Zugzwang

From Wikipedia, the free encyclopedia

This article uses algebraic notation to describe chess moves.

Zugzwang (German for "compulsion to move", pronounced [ˈtsuːktsvaŋ]) is a term originally used in chess which also applies to various other games. The concept finds its formal definition in combinatorial game theory. It describes a situation where 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 game theory, it specifically means that it directly changes the outcome of the game from a win to a loss. The term is used less precisely in games such as chess; e.g., the game theory definition is not necessarily used in chess (Berlekamp, Conway & Guy 1982:16), (Elkies 1996:136). For instance, it may be defined loosely, as "a player to move cannot do anything without making an important concession" (van Perlo 2006:479). Zugzwang is a common technique to help the superior side win a game and sometimes it is necessary to make the win possible (Müller & Pajeken 2008:173).

The term zugzwang is frequently used in chess. A player whose turn it is to move who has no move that does not worsen their position is said to be in zugzwang (Soltis 2003:78). Thus every move would make their position worse, and they would be better off if they could pass and not move. 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 & Whyld 1992).

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.

Positions with zugzwang occur fairly often in chess endgames. For instance, twelve of the 105 endgames in the book Endgame Virtuoso Anatoly Karpov involve zugzwang (Karolyi & Aplin 2007:358). According to John Nunn, positions of reciprocal zugzwang (see below) are surprisingly important in the analysis of endgames (Nunn 1995:6), (Nunn 1999:7).

The remainder of this article is about zugzwang in chess.

Contents 1 Introduction 2 Examples from games 2.1 Fischer versus Taimanov, 1971, second match game 2.2 Fischer versus Taimanov, 1971, fourth match game 2.3 Tseshkovsky versus Flear, 1988 3 Reciprocal zugzwang 3.1 Second example 3.2 Example from play 3.3 Trébuchet 3.3.1 Example 3.3.2 Analysis from actual game 3.3.3 In endgame study 4 Mined squares 5 Zugzwang required to win 6 Zugzwang helps the defense 7 Zugzwang in the middlegame and complex endgames 7.1 Sämisch versus Nimzowitsch 7.2 Harper versus Zuk 7.3 Dongen versus Wijsman 7.4 Zhilin versus Chernov 8 Quotes 9 See also 10 Notes 11 References 12 Further reading 13 External links

[edit] Introduction

There are three types of chess positions:

1. both sides would benefit by it being their turn to move
2. only one player would be at a disadvantage if it were his turn to move
3. both players would be at a disadvantage if it were their turn to move.

The great majority of positions are of the first type. In chess literature, most writers call positions of the second type zugzwang, and the third type reciprocal zugzwang or mutual zugzwang. Some writers call the second type a squeeze and the third type zugzwang (Hooper & Whyld 1992), (Hooper 1970:196-97).

Normally in chess, having tempo is a good thing, since the player with the chance to move has greater power by being able to choose the "best" next move. Zugzwang typically occurs when all the moves available are "bad" moves, tangibly weakening the moving player's position (usually from a draw to a loss or from a win to a draw) (Müller & Lamprecht 2001:22).

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 diagram on the right 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 the king must retreat and Black is out of danger (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; that article has in illustrative example. Zugzwang is very common in king and pawn endgames, where it is frequently achieved through triangulation. 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.

[edit] Examples from games

[edit] Fischer versus Taimanov, 1971, second match game

Some zugzwang positions occurred in the second game of the 1971 candidates match between Bobby Fischer and Mark Taimanov. In the position in the diagram, Black is in zugzwang because he would rather not move, but he must: a king move would lose the knight, while a knight move would allow the passed pawn to advance (Wade & O'Connell 1972:413). The game continued:

• 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):

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

[edit] Fischer versus Taimanov, 1971, fourth match game

In the position on the right, White has just gotten his king to a6, where it attacks the black pawn on b6, tying down the black king to defending it. White now needs to get his bishop to f7 or e8 to attack the pawn on g6. Play continued:

• 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.

• 61. Be8

and Black is in zugzwang. Knights are unable to make a tempo move (Nunn 1995:7), so moving the knight would allow the bishop to capture the kingside pawns. The black king must give way.

• 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), (Averbakh 1984:113-14), (Flear 2007:286-87).

[edit] Tseshkovsky versus Flear, 1988

This position from a 1988 game between Vitaly Tseshkovsky and Glenn Flear shows an instance of "zugzwang" where the obligation to move makes the defense more difficult but it doesn't mean the loss of the game. A draw by agreement was reached eleven moves later (Flear 2007:241).

[edit] Reciprocal zugzwang

A special case of zugzwang is reciprocal zugzwang or mutual zugzwang, which is a position such that who ever is to move is in zugzwang. Positions of reciprocal zugzwang are surprisingly important in the analysis of endgames (Nunn 1995:6), (Nunn 1999:7).

The diagram on the right shows a position of reciprocal zugzwang. If Black is to move, he must move 1... Kd7 and lose because White will move 2. Kb7, promote the pawn, and win. If White is to move, he must either abandon protecting the pawn (any move other than 1. Kc6), or move 1. Kc6, which is also a draw because it stalemates Black. Both sides are in zugzwang, so it is a reciprocal zugzwang (Hooper 1970:21), (Averbakh 1993:35).

Of course, reciprocal zugzwang is a hypothetical construct, as it will never occur in an actual game: it must always be one player's move or the other's. Though the positions exemplified may occur, and even occur often, they can only mean zugzwang for one player: the player that must move.

[edit] Second example

Another example is shown in the diagram on the right—if White is to move the game is drawn; if Black is to move he loses (Flear 2004:22).

With White to move:

• 1. Kd5 Kd7
• 2. c5 Kc7
• 3. c6 Kc8!
• 4. Kd6 Kd8!

Black has the opposition and draws because 5. c7+ Kc8 6. Kc6 is stalemate.

If Black is to move, White wins

• 1. ... Kd7
• 2. Kb6 Kc8
• 3. Kc6 Kd8

and White wins with

• 4. c5

or

• 4. Kb7.

[edit] Example from play

The position at right is a position that could have occurred in the 1961 game between Viacheslav Kalashnikov and Anatoly Karpov. White to move in this position draws, but Black to move loses. Karpov's 49th move in the actual game avoided the zugzwang and the game was drawn (Karolyi & Aplin 2007:22). This is one of 209 mutual zugzwang positions in the rook and pawn versus rook endgame (Nunn 1999:7).

[edit] Trébuchet

An extreme type of reciprocal zugzwang, called trébuchet is shown in the third diagram. It is also called a full-point mutual zugzwang because a full point (win versus loss) is at stake. Whoever is to move in this position loses the game—they must abandon their own pawn, thus allowing their opponent to capture it and proceed to promote their own pawn (Flear 2004:13).

[edit] Example

This diagram shows a position in which a trébuchet can be reached to win the game. The first king to reach the blocked pawns will win. Play continues:

• 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 endgame) (Silman 2007:98).

[edit] Analysis from actual game

In this analysis from a 1978 game between Miguel Najdorf and Henrique Mecking, whoever is to move loses. (It would have been White's move had the analysis position occurred in the game.) (Silman 2007:385-87)

[edit] In endgame study

Marc Bourzutschky has used computer analysis to find some complicated trébuchet positions. If White is on move, Black quickly drives White's king toward the corner and mates no later than move 8, e.g. 1.Kb2 (1.Nhg7 Qf4+ or 1.Nh4 Qe3+ also leaves White's king in trouble) Qg2+ 2.Kb3 Qb7+! 3.Ka3 Qb6 4.Nf4+ Kc4! 5.Ka2 Qb3+! 6.Ka1 Kb4 7.Ng7 Ka3 8.Nge6 Qb2#. Black on move must give ground, enabling White to gradually improve the positions of his pieces, e.g. 1...Kc4 (1...Kc3 allows 2.Nf2 Qxf2?? 3.Ne4+) 2.Kd2! Kd5 3.Ne3+ Ke5 4.Ng7 and White mates by move 42 according to Bourzutschky.-- scroll down to No. 282

[edit] Mined squares

Mined squares are squares such that a player will fall into zugzwang if he moves onto the square. In the diagram on the right, if either king moves onto the square marked with the dot of the same color, he falls into zugzwang if the other king moves into the mined square near him. These are a type of corresponding squares (Dvoretsky 2006:19).

[edit] Zugzwang required to win

In some endgames, placing the opponent in zugzwang is required to force a win. These include:

• rook (and king) versus king checkmate
• two bishops versus king checkmate
• two knights versus pawn checkmate
• Bishop and knight checkmate
• queen versus rook
• queen versus knight
• queen versus two knights, and
• queen versus two bishops (Soltis 2003:79).

In addition, zugzwang is required in many King and pawn versus king endings in order to force promotion of the pawn. (See pawnless chess endgames and fortress (chess) for some discussion of some of these endings.)

[edit] Zugzwang helps the defense

Zugzwang usually works in favor of the stronger side, but sometimes it aids the defense. In this position based on a game between Zoltán Varga and Peter Acs, it saves the game for the defense:

• 1... Kc4!! Reciprocal zugzwang
• 2. Nc3 Kb4 Reciprocal zugzwang again
• 3. Kd3 Bg7 Reciprocal zugzwang again
• 4. Kc2 Bb6
• 5. Kd3 Bg7
• 6. Nd5+ Kxa4
• 7. Ke4 Kb5
• 8. Kf5 Kc5
• 9. Kg6 Bd4
• 10. Nf4 Kd6
• 11. h6 Ke7
• 12. h7 Bb2 ½-½ (Müller & Pajeken 2008:179-80).

[edit] Zugzwang in the middlegame and complex endgames

[edit] Sämisch versus Nimzowitsch

Main article: Immortal Zugzwang game

The game Fritz Sämisch versus Aron Nimzowitsch, Copenhagen 1923,^[1] is sometimes called the "Immortal Zugzwang game" because the final position is widely accepted as being an extremely rare instance of zugzwang occurring in the middlegame. It ended with White resigning in the position in the diagram.

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). Harry Golombek states that it is a misnomer to call this a true zugzwang position (Golombek 1977). Black would win even without the zugzwang (Nunn 1981:86).

[edit] Harper versus Zuk

Harper-Zuk, Halloween Open, Burnaby, British Columbia 1971^[2] is a grisly example of zugzwang in the middlegame. White's queen, rook, knight, and king have a total of one legal move (Qh3), and that move loses the queen and then the game (... gxh3 followed by ... Qxg2#). The game concluded: 37.b5 Kh8 37...Nf5 and Nd4-e2 was crushing, but letting White self-destruct is even quicker. 38.a4 Kh7 39.a5 Kg8 0-1 After 40.axb6 axb6, white is forced to play 41.Qh3, and then it's mate in two: gxh3 42.Kh2 Qxg2#.

[edit] Dongen versus Wijsman

An unusual example of zugzwang in a complicated endgame occurred in the position at right. On the previous move Black, with a winning position, had played 73...d4? and White responded 74.Rd2-d3!!, when Black, a knight up with three dangerous passed pawns, suddenly must fight for a draw. Tim Krabbé explains that the pawns on d4 and e4 are blocked and pinned, the knight is bound to the defense of e4, the rook is bound to the defense of d4, and the pawn on b4 is bound to the defense of the knight. Krabbé analyzes as best for Black 74...b3! 75.Rxd4 Rxd4 76.Rxc3 Rd8 77.Rxb3 Re8 78.Re3 Re5 79.Rc3 (79.Kxf6? Rxa5 82.Kg6 Ra1 83.f6 Rg1+ wins) Re8 80.Re3 Re5 81.Rc3 and the game will end in a draw by repetition of moves. Instead, Black played 74...Nb5? 75.Rxe4 Nd6 76.Re6 Rc6 77.Rxd4 Rxh6+ 78.Kxh6 Nxf5+ 79.Kg6 1-0 ^[3].

[edit] Zhilin versus Chernov

In the game between Vitaly Valentinovich Zhilin and Chernov (or Tchernov), White was a pawn down and just sacrificed a bishop on h3. After 1. Kh4! Black is placed in zugzwang after moving his b- and h-pawns. The game continued:

• 1. Kh4! b6
• 2. Kh5 b5
• 3. Kh4 h5
• 4. Kxh5

Now Black is in zugzwang and resigned (Nunn 1981:86-87), (van Perlo 2006:71).

[edit] Quotes

• "Zugzwang is like getting trapped on a safety island in the middle of a highway when a thunderstorm starts. You don't want to move but you have to." - Arthur Bisguier (Müller & Pajeken 2008:173)

[edit] See also

• Opposition (chess)
• Null-move heuristic
• Seki
• Combinatorial game theory, in which all mutual zugzwangs are equivalent to 0.
• Triangulation (chess)
• King and pawn versus king endgame
• Corresponding squares

[edit] Notes

[edit] References

• Averbakh, Yuri (1984), Comprehensive Chess Endings, vol. 2, Pergammon, ISBN 0-08-026902-8 
• Averbakh, Yuri (1993), Chess Endings: Essential Knowledge (second ed.), Everyman Chess, ISBN 1-85744-022-6 
• Berlekamp, Elwyn R.; Conway, John H. & Guy, Richard K. (1982), Winning Ways for your Mathematical Plays, vol. 1, Academic Press, ISBN 0-12-091101-9 
• Dvoretsky, Mark (2006), Dvoretsky's Endgame Manual (second ed.), Russell Enterprises, ISBN 1-888690-28-3 
• Elkies, Noam D. (1996), “On Numbers and Endgames: Combinatorial Game Theory in Chess Endgames”, in Nowakowski, Richard, Games of No Chance, Cambridge University Press, ISBN 0-521-57411-0 
• Flear, Glenn (2000), Improve Your Endgame Play, Everyman Chess, ISBN 1-85744-246-6 
• Flear, Glenn (2004), Starting Out: Pawn Endings, Everyman Chess, ISBN 1-85744-362-4 
• Flear, Glenn (2007), Practical Endgame Play - beyond the basics: the definitive guide to the endgames that really matter, Everyman Chess, ISBN 978-1-85744-555-8 
• Golombek, Harry (1977), Golombek's Encyclopedia of Chess, Crown Publishing, ISBN 0-517-53146-1 
• Hooper, David (1970), A Pocket Guide to Chess Endgames, Bell & Hyman, ISBN 0-7135-1761-1 
• Hooper, David & Whyld, Kenneth (1992), The Oxford Companion to Chess (second ed.), Oxford University Press, ISBN 0-19-866164-9 
• Horowitz, I. A. (1971), All About Chess, Collier Books 
• Karolyi, Tibor & Aplin, Nick (2007), Endgame Virtuoso Anatoly Karpov, New In Chess, ISBN 978-90-5691-202-4 
• Kasparov, Gary (2004), My Great Predecessors, part IV, Everyman Chess, ISBN 1-85744-395-0 
• 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 
• Nunn, John (1981), Tactical Chess Endings, Batsford, ISBN 0-7134-5937-9 
• Nunn, John (1995), Secrets of Minor-Piece Endings, Batsford, ISBN 0-8050-4228-8 
• Nunn, John (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 
• Soltis, Andy (2003), Grandmaster Secrets: Endings, Thinker's Press, ISBN 0-938650-66-1 
• van Perlo, Gerardus C. (2006), Van Perlo's Endgame Tactics, New In Chess, ISBN 978-90-5691-168-3 
• Wade, Robert & O'Connell, Kevin (1972), The Games of Robert J. Fischer, Batsford, ISBN 0-7134-2099-5 

[edit] Further reading

• Ward, Chris (1996), Endgame Play, Batsford, ISBN 0-7134-7920-5 

[edit] External links

• Fischer-Taimanov 1971
• Friedrich Samisch vs Aron Nimzowitsch 1923 ("The immortal zugzwang game")
• Levitsky-Frank James Marshall 1912
• Tseshkovsky-Flear, 1988