of International Grandmaster at the age of 15 years and 4 months....
, Monaco Amber 1994. 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

Game where a grandmaster failed to mate



In this game between two grandmasters, both players made suboptimal moves, but the superior side had no idea how to win and ended up stalemating several moves after the inferior side could have claimed a draw under the fifty-move rule.

Robert Kempinski
Robert Kempinski

Robert Kempinski is a Poland chess Grandmaster . At the age of 14 he won the Polish junior championship in his age category, and the year after that he won the Polish junior championship for U20....
 (2498) - Vladimir Epishin
Vladimir Epishin

Vladimir Epishin is a Russian chess International Grandmaster with an Elo-rating of 2587. He was one of the assistants to Anatoly Karpov during the late stages of Karpov's career ....
 (2567) [E60] Bundesliga
Chess Bundesliga

The term Chess Bundesliga , normally refers to the premier league of team chess in Germany. It is arguably the strongest and longest running league of its kind, attracting many top grandmasters from Europe and beyond....
 0001 Germany (5.3), 07.01.2001

1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.e3 0-0 5.b4 b6 6.Bb2 d6 7.Be2 c5 8.b5 Bb7 9.0-0 e6 10.Nbd2 Nbd7 11.a4 a5 12.bxa6 Rxa6 13.Qc2 Ra8 14.Rfc1 Re8 15.Ne1 cxd4 16.exd4 e5 17.d5 Nc5 18.Nd3 Nxd3 19.Bxd3 Rc8 20.Qb1 Ba6 21.Bf1 Bh6 22.Bc3 Rc5 23.Qb2 Bc8 24.Re1 Bf5 25.a5 bxa5 26.Nb3 Rc8 27.Nxa5 Bd7 28.Bb4 Bf8 29.Qa3 Ra8 30.Qc3 Qb6 31.g3 Reb8 32.Reb1 Qc7 33.Qe1 Bf5 34.Rb2 Bd7 35.h3 Rb6 36.Bc3 Rxb2 37.Bxb2 h5 38.Bg2 Qc5 39.Bc3 Rb8 40.Rb1 Rxb1 41.Qxb1 Bf5 42.Qb4 Qc8 43.h4 Be4 44.Bd2 Qg4 45.Qb3 Qe2 46.Qe3 Qd1+ 47.Qe1 Qc2 48.f3 Bd3 49.Qc1 Qa2 50.Qc3 e4 51.Nb3 Bg7 52.fxe4 Qb1+ 53.Nc1 Nxe4 54.Qxd3 Qxd3 55.Nxd3 Nxd2 56.c5 Bd4+ 57.Kh2 Bxc5 58.Kh3 Be3 59.g4 hxg4+ 60.Kxg4 Kg7 61.Kg3 Kh6 62.Bh3 f5 63.Bg2 Bd4 64.Kh3 Kg7 65.Ne1 Bf2 66.Nf3 Nc4 67.Ng5 Kf6 68.Nh7+ Kg7 69.Ng5 Ne5 70.Bf1 Be3 71.Ne6+ Kf6 72.Be2 Bf2 73.Ng5 Be3 74.Ne6 Bh6 75.Nd4 Bc1 76.Kg3 Bd2 77.Kh3 Be3 78.Nc6 Nd7 79.Bf3 Bf2 80.Nd8 Nc5 81.Bg2 Be1 82.Bf3 Ba5 83.Nc6 Bb6 84.Kg3 Nb3 85.Bg2 Nd2 86.Bh1 Nf1+ 87.Kh3 Bc5 88.Bf3 Nd2 89.Bg2 Bf2 90.Nd8 Nc4 91.Nc6 Ne3 92.Bf3 Be1 93.Bh1 Nd1 94.Bf3 Nf2+ 95.Kg2 Nd3 96.h5 g5 97.Bd1 Nf4+ 98.Kf1 Bc3 99.h6 Nxd5 100.Bb3 Ne3+ 101.Ke2 f4 102.Kd3 Bb2 103.h7 Kg7 104.Bg8 Bf6 105.Ke4 d5+ 106.Kf3 Kh8 107.Nb4 d4 108.Nd3 Nf5 109.Ke4 Ne7 110.Bc4 Kxh7 111.Nxf4 gxf4 112.Kxf4 Kg7 113.Kg4 Nc6 114.Kf5 Bh4 115.Ke4 Bf2 116.Bb5 Nb4 117.Bc4 Kf6 118.Be2 Ke6 119.Bc4+ Kd6 120.Be2 Kc5 121.Bf1 Nc6 122.Be2 Kb4 123.Bf1 Kc3 124.Bb5 Nb4 125.Bf1 d3 126.Bxd3 Nxd3 (see diagram at left) 127.Kf3 Bc5 128.Ke4 Kc4 129.Kf5 Kd5 130.Kf6 Bd6 131.Kf7 Ne5+ 132.Ke8 Ke6 133.Kd8 Nf7+ 134.Kc8 Kd5 135.Kb7 Kc5 136.Ka6 Bc7 137.Kb7 Kd6 138.Ka6 Kc6 139.Ka7 Nd6 140.Ka8 (see diagram at right) Bd8? 140...Nc4 141.Ka7 Nb6 142.Ka6 Bb8 is the standard win. 141.Ka7 Kb5 142.Kb8 Kb6 143.Ka8 Nb7 144.Kb8 Bc7+ 145.Ka8 Kc6 146.Ka7 Nc5 147.Ka8 Nd7 148.Ka7 Nb6 149.Ka6 Bb8! Reaching the same position Black could have forced earlier (see previous note). 150.Ka5 Kc5? 150...Nd5 is the standard win. 151.Ka6 Bd6? 152.Kb7 Kb5 153.Ka7 Kc6 154.Ka6 Bb8! Reaching the same position as after Black's 149th move. 155.Ka5 Nd5! Belatedly finding the winning move he missed five moves ago. 156.Ka6 Objectively best was 151.Ka4. Bc7? Missing the standard 156...Nb4+. 157.Ka7 Bb6+ 158.Kb8 Bc5 159.Ka8 Nc7+ 160.Kb8 Nb5 161.Ka8 Kb6 162.Kb8 Na7 163.Ka8 Ka6 164.Kb8 Bb6 165.Ka8 Nb5 166.Kb8 Nd6 167.Ka8 Kb5 168.Kb8 Kc6 169.Ka8 Bc7 170.Ka7 Nb7 171.Ka8 Nc5 172.Ka7 Bb6+ 173.Ka8 Bc7 174.Ka7 Nd7 175.Ka8 Bd6 176.Ka7 Nb6 177.Ka6 Bb8 178.Ka5 Bc7 179.Ka6 Nc8 stalemate ½-½

After the basic king, bishop, and knight versus king position arrived, White was kind enough to allow his king to retreat to the last rank in only six moves. But Black seemed to try to mate White in the wrong corner. Black eventually found the standard winning line, up to a point, but then failed to find 156... Nb4+ and instead tried again to mate in the wrong corner.

A stalemate trap



A surprising stalemate trap, not mentioned in endgame treatises, was noted by the American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 master
Chess master

A chess master is a chess player of such skill that he/she can usually beat chess experts, who themselves typically can nearly always prevail against most amateurs....
 Frederick Rhine in 2000 and published in Larry Evans
Larry Evans

For the football player of the same name, see Larry Evans .Larry Melvyn Evans is an United States chess Grandmaster and journalist. He won or co-won the U.S....
' "What's the Best Move?" column in Chess Life
Chess Life

Chess Life is a monthly chess magazine published in the United States. The official publication of the United States Chess Federation , it reaches more than a quarter of a million readers every month....
 magazine. In the position at left, after 1...Nb6+?? 2.Kb7?? Nd5, Black would be well on his way to setting up Deletang's second triangle. 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
Stalemate

Stalemate is a situation in chess where the player whose turn it is to move is not in check but has no legal moves. One of the rules of chess is that stalemate ends the game, with the result a draw ....
. 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
Stalemate

Stalemate is a situation in chess where the player whose turn it is to move is not in check but has no legal moves. One of the rules of chess is that stalemate ends the game, with the result a draw ....
. A stalemate idea essentially identical to that shown in the diagram at right occurs at the climax of a study by A. H. Branton, second prize, New Statesman, 1966 (White: king on c1; Black: king on c3, knight on a3, bishop on d1), though it may have been known even earlier.

From the diagram position at left, instead of 1...Nb6+??, Black would win quickly by setting up Deletang's second triangle via the alternate route 1...Ne3, e.g. 2.Kd8 Bb5 3.Kc8 Nd5.

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


  • "Some masters have already gone back home red with embarrassment after failing or showing poor technique in the execution of this checkmate." – Jesus de la Villa


  • "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


See also

  • Checkmate
    Checkmate

    Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured....
  • Pawnless chess endgames
    Pawnless chess endgames

    Pawnless chess endgames are chess Chess endgame in which only a few chess piece remain, and none of them are pawn . The basic checkmates are a type of pawnless endgame....


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