Zugzwang (German for "compulsion to move", pronounced [ˈtsuːktsvaŋ]) is a situation found in chess and other games, where one player is put at a disadvantage because he must make a move when he would prefer to pass and not to move. The fact that the player is compelled to move means that his position will become significantly weaker. A player is said to be "in zugzwang" when any possible move will worsen his position.
The term is also used in combinatorial game theory, where it means that it directly changes the outcome of the game from a win to a loss, but the term is used less precisely in games such as chess. Putting the opponent in zugzwang is a common way to help the superior side win a game, and in some cases, it is necessary in order to make the win possible.
The term "zugzwang" was used in German chess literature in 1858 or earlier, and the first known use of the term in English was by World Champion Emanuel Lasker in 1905. The concept of zugzwang was known to players many centuries before the term was coined, appearing in an endgame study published in 1604 by Alessandro Salvio, one of the first writers on the game, and in shatranj studies dating back to the early 9th century, over 1000 years before the first known use of the term.
- 1 Etymology
- 2 History
- 3 Zugzwang in chess
- 4 Examples from games
- 5 Reciprocal zugzwang
- 6 Mined squares
- 7 Zugzwang helps the defense
- 8 Zugzwang in the middlegame and complex endgames
- 9 Zugzwang Lite
- 10 See also
- 11 References
- 12 Further reading
- 13 External links
|This article uses algebraic notation to describe chess moves.|
Pages 353–358 of the September 1858 Deutsche Schachzeitung had an unsigned article 'Zugzwang, Zugwahl und Privilegien'. F. Amelung employed the terms Zugzwang, Tempozwang and Tempozugzwang on pages 257–259 of the September 1896 issue of the same magazine. When a perceived example of zugzwang occurred in the third game of the 1896–97 world championship match between Steinitz and Lasker, after 34...Rg8, the Deutsche Schachzeitung (December 1896, page 368) reported that 'White has died of zugzwang'.
The earliest known use of the term "zugzwang" in English was on page 166 of the February 1905 issue of Lasker's Chess Magazine. The term did not become common in English-language chess sources until the 1930s, after the publication of the English translation of Nimzowitsch's My System in 1929.
The concept of zugzwang, if not the term, must have been known to players for many centuries. Zugzwang is required to win the elementary (and common) king and rook versus king endgame, and the king and rook (or differently-named pieces with the same powers) have been chess pieces since the earliest versions of the game.
- 1. Re3 Ng1
- 2. Kf5 Kd4
- 3. Kf4
puts Black in zugzwang, since 3... Kc4 4. Kg3 Kd4 5. Re1 and White wins.
The concept of zugzwang is also seen in the 1585 endgame study by Giulio Cesare Polerio, published in 1604 by Alessandro Salvio, one of the earliest writers on the game. The only way for White to win is 1.Ra1 Kxa1 2.Kc2, placing Black in zugzwang. The only legal move is 2...g5, whereupon White promotes a pawn first and then checkmates with 3.hxg5 h4 4.g6 h3 5.g7 h2 6.g8(Q) h1(Q) 7.Qg7#.
Joseph Bertin refers to zugzwang in The Noble Game of Chess (1735), wherein he documents 19 rules about chess play. His 18th rule is: "To play well the latter end of a game, you must calculate who has the move, on which the game always depends."
François-André Danican Philidor wrote in 1777 of the position at below right that after White plays 36.Kc3, Black "is obliged to move his rook from his king, which gives you an opportunity of taking his rook by a double check [sic], or making him mate". Lasker explicitly cited a mirror image of this position (White: king on f3, queen on h4; Black: king on g1, rook on g2) as an example of zugzwang in Lasker's Manual of Chess. The British master George Walker analyzed a similar position in the same endgame, giving a maneuver that resulted in the superior side reaching the initial position, but now with the inferior side on move and in zugzwang. Walker wrote of the superior side's decisive move: "throwing the move upon Black, in the initial position, and thereby winning".
The great American player Paul Morphy (1837–1884), like Salvio and Philidor an unofficial World Champion, is credited with composing the position at right "while still a young boy". After 1.Ra6, Black is in zugzwang and must allow mate on the next move with 1...bxa6 2.b7# or 1...B (moves) 2.Rxa7#.
Zugzwang in chess
There are three types of chess positions:
- each side would benefit if it were his or her turn to move
- only one player would be at a disadvantage if it were his or her turn to move
- 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.
Normally in chess, having tempo is desirable because the player who is to move has the advantage of being able to choose a move that improves his or her situation. Zugzwang typically occurs when "the player to move cannot do anything without making an important concession".
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 at right shows the simplest possible example of zugzwang. If it is White's move, he must either stalemate Black with 1. Kc6 or abandon the pawn, allowing 1... Kxc7 with a draw. If it is Black's move, the only legal move is 1... Kb7, which allows White to win with 2. Kd7 followed by queening the pawn on the next move.
The second diagram at right is another simple example. Black, on move, must allow White to play Kc5 or Ke5, when White wins one or more pawns and can advance his own pawn toward promotion). White, on move, must retreat his king, when Black is out of danger. 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. This often occurs in king and pawn endgames. Pieces other than the king can also triangulate to achieve zugzwang, such as in the Philidor position. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies.
Examples from games
Fischer versus Taimanov, 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. The game continued:
- 85... Nf3
- 86. h6 Ng5
- 87. Kg6
- 87... Nf3
- 88. h7 Ne5+
- 89. Kf6 1–0
Fischer versus Taimanov, 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
- 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. Andy Soltis says that this is "perhaps Fischer's most famous endgame".
Tseshkovsky versus Flear, 1988
This position from a 1988 game between Vitaly Tseshkovsky and Glenn Flear at Wijk aan Zee shows an instance of "zugzwang" where the obligation to move makes the defense more difficult but it does not mean the loss of the game. A draw by agreement was reached eleven moves later.
A special case of zugzwang is reciprocal zugzwang or mutual zugzwang, which is a position such that whoever is to move is in zugzwang. Studying positions of reciprocal zugzwang is in the analysis of endgames. A position of mutual zugzwang is closely related to a game with a Conway value of zero in game theory.
In a position with reciprocal zugzwang, only the player to move is actually in zugzwang. However, the player who is not in zugzwang must play carefully because one inaccurate move can cause him to be put in zugzwang. That is in contrast to regular zugzwang, because the superior side usually has a waiting move to put the opponent in zugzwang.
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 move 1. Kc6 which is a draw because it stalemates Black or he must abandon the pawn, which is also a draw after Black captures the pawn. Since each side would be in zugzwang if it were his move, it is a reciprocal zugzwang.
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. 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. Kb7
Examples from play
The position at right is a position that could have occurred in the 1961 game between Viacheslav Kalashnikov and the young 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. This is one of 209 mutual zugzwang positions in the rook and pawn versus rook endgame.
The second position is an analysis position from the ninth game of the 1984 World Chess Championship between Anatoly Karpov and Garry Kasparov. The alternate move 45... Ke6 is considered and this position could result after move 57. White to move draws; Black to move loses. It would have been White's move in this analysis position. Kasparov played a different 45th move and Karpov won after seventy moves.
An extreme type of reciprocal zugzwang, called trébuchet, is shown in the third diagram. It is also called a full-point mutual zugzwang because it will result in a loss for the player in zugzwang, resulting a full point for his opponent. Whoever is to move in this position must abandon his own pawn, thus allowing his opponent to capture it and proceed to promote the remaining pawn, resulting in an easily winnable position.
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!
Another simple example is seen in the diagram at right. Black, on move, must play 1...b3, allowing 2.axb3#. White, on move, must move the king away, allowing 1...b3, with an easy win for Black.
Example in study
This position is a mutual zugzwang from a 1792 study. The first player to move runs out of moves and loses.
Analysis from game
Example in game
In endgame study
Marc Bourzutschky has used computer analysis to find some complicated trébuchet positions. If White is to move in this position, 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
Corresponding squares are squares of mutual zugzwang. When there is only one pair of corresponding squares they are called mined squares. A player will fall into zugzwang if he moves his king onto the square and his opponent is able to move onto the corresponding 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.
Zugzwang helps the defense
- 1... Kc4!! Reciprocal zugzwang
- 2. Nc3 Kb4 Reciprocal zugzwang again
- 3. Kd3 Bg7 Reciprocal zugzwang again
- 4. Kc2 Bh6
- 5. Kd3 Bg7
- 6. Nd5+ Kxa4
- 7. Ke4 Kb5
- 8. Kf5 Kc5
- 9. Kg6 Bd4
- 10. Nf4 Kd6
- 11. h6 Ke7
- 12. h7 Bb2
In this position from Benko, White should win but makes an error and gets into zugzwang, which enables Black to draw.
- 1. Kd6? Bb7
- 2. Bd7 Bf3
- 3. Be6 Bb7!
and Black draws because White is in zugzwang.
In a study
This position is a 1901 endgame study by Amelung. White to move wins by taking the opposition after 1. Kb7! and putting Black in zugzwang, e.g. 1... Kc4 2. Kb6 b3 3. Ka5 Kc3 4. Ka4 b2 5. Ka3 and White wins the pawn. In 1956 Ilyia Maizelis pointed out that Black to move can take the opposition and put White in zugzwang:
- 1... Kc5!
- 2. Kb7 Kb5!
- 3. Ka7 Ka5!
and White cannot make progress.
Zugzwang in the middlegame and complex endgames
Sämisch versus Nimzowitsch
The game Fritz Sämisch versus Aron Nimzowitsch, Copenhagen 1923, is often called the "Immortal Zugzwang Game". According to Nimzowitsch, writing in the Wiener Schachzeitung in 1925, this term originated in "Danish chess circles". Some consider the final position to be 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, since White cannot play 2.Bxf3 because the bishop is pinned to the king; 1.g4 runs into 1...R5f3 2.Bxf3? Rh2 mate. Angos analyzes 1.a3 a5 2.axb4 axb4 3.h4 Kh8 (waiting) 4.b3 Kg8 and White has run out of waiting moves and must lose material. Best in this line is 5.Nc3!? bxc3 6.bxc3, which just leaves Black with a serious positional advantage and an extra pawn. Other moves lose material in more obvious ways.
However, since Black would win even without the zugzwang, it is debatable whether the position is true zugzwang. 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. Wolfgang Heidenfeld thus considers it a misnomer to call this a true zugzwang position. See also Immortal Zugzwang Game: Objections to the sobriquet.
Steinitz versus Lasker
This game between Wilhelm Steinitz versus Emanuel Lasker in the 1896–97 World Chess Championship, is an early example of zugzwang in the middlegame. After Lasker's 34...Re8–g8!, Steinitz had no playable moves, and resigned. White's bishop cannot move because that would allow the crushing ...Rg2+. The queen cannot move without abandoning either its defense of the bishop on g5 or of the g2 square, where it is preventing ...Qg2#. White's move 35.f6 loses the bishop: 35...Rxg5 36. f7 Rg2+, forcing mate. The move 35.Kg1 allows 35...Qh1+ 36.Kf2 Qg2+ followed by capturing the bishop. The rook cannot leave the first rank, as that would allow 35...Qh1#. Rook moves along the first rank other than 35.Rg1 allow 35...Qxf5, when 36.Bxh4 is impossible because of 36...Rg2+; for example, 35.Rd1 Qxf5 36.d5 Bd7, winning. That leaves only 35.Rg1, when Black wins with 35...Rxg5! 36.Qxg5 (36.Rxg5? Qh1#) Qd6+ 37.Rg3 hxg3+ 38.Qxg3 Be8 39.h4 Qxg3+ 40.Kxg3 b5! 41.axb5 a4! and Black queens first. Colin Crouch calls the final position, "An even more perfect middlegame zugzwang than ... Sämisch–Nimzowitsch ... in the final position Black has no direct threats, and no clear plan to improve the already excellent positioning of his pieces, and yet any move by White loses instantly".
Podgaets versus Dvoretsky
Soltis writes that his "candidate for the ideal zugzwang game" is the following game Soltis 1978, p. 55 : Podgaets–Dvoretsky, USSR 1974 1.d4 c5 2.d5 e5 3.e4 d6 4.Nc3 Be7 5.Nf3 Bg4 6.h3 Bxf3 7.Qxf3 Bg5! 8.Bb5+ Kf8! Black exchanges off his bad bishop, but does not allow White to do the same. 9.Bxg5 Qxg5 10.h4 Qe7 11.Be2 h5 12.a4 g6 13.g3 Kg7 14.0-0 Nh6 15.Nd1 Nd7 16.Ne3 Rhf8 17.a5 f5 18.exf5 e4! 19.Qg2 Nxf5 20.Nxf5+ Rxf5 21.a6 b6 22.g4? hxg4 23.Bxg4 Rf4 24.Rae1 Ne5! 25.Rxe4 Rxe4 26.Qxe4 Qxh4 27.Bf3 Rf8!! 28. Bh1 28.Qxh4? Nxf3+ and 29...Nxh4 leaves Black a piece ahead. Ng4 29.Qg2 (see diagram at left) Rf3!! 30.c4 Kh6!! (diagram at right) Now all of White's piece moves allow checkmate or ...Rxf2 with a crushing attack (e.g. 31.Qxf3 Qh2#; 31.Rb1 Rxf2 32.Qxg4 Qh2#). That leaves only moves of White's b-pawn, which Black can ignore, e.g. 31.b3 Kg7 32.b4 Kh6 33.bxc5 bxc5 and White has run out of moves. 0–1
Harper versus Zuk
Harper–Zuk, Halloween Open, Burnaby, British Columbia 1971 is a grisly example of zugzwang in the middlegame. White's queen, rook, knight, and king have a total of one legal move (Qh3), which loses the queen, rook and king on successive moves (... 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 is mate in two: gxh3 42.Kh2 Qxg2#.
Van 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.
Zhilin versus Chernov
In the game between Vitaly Valentinovich Zhilin and Chernov (or Tchernov) in the 1960 USSR championship, 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
Fischer versus Rossetto
In this 1959 game between future World Champion Bobby Fischer and Héctor Rossetto, 33. Bb3! puts Black in zugzwang. If Black moves the king, White plays Rb8, winning a piece (...Rxc7 Rxf8); if Black moves the rook, 33...Ra8 or R...e8, then 34.c8=Q+ and the black rook will be lost after 35.Qxa8, 35.Qxe8 or 35.Rxe7+ (depending on Black's move); if Black moves the knight, Be6 will win Black's rook. That leaves only pawn moves, and they quickly run out. The game concluded:
- 34.a4 h6
- 35.h3 g5
- 36.g4 fxg4
- 37.hxg4 1–0.
Example from Euwe and Meiden
Jonathan Rowson coined the term Zugzwang Lite to describe a situation, sometimes arising in symmetrical opening variations, where White's "extra move" is a burden. He cites as an example of this phenomenon in Hodgson versus Arkell at Newcastle 2001. The position at left arose after 1.c4 c5 2.g3 g6 3.Bg2 Bg7 4.Nc3 Nc6 5.a3 a6 6.Rb1 Rb8 7.b4 cxb4 8.axb4 b5 9.cxb5 axb5 Here Rowson remarks, "Both sides want to push their d-pawn and play Bf4/...Bf5, but White has to go first so Black gets to play ...d5 before White can play d4. This doesn't matter much, but it already points to the challenge that White faces here; his most natural continuations allow Black to play the moves he wants to. I would therefore say that White is in 'Zugzwang Lite' and that he remains in this state for several moves." The game continued 10.Nf3 d5 11.d4 Nf6 12.Bf4 Rb6 13.0-0 Bf5 14.Rb3 0-0 15.Ne5 Ne4 16.h3 h5!? 17.Kh2 The position is still almost symmetrical, and White can find nothing useful to do with his extra move. Rowson whimsically suggests 17.h4!?, forcing Black to be the one to break the symmetry. 17...Re8! Rowson notes that this is a useful waiting move, covering e7, which needs protection in some lines, and possibly supporting an eventual ...e5 (as Black in fact played on his 22nd move). White cannot copy it, since after 18.Re1? Nxf2 Black would win a pawn. After 18.Be3?! Nxe5! 19.dxe5 Rc6! Black seized the initiative and went on to win in 14 more moves.
Another instance of Zugzwang Lite occurred in Lajos Portisch versus Mikhail Tal, Candidates Match 1965, again from the Symmetrical Variation of the English Opening, after 1.Nf3 c5 2.c4 Nc6 3.Nc3 Nf6 4.g3 g6 5.Bg2 Bg7 6.0-0 0-0 7.d3 a6 8.a3 Rb8 9.Rb1 b5 10.cxb5 axb5 11.b4 cxb4 12.axb4 d6 13.Bd2 Bd7. Soltis wrote, "It's ridiculous to think Black's position is better. But Mikhail Tal said it is easier to play. By moving second he gets to see White's move and then decide whether to match it." 14.Qc1 Here, Soltis wrote that Black could maintain equality by keeping the symmetry: 14...Qc8 15.Bh6 Bh3. Instead, he plays to prove that White's queen is misplaced. 14...Rc8! 15.Bh6 Nd4! Threatening 15...Nxe2+. 16.Nxd4 Bxh6 17.Qxh6 Rxc3 18.Qd2 Qc7 19.Rfc1 Rc8 Although the pawn structure is still symmetrical, Black's control of the c-file gives him the advantage. Black ultimately reached an endgame two pawns up, but White managed to hold a draw in 83 moves. See First-move advantage in chess#Symmetrical openings for more details.
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