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Encyclopedia > Zugzwang

Zugzwang (German for "compulsion to move", IPA: [ˈtsuːk.tsvaŋ]) is a term used in combinatorial game theory and in other types of games (particularly in chess). Zugzwang means that one player is put at a disadvantage because he has to make a move — the player would like to pass and make no move. The fact that the player must make a move means that his position will be significantly weaker than the hypothetical one in which it is his opponent's turn to move. In combinatorial game theory, it means that it directly changes the outcome of the game from a win to a loss. The term is used less precisely in other games. Not to be confused with the NATO phonetic alphabet, which has also informally been called the â€œInternational Phonetic Alphabetâ€. For information on how to read IPA transcriptions of English words, see IPA chart for English. ... Mathematicians playing Konane at a Combinatorial game theory workshop (for technical content, see external link) This article is on the theory of combinatorial games. ... Chess is a recreational and competitive game for two players. ...

The term is frequently used in chess, to mean that one player (having the move) has no move that does not worsen their position (Soltis 2003:78). Game theory does not apply directly to chess (Berlekamp, et al. 1982:16) (Elkies 1996:136). Sometimes different chess authors use the term zugzwang in different ways (Flear 2004:11-12). In some literature a reciprocal zugzwang (see below) is called zugzwang and a one-sided zugzwang is called a squeeze (Hooper and Whyld 1992). Chess is a recreational and competitive game for two players. ...

In a chess endgame, being in zugzwang usually means going from a drawn position to a loss or a won position to a draw, but it can be from a win to a loss, or a substantial loss of material which probably affects the outcome of the game. A chess position of reciprocal zugzwang or mutual zugzwang is equivalent to the more precise definition of zugzwang in game theory. Opposition is a special kind of zugzwang (Flear 2000:36). Trébuchet is a special type of zugzwang that is discussed below. In chess, the endgame (or end game or ending) refers to the stage of the game when there are few pieces left on the board. ... In chess, a draw is one of the possible outcomes of a game, the others being a win for white and a win for black. ... // Definition Diagram 1. ...

## Zugzwang in chess GA_googleFillSlot("encyclopedia_square");

Black to move is in zugzwang, and loses (Flear 2004, page 11).

Zugzwang most often occurs in the endgame when the number of pieces, and so the number of possible moves, is reduced, and the exact move chosen is often critical. The first diagram gives a simple example. If it is Black's move, he gets to a lost position (the white king gets to either the c5 or e5 square and wins one or more pawns and can advance his own pawn toward promotion). If it is White's move, there is no zugzwang (Flear 2004:11-12). The squares d4 and d6 are corresponding squares. Whenever the white king is on d4 with White to move, the black king must be on d6 to prevent the advance of the white king. In many cases, the player having the move can put the other player in zugzwang by using triangulation. Zugzwang is very common in king and pawn endgames, where it is frequently achieved through triangulation. In chess, the endgame (or end game or ending) refers to the stage of the game when there are few pieces left on the board. ... Staunton chess pieces, left to right: pawn, rook, knight, bishop, queen, and king. ... Initial placement of the pawns. ... Promotion is a chess term describing the transformation of a pawn that reaches the eighth square into the players choice of a queen, knight, bishop, or rook. ... Corresponding squares in chess are squares of reciprocal (or mutual) zugzwang. ... Triangulation is a tactic used in chess endgames to put ones opponent in zugzwang. ...

Pieces other than the king can also triangulate to achieve zugzwang — e.g., see the queen versus rook position at Philidor position. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies. Philidors position is an important chess endgame. ... Excelsior by Sam Loyd. ... Richard RÃ©ti Neueste Schachnachrichten, 1922 White to play and draw. ...

### Examples from actual play

Here are some examples of zugzwang from actual games.

#### Fischer-Taimanov, 1971, second match game

Fischer-Taimanov, 1971, after 85. Bf5. Black is in zugzwang.

• 85... Nf3
• 86. h6 Ng5
• 87. Kg6

and Black is again in zugzwang. The game ended shortly (because the pawn will slip through and promote) (Kasparov 2004:385): Promotion is a chess term describing the transformation of a pawn that reaches the eighth square into the players choice of a queen, knight, bishop, or rook. ... Zugzwang (German for compulsion to move, IPA: ) is a term used in combinatorial game theory and in other types of games (particularly in chess). ...

• 87... Nf3
• 88. h7 Ne5+
• 89. Kf6 1-0.

#### Fischer-Taimanov, 1971, fourth match game

Fischer-Taimanov, 1971, fourth match game, after 57. Ka6

• 57... Nc8
• 58. Bd5 Ne7
• 59. Bc4! Nc6
• 60. Bf7 Ne7

Now the bishop is able to make a tempo move. It is able to move while still attacking the pawn on g6, and preventing the black king from moving to c6. In chess, tempo refers to the time taken by a move. ...

• 61. Be8

and Black is in zugzwang. The knight is unable to make a tempo move; moving it would allow the bishop to capture the kingside pawns. The black king must give way. This page explains commonly used terms in chess in alphabetical order. ...

• 61... Kd8
• 62. Bxg6! Nxg6
• 63. Kxb6 Kd7
• 64. Kxc5

and White has a won position. Either one of White's queenside pawns will promote or the white king will attack and win the black kingside pawns and a kingside pawn will promote. Black resigned seven moves later (Silman 2007:516-17). This page explains commonly used terms in chess in alphabetical order. ... Zugzwang (German for compulsion to move, IPA: ) is a term used in combinatorial game theory and in other types of games (particularly in chess). ...

### Reciprocal zugzwang

Reciprocal zugzwang or mutual zugzwang: White to move draws, Black to move loses

#### Trébuchet

Trébuchet (extreme mutual zugzwang), whoever moves loses. From Flear 2004, page 13.

White to move. Black wins by reaching a trébuchet. From Silman, page 98.

• 1. Kxh6 Kxc3
• 2. Kg5 Kd3!

2... Kd4?? loses because after 3. Kf5 Black is on the wrong side of the trébuchet.

• 3. Kf5 Kd4!

and Black wins the pawn and the game (see King and pawn versus king) (Silman 2007:98). The chess endgame with a king and a pawn versus a king is the most important and fundamental endgame, other than the basic checkmates. ... Zugzwang (German for compulsion to move, IPA: ) is a term used in combinatorial game theory and in other types of games (particularly in chess). ...

Position discovered by Bourzutschky. Whoever moves loses.

### Mined squares

Squares marked "1" are mined squares

### Zugzwang required to win

In some endgames, zugzwang is required to force a win. These include: rook (and king) versus king checkmate, two bishops versus king checkmate, bishop and knight versus king checkmate, queen versus rook, queen versus knight, queen versus two knights, and queen versus two bishops (Soltis 2003:79). Checkmate (frequently shortened to mate) is a situation in chess (and in other boardgames of the chaturanga family) in which one players king is under attack and there is no way to meet that threat; it is a check from which there is no escape. ... This checkmate can only be forced in the corner of the same square as your Bishop. ...

### Zugzwang in the middlegame and complex endgames

Sämisch vs. Nimzowitsch, Copenhagen, 1923. White resigned.

White has a few pawn moves which do not lose material, but eventually he will have to move one of his pieces. If he plays 1.Rc1 or Rd1 then 1...Re2 traps white's Queen; 1.Kh2 fails to 1...R5f3, also trapping the queen (white cannot play Bxf3 here because the bishop is pinned to the king); 1.g4 runs into 1...R5f3 2.Bxf3? Rh2 mate. 1.a3 is met by 1...a5 2.axb4 axb4 3.b3 Kh8 (waiting) 4.h4 Kg8 and White has run out of waiting moves and must lose material. Other white moves lose material in more obvious ways. Whether the position is true zugzwang is debatable, however, because even if white could pass his move he would still lose, albeit more slowly, after 1...R5f3 2.Bxf3 Rxf3, trapping the queen and thus winning queen and bishop for two rooks (Horowitz 1971:182). Here there is an absolute pin on the black knight because moving it would illegally expose the black king to check from the white bishop. ...

Harper-Zuk, position after 36...Rf1: White is utterly helpless.

Van Dongen vs. Wijsman, Eindhoven 2005, position after White's 74th move.

// Definition Diagram 1. ... In computer chess programs, the null-move heuristic is a heuristic technique used to enhance the speed of the alpha-beta pruning algorithm. ... Go terms and concepts are important in the game of Go. ... Mathematicians playing Konane at a Combinatorial game theory workshop (for technical content, see external link) This article is on the theory of combinatorial games. ... Triangulation is a tactic used in chess endgames to put ones opponent in zugzwang. ... The chess endgame with a king and a pawn versus a king is the most important and fundamental endgame, other than the basic checkmates. ... This checkmate can only be forced in the corner of the same square as your Bishop. ...

## Notes

1. ^ http://www.chessgames.com/perl/chessgame?gid=1102400
2. ^ http://www.chessgames.com/perl/chessgame?gid=1289113
3. ^ http://www.xs4all.nl/~timkr/chess2/diary_14.htm

## References

•   Dvoretsky, Mark (2003). Dvoretsky's Endgame Manual. Russell Enterprises. ISBN 1-888690-19-4.
•  Noam D. Elkies (1996). "On numbers and endgames: combinatorial game theory in chess endgames". Games of No Chance 29: 135-50.
•  Glenn Flear (2000). Improve Your Endgame Play. Everyman Chess. ISBN 1-85744-246-6.
•  Glenn Flear (2004). Starting Out: Pawn Endings. Everyman Chess. ISBN 1-85744-362-4.
•   Hooper, David and Whyld, Kenneth (1992). The Oxford Companion to Chess, 2nd Edition. Oxford University Press. ISBN 0-19-866164-9.  Reprint: (1996) ISBN 0-19-280049-3
• Kasparov, Gary (2004), My Great Predecessors, part IV, Everyman Chess, ISBN 1-85744-395-0
•   Karsten Müller and Frank Lamprecht (2001). Fundamental Chess Endings. Gambit Publications. ISBN 1-901983-53-6.
•  John Nunn (1999). Secrets of Rook Endings. Gambit Publications. ISBN 1-901983-18-8.
• Silman, Jeremy (2007), Silman's Complete Endgame Course: From Beginner to Master, Siles Press, ISBN 1-890085-10-3
•  Andrew Soltis (2003). Grandmaster Secrets: Endings. Thinkers' Press. ISBN 0-938650-66-1.
• Wade, Robert & Kevin O'Connell (1972), The Games of Robert J. Fischer, Batsford, ISBN 0-7134-2099-5

John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ... Richard Kenneth Guy (born 1916) is a Professor Emeritus in the Department of Mathematics at the University of Calgary. ... Academic Press (London, New York and San Diego) was an academic book publisher that is now part of Elsevier. ... Collier Books was a publisher established by the Collier family. ... Kasparov, Chess Classics, 1999 in Frankfurt am Main Garry Kimovich Kasparov (Russian: ; IPA: ) (born April 13, 1963, in Baku, Azerbaijan) is a chess grandmaster and former World Chess Champion. ... Frank Lamprecht (born 21 June 1968) is a German chess international master and chess trainer. ... Jeremy Silman (born August 25, 1954) is an American International Master of chess. ... Robert Wade, Chess player and author, (born April 10, 1921 Dunedin New Zealand) After winning the New Zealand Chess Championship in 1948, Bob Wade travelled to Europe to further his chess career. ...

Results from FactBites:

 Zugzwang - Wikipedia, the free encyclopedia (1095 words) Zugzwang means that one player is put at a disadvantage because he or she has to make a move — the player would like to pass and make no move, but the fact that the player must make a move means being forced into a significantly weaker position. Zugzwang most often occurs in the endgame when the number of pieces, and so the number of possible moves, is reduced, and the exact move chosen is often more critical. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies.
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