The bishop and knight checkmate in chess

Chess

Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

 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 that player's fifteen other pieces have been captured....

 king

King (chess)

In chess, the king is the most important piece. The object of the game is to trap the opponent's king so that its escape is not possible . If a player's king is threatened with capture, it is said to be in check, and the player must remove the threat of capture on the next move. If this cannot be...

 which can be forced by a bishop

Bishop

A bishop is an ordained or consecrated member of the Christian clergy who is generally entrusted with a position of authority and oversight. Within the Catholic Church, Eastern Orthodox, Oriental Orthodox Churches, in the Assyrian Church of the East, in the Independent Catholic Churches, and in the...

, knight

Knight

A knight was a member of a class of lower nobility in the High Middle Ages.By the Late Middle Ages, the rank had become associated with the ideals of chivalry, a code of conduct for the perfect courtly Christian warrior....

, and king. With the stronger side to move and with perfect play, checkmate can be forced in at most thirty-three moves from any starting position where the defender cannot quickly win one of the pieces , , and the position is not in the "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. A stalemate ends the game in a draw. Stalemate is covered in the rules of chess....

 trap" (see below). Checkmate can be forced only with the defending king in a corner controlled by the bishop or on a square on the edge next to such a corner. 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 piece in the game of chess, able to move any number of squares vertically, horizontally, or diagonally. Each player starts the game with one queen, placed in the middle of the first rank next to the king. With the chessboard oriented correctly, the white queen starts...

; king and rook

Rook (chess)

A rook is a piece in the strategy board game of chess. Formerly the piece was called the castle, tower, marquess, rector, and comes...

; or king and two bishops against a lone king), it only occurs in practice approximately once in every 5000 games .

History and methods

A method for checkmate using the "W" method was given by
Philidor

François-André Danican Philidor

François-André Danican Philidor , often referred to as André Danican Philidor during his lifetime, was a French composer and chess player. He contributed to the early development of the opéra comique...

 in his famous 1749 treatise, Analyse du jeu des Échecs. 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 90-degree angle of the triangle. Some of the ideas of this method date back to 1780 but the complete system was first published in 1923 by Daniel Deletang . This method takes five to ten more moves than Philidor's W method but there are fewer rules and it can still be accomplished before the fifty move rule

Fifty move rule

The fifty-move rule in chess states that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves . The intended reason for the rule is so that a player with no chance to win cannot be obstinate and play on indefinitely , or seek a win...

 takes effect. His "second triangle" or "middle triangle" comes up in the more standard methods (see below). Checkmate can be forced without strictly using either of the methods. Incidentally, checkmate can be delivered in 460 different ways (positions) .

Importance

Opinions differ as to whether or not a player should learn this checkmate procedure. James Howell omits the checkmate with two bishops in his book because it rarely occurs but includes the bishop and knight checkmate. Howell says that he has had it three times (always on the defending side) and that it occurs more often than the checkmate with two bishops . On the other hand, Jeremy Silman

Jeremy Silman

Jeremy Silman is an American International Master of chess. He has won the US Open, the American Open, and the National Open, and was the coach of the US junior national chess team...

 includes the checkmate with two bishops but not the bishop plus knight checkmate because he has encountered the latter only once and his friend John Watson

John L. Watson

John Leonard Watson is a chess International Master and author.Watson was born in Milwaukee and grew up in Omaha, Nebraska. He was educated at Brownell-Talbot, Harvard, and the University of California at San Diego, where he took his degree in engineering...

 has never encountered it . Silman says

"...mastering it would take a significant chunk of time. Should the chess hopeful really spend many of his precious hours he's put aside for chess study learning an endgame he will achieve (at most) only once or twice in his lifetime?"

Andy Soltis says that he has never played this endgame and most players will never have it in their career. However, learning it teaches techniques that can be applied elsewhere .

Although king, bishop and knight versus king may never be encountered in the careers of many chessplayers, a notable example of it occurring in an important occasion was in Tal Shaked

Tal Shaked

Tal Shaked is an American chess grandmaster, who is best known for winning the World Junior Championship in 1997....

's victory over Alexander Morozevich

Alexander Morozevich

Alexander Morozevich is a Russian chess Grandmaster. In the November 2011 FIDE list, he had an Elo rating of 2762, making him the 9th-highest rated player in the world, although he has previously ranked as high as second, in the July 2008 list....

 in the penultimate round of the 1997 World Junior Chess Championship

World Junior Chess Championship

The World Junior Chess Championship is an under-20 chess tournament organized by the World Chess Federation ....

. Shaked knew the correct mating pattern; and his victory catapulted him to becoming World Junior Champion, whereas a draw

Draw (chess)

In chess, a draw is when a game ends in a tie. It is one of the possible outcomes of a game, along with a win for White and a win for Black . Usually, in tournaments a draw is worth a half point to each player, while a win is worth one point to the victor and none to the loser.For the most part,...

 would have prevented him from winning the title.

Standard "W" manoeuvre

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:

Defense 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#

Defense 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. White'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.
Continue the W manoeuvre

One continuation from the position after Black's seventh move 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# (the first checkmate diagram).
Deletang's second triangle


Alternatively, from the position after Black's seventh move, gives 8.Bb5 Kd8 9.Nf6 Kc7 10.Nd5+ Kd8, reaching this position. This bishop and knight configuration (right) is a very important position which can also be reached if the defender's king does not head for the "wrong" corner from the attacker's point of view (also known as Deletang's second triangle). Now 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# (the second checkmate position)

Deletang's triangle method

Deletang's Triangle Method produces checkmate by confining the king in successively smaller areas. In the first set of three diagrams, the king is confined inside the marked area and a corner in which the checkmate can occur is in the area. The king cannot escape the area nor attack the bishop or knight. The second set of three diagrams shows the triangles and how the bishop controls the hypotenuse

Hypotenuse

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the...

 of the triangle .
In the first net all three pieces are required to confine the king. In the second net only the bishop and knight are needed. In the third net, the king and bishop confine the king, allowing the knight to either checkmate or assist in the checkmate . The winning procedure consists of making the king move so that the bishop can reach the hypotenuse of the next smaller triangle .

Starting from the position of the first triangle, White wins:

1. Bc2 (to push the king toward the corner

1... Ke3 (the king stays as close to the middle as possible)

2. Kc1 (plan is to guard e2, probably from d1)

2... Ke2

3. Bg6 (a waiting move)

3... Ke3

4. Kd1 (guarding e2)

4... Kf2

5. Kd2 Kf3

6. Kd3 (still guarding e2)

6... Kg4

7. Ke3 Kh4 (preventing the bishop from going to h5)

8. Kf4 Kh3

9. Bh5! (the bishop is on the hypotenuse of the second triangle)

9... Kg2

10. Nc5 Kf2

11. Ne4+ Kg2

12. Bg4 (the second net)

12... Kf1

13. Kf3 Ke1

14. Ke3 Kf1

15. Kd2 Kg2

16. Ke2 Kg1

17. Bh3! (the hypotenuse of the third triangle)

17... Kh2

18. Bf1 Kg1

19. Ng5 (preparing to guard h2)

19... Kh1

20. Kf2 Kh2

21. Nf3+ Kh1

22. Bg2# .

The "W manoeuvre"

This game between Mika Karttunen

Mika Karttunen

Mika Karttunen is a Finnish chess player, International Master.-Chess career:He won the Finnish Championship in 2002, 2006, 2007, 2009 and 2010...

 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#.

Grandmaster game, neither technique

This position is from the blindfold

Blindfold chess

Blindfold chess is a form of chess play wherein the players do not see the positions of the pieces or touch them. This forces players to maintain a mental model of the positions of the pieces...

 game between Ljubomir Ljubojević

Ljubomir Ljubojevic

Ljubomir Ljubojević is a Grandmaster of chess. He was born on November 2, 1950, in Titovo Užice, Yugoslavia . Ljubojević was awarded the International Master title in 1970 and the GM title in 1971. He was Yugoslav champion in 1977 and 1982. He won the 1974 Canadian Open Chess Championship...

 and Judit Polgár

Judit Polgár

Judit Polgár is a Hungarian chess grandmaster. She is by far the strongest female chess player in history. In 1991, Polgár achieved the title of Grandmaster at the age of 15 years and 4 months, the youngest person ever to do so at that time.Polgár was ranked No...

, 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

Grandmaster failed to mate

In this game between two grandmasters, both players made suboptimal moves. The superior side had no idea how to win and ended up stalemating

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. A stalemate ends the game in a draw. Stalemate is covered in the rules of chess....

 several moves after the inferior side could have claimed a draw under the fifty-move rule.

Robert Kempinski

Robert Kempinski

Robert Kempiński is a Polish 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. In the following years he represented Poland in international competitions...

 (2498) - Vladimir Epishin

Vladimir Epishin

Vladimir Epishin is a Russian chess grandmaster with an Elo-rating of 2610.He finished third in the 58th USSR Chess Championship...

 (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

(Diagrammed position on 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 constitutional republic comprising fifty states and a federal district...

 master

Chess master

A chess master is a chess player of such skill that he/she can usually beat chess experts, who themselves typically prevail against most amateurs. Among chess players, the term is often abbreviated to master, the meaning being clear from context....

 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 was an American chess grandmaster, author, and journalist. He won or shared the U.S. Chess Championship five times and the U.S. Open Chess Championship four times...

' "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. A subscription to Chess Life is one of the benefits of Full Adult, Youth, or Life membership in...

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. A stalemate ends the game in a draw. Stalemate is covered in the rules of chess....

. 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. 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

External links

There is a bishop and knight checkmate in a game between V.Ivanchuk and A.Morozevich in the last round of a tournament at Reggio Emilia

Reggio Emilia

Reggio Emilia is an affluent city in northern Italy, in the Emilia-Romagna region. It has about 170,000 inhabitants and is the main comune of the Province of Reggio Emilia....

on 6 January 2011: http://www.chess.co.uk/twic/chessnews/events/53rd-reggio-emilia-2010-11/gashimov-wins-reggio-on-tie-break-from-vallejo (last-but-one game on page), http://www.chessgames.com/perl/chesslike.pl?gid=1602817 (click on text "Vassily Ivanchuk vs Alexander Morozevich" to get animated board-display version).

External links

• Video explaining the bishop and knight checkmate
• Video by Majnu Michaud explaining the bishop and knight checkmate using Deletang's triangles
• Interactive bishop and knight checkmate practice