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Zugzwang

From Wikipedia, the free encyclopedia
This article is about the disadvantageous requirement to move. For the move interposition tactic, see Zwischenzug. For other uses, see Zugzwang (disambiguation).

Zugzwang (from German 'compulsion to move'; pronounced [ˈtsuːktsvaŋ]) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal move will worsen their position.[1]

Although the term is used less precisely in games such as chess, it is used specifically in combinatorial game theory to denote a move that directly changes the outcome of the game from a win to a loss.[2][3] 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.[4] More generally, the term can also be used to describe a situation where none of the available options lead to a good outcome.[5][6][7]

The term zugzwang was used in German chess literature in 1858 or earlier,[8] and the first known use of the term in English was by World Champion Emanuel Lasker in 1905.[9] The concept of zugzwang was known to chess 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. International chess notation uses the symbol "⊙" to indicate a zugzwang position.

Positions with zugzwang occur fairly often in chess endgames, especially in king and pawn endgames and elementary checkmates (such as a rook and king against a lone king). According to John Nunn, positions of reciprocal zugzwang are surprisingly important in the analysis of endgames.[10][11]

This article uses algebraic notation to describe chess moves.

Etymology

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The word comes from German Zug 'move' + Zwang 'compulsion', so that Zugzwang means 'being forced to make a move'. Originally the term was used interchangeably with the term Zugpflicht 'obligation to make a move' as a general game rule. Games like chess and checkers have "zugzwang" (or "zugpflicht"): a player must always make a move on their turn even if this is to their disadvantage. Over time, the term became especially associated with chess.

According to chess historian Edward Winter, the term had been in use in German chess circles in the 19th century.[8]

Pages 353–358 of the September 1858 Deutsche Schachzeitung had an unsigned article "Zugzwang, Zugwahl und Privilegien". Friedrich 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.[9] 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.[8]

History

[edit]
Katai, 9th century
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c5 black king
e5 white king
d3 white rook
e2 black knight
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White to move and win

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,[12] and the king and rook (or differently-named pieces with the same powers) have been chess pieces since the earliest versions of the game.[13]

Other than basic checkmates, the earliest published use of zugzwang may be in this study by Zairab Katai, which was published sometime between 813 and 833, discussing shatranj. After

1. Re3 Ng1
2. Kf5 Kd4
3. Kf4

puts Black in zugzwang, since the black king must abandon its attack on the white rook and thus allow the white king to trap the knight: 3...Kc4 4.Kg3 (or Kg4) Kd4 5.Re1 and White wins.[14]

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.[15] 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#.[16]

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."[17]

François-André Danican Philidor wrote in 1777 of the position illustrated 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".[18] 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.[19] The British master George Walker analyzed a similar position in the same endgame, giving a maneuver (triangulation) 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".[20]

Morphy, 1840s?
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a8 black king
b8 black bishop
c8 white king
a7 black pawn
b7 black pawn
b6 white pawn
a2 white rook
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White to play and mate in two moves

Paul Morphy is credited with composing the position illustrated "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#.[21]

Zugzwang in chess

[edit]

There are three types of chess positions: either none, one, or both of the 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.[22]

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 their situation. Zugzwang typically occurs when "the player to move cannot do anything without making an important concession".[23][24]

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.[25] The first diagram shows the simplest possible example of zugzwang. If it is White's move, they 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 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 their own pawn toward promotion. White, on move, must retreat their king, when Black is out of danger.[26] 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

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Fischer vs. Taimanov, second match game

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Fischer vs. Taimanov, 1971, game 2
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f6 white king
f5 white bishop
g5 black knight
h5 white pawn
f4 black king
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Position after 85.Bf5, Black is in zugzwang.

Some zugzwang positions occurred in the second game of the 1971 candidates match between Bobby Fischer and Mark Taimanov.[27] 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.[28] 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):[29]

87... Nf3
88. h7 Ne5+
89. Kf6 1–0

Fischer vs. Taimanov, fourth match game

[edit]
Fischer vs. Taimanov, 1971, game 4
abcdefgh
8
c7 black king
e7 black knight
a6 white king
b6 black pawn
g6 black pawn
a5 black pawn
c5 black pawn
f5 black pawn
h5 black pawn
a4 white pawn
f4 white pawn
h4 white pawn
c3 white pawn
f3 white bishop
g3 white pawn
b2 white pawn
8
77
66
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Position after 57.Ka6

In the position shown, White has just gotten his king to a6, where it attacks the black pawn on b6, tying down the black king to defend 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 lose a tempo,[30] 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 winning 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.[31][32][33] Andy Soltis says that this is "perhaps Fischer's most famous endgame".[34]

Tseshkovsky vs. Flear, 1988

[edit]
Tseshkovsky vs. Flear, 1988
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8
d7 black bishop
f7 black rook
h7 black king
d6 white pawn
e5 white king
g5 white queen
8
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66
55
44
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Position after 86.Ke5. Black to move is able to hold the draw.

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.[35][36]

Reciprocal zugzwang

[edit]
Hooper 1970, p. 21
abcdefgh
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c8 black king
c7 white pawn
b6 white king
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Reciprocal zugzwang, White to move draws, Black to move loses.

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.[10][11] A position of mutual zugzwang is closely related to a game with a Conway value of zero in game theory.[37]

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 them to be put in zugzwang.[38] That is in contrast to regular zugzwang, because the superior side usually has a waiting move or can triangulate to put the opponent in zugzwang.[11]

The diagram shows a position of reciprocal zugzwang. If Black is to move, 1... Kd7 is forced, which loses because White will move 2. Kb7, promote the pawn, and win. If White is to move the result is a draw as White must either stalemate Black with 1. Kc6 or allow Black to capture the pawn. Since each side would be in zugzwang if it were their move, it is a reciprocal zugzwang.[39][40]

Trébuchet

[edit]
Flear 2004, p. 13
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d5 black pawn
e5 white king
c4 black king
d4 white pawn
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Trébuchet (extreme mutual zugzwang), whoever moves loses.

An extreme type of reciprocal zugzwang, called trébuchet, is shown in the diagram. It is also called a full-point mutual zugzwang because it will result in a loss for the player in zugzwang, resulting in a full point for the opponent.[41] Whoever is to move in this position must abandon their own pawn, thus allowing the opponent to capture it and proceed to promote their own pawn, resulting in an easily winnable position.[42]

Mined squares

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b6 black king
d6 black pawn
e6 white circle
c5 black circle
d5 white pawn
f5 white king
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Squares marked with dots are mined squares for the king of that color.

Corresponding squares are squares of mutual zugzwang. When there is only one pair of corresponding squares, they are called mined squares.[43] A player will fall into zugzwang if they move their king onto the square and their opponent is able to move onto the corresponding square. In the diagram here, if either king moves onto the square marked with the dot of the same color, it falls into zugzwang if the other king moves into the mined square near them.[44]

Zugzwang helps the defense

[edit]
Based on Varga vs. Acs
abcdefgh
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h6 black bishop
b5 white knight
c5 black king
h5 white pawn
a4 white pawn
c2 white king
8
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Black to move puts White in zugzwang.

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 Péter Ács, 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 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

This position is a draw and the players agreed to a draw a few moves later.[45]

Zugzwang in middlegames and complex endgames

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Alex Angos notes that, "As the number of pieces on the board increases, the probability for zugzwang to occur decreases."[46] As such, zugzwang is very rarely seen in the middlegame.[47]

Sämisch vs. Nimzowitsch

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Main article: Immortal Zugzwang Game
Sämisch vs. Nimzowitsch, 1923
abcdefgh
8
g8 black king
d7 black queen
g7 black pawn
a6 black pawn
d6 black bishop
e6 black pawn
h6 black pawn
d5 black pawn
f5 black rook
b4 black pawn
d4 white pawn
e4 black pawn
d3 black bishop
e3 white queen
g3 white pawn
h3 white pawn
a2 white pawn
b2 white pawn
d2 white bishop
f2 black rook
g2 white bishop
b1 white knight
e1 white rook
g1 white rook
h1 white king
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White resigned.

The game Fritz Sämisch–Aron Nimzowitsch, Copenhagen 1923,[48] is often called the "Immortal Zugzwang Game". According to Nimzowitsch, writing in the Wiener Schachzeitung in 1925, this term originated in "Danish chess circles".[8] Some consider the final position to be an extremely rare instance of zugzwang occurring in the middlegame.[49] 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.[50] Other moves lose material in more obvious ways.

However, since Black would win even without the zugzwang,[51] 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.[52] Wolfgang Heidenfeld thus considers it a misnomer to call this a true zugzwang position.[53] See also Immortal Zugzwang Game § Objections to the sobriquet.

Steinitz vs. Lasker

[edit]
Steinitz vs. Lasker, 1896–97
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8
g8 black rook
b7 black king
c7 black pawn
b6 black pawn
c6 black bishop
a5 black pawn
d5 black queen
f5 white pawn
g5 white bishop
a4 white pawn
c4 black pawn
d4 white pawn
h4 black pawn
c3 white pawn
h3 white pawn
d2 white queen
h2 white king
f1 white rook
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Position after 34...Rg8!

This game between Wilhelm Steinitz and Emanuel Lasker in the 1896–97 World Chess Championship,[54] is an early example of zugzwang in the middlegame. After Lasker's 34...Re8–g8!, Steinitz had no playable moves, and resigned.[55][56][57][58] 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#. Attempting to push the f-pawn to promotion with 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.[55] 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."[59]

Podgaets vs. Dvoretsky

[edit]
Podgaets vs. Dvoretsky, USSR 1974

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 If instead 28.Qxh4 then 28...Nxf3+ followed by 29...Nxh4 leaves Black a piece ahead. 28... Ng4 29. Qg2 (first diagram) Rf3!! 30. c4 Kh6!! (second diagram) 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.[60] 0–1

Fischer vs. Rossetto

[edit]
Fischer vs. Rossetto, 1959
abcdefgh
8
c8 black rook
f8 black knight
b7 white rook
c7 white pawn
g7 black king
h7 black pawn
a6 black pawn
g6 black pawn
e5 black pawn
f5 black pawn
b3 white bishop
f3 white pawn
a2 white pawn
g2 white pawn
h2 white pawn
g1 white king
8
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Position after 33.Ba4–b3!, Black is in zugzwang.

In this 1959 game[61] between future World Champion Bobby Fischer and Héctor Rossetto, 33.Bb3! puts Black in zugzwang.[62] If Black moves the king, White plays Rb8, winning a piece (...Rxc7 Rxf8); if Black moves the rook, 33...Ra8 or Re8, then not only does White gain a queen with 34.c8=Q+, but the black rook will also 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.[63] The game concluded:

33... a5
34. a4 h6
35. h3 g5
36. g4 fxg4
37. hxg4 1–0[64]

Zugzwang Lite

[edit]
See also: First-move advantage in chess § Symmetrical openings
Hodgson vs. Arkell, 2001
abcdefgh
8
b8 black rook
c8 black bishop
d8 black queen
e8 black king
g8 black knight
h8 black rook
d7 black pawn
e7 black pawn
f7 black pawn
g7 black bishop
h7 black pawn
c6 black knight
g6 black pawn
b5 black pawn
b4 white pawn
c3 white knight
g3 white pawn
d2 white pawn
e2 white pawn
f2 white pawn
g2 white bishop
h2 white pawn
b1 white rook
c1 white bishop
d1 white queen
e1 white king
g1 white knight
h1 white rook
8
77
66
55
44
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Position after 9...axb5. According to Rowson, White is in Zugzwang Lite.

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.[65] He cites as an example of this phenomenon in Hodgson versus Arkell at Newcastle 2001. The position diagrammed 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 (see diagram). 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.

Portisch vs. Tal, 1965
abcdefgh
8
b8 black rook
d8 black queen
f8 black rook
g8 black king
d7 black bishop
e7 black pawn
f7 black pawn
g7 black bishop
h7 black pawn
c6 black knight
d6 black pawn
f6 black knight
g6 black pawn
b5 black pawn
b4 white pawn
c3 white knight
d3 white pawn
f3 white knight
g3 white pawn
d2 white bishop
e2 white pawn
f2 white pawn
g2 white bishop
h2 white pawn
b1 white rook
d1 white queen
f1 white rook
g1 white king
8
77
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Position after 13...Bd7. White to play, but Black has the easier game.

Another instance of Zugzwang Lite occurred in Lajos Portisch–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 (see diagram). 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."[66] 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 by breaking the symmetry. 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.[66] Black ultimately reached an endgame two pawns up, but White managed to hold a draw in 83 moves.[67]

Zugzwang required to win

[edit]

Soltis listed some endgames in which zugzwang is required to win:

  • King and rook versus king
  • King and two bishops versus king
  • King, bishop, and knight versus king
  • Queen versus rook
  • Queen versus knight
  • Queen versus two bishops
  • Queen versus two knights.[68]

Positions where the stronger side can win in the ending of king and pawn versus king also generally require zugzwang to win.[a]

See also

[edit]

Notes

[edit]
  1. ^ There are several possibilities in the king and pawn versus king endgame. One is that the pawn can be captured before it promotes. Another one is that the pawn can promote without being blocked by the opposing king. The interesting cases are when the opposing king can block the pawn. In that case, whether or not the pawn can promote depends on the positions of the pieces and which side is to move. In the cases in which the pawn can be forced to promotion, zugzwang is required.

References

[edit]
  1. ^ Soltis 2003a, p. 78
  2. ^ Berlekamp, Conway & Guy 1982, p. 16
  3. ^ Elkies 1996, p. 136
  4. ^ Müller & Pajeken 2008, pp. 173
  5. ^ Gabor, Daniela (8 September 2022). "Zugzwang central banking (ECB edition)". Financial Times. Archived from the original on 17 September 2022. Retrieved 8 August 2023. Take the ECB, the posterchild for zugzwang central banking. It has four possible moves: raising rates, QT, holding rates and admitting regime defeat.
  6. ^ Bhopal, Raj S. (November 2020). "COVID-19 zugzwang: Potential public health moves towards population (herd) immunity". Public Health in Practice. 1: 100031. doi:10.1016/j.puhip.2020.100031. PMC 7361085. PMID 34173570.
  7. ^ Ohle, Maximilian; Cook, Richard J.; Han, Zhaoying (January 2020). "China's engagement with Kazakhstan and Russia's Zugzwang : Why is Nur-Sultan incurring regional power hedging?". Journal of Eurasian Studies. 11 (1): 86–103. doi:10.1177/1879366519900996. ISSN 1879-3665. Nevertheless, Russia has not yet entirely released itself from the zugzwang situation, as it has to further resort to reactionary acts to restrain a rising China, despite the fact that any move possible would further constrain Russia geopolitically stemming from Beijing's increasing power projection, chiefly in the economic domain (SREB).
  8. ^ a b c d Winter 1997
  9. ^ a b Winter 2008
  10. ^ a b Nunn 1995, p. 6
  11. ^ a b c Nunn 1999, p. 7
  12. ^ Soltis 2003a, p. 79
  13. ^ Davidson 1981, pp. 21–22, 41
  14. ^ Soltis 2009, p. 15
  15. ^ Angos 2005, pp. 108–9
  16. ^ Sukhin 2007, pp. 21, 23
  17. ^ Hooper & Whyld 1992, pp. 38–39
  18. ^ Philidor 2005, pp. 272–73
  19. ^ Lasker 1960, pp. 37–38
  20. ^ Walker 1846, p. 245
  21. ^ Shibut 2004, p. 297
  22. ^ Hooper 1970, pp. 196–97
  23. ^ van Perlo 2006, p. 479
  24. ^ Müller & Lamprecht 2001, p. 22
  25. ^ "Mastering the Art of Deception with Zwischenzug". Knightly Chess. Retrieved 12 June 2024.
  26. ^ Flear 2004, pp. 11–12
  27. ^ Fischer vs. Taimanov 1971
  28. ^ Wade & O'Connell 1972, p. 413
  29. ^ Kasparov 2004, p. 385
  30. ^ Nunn 1995, p. 7
  31. ^ Silman 2007, pp. 516–17
  32. ^ Averbakh 1984, pp. 113–14
  33. ^ Flear 2007, pp. 286–87
  34. ^ Soltis 2003b, p. 246
  35. ^ Flear 2007, p. 241
  36. ^ Tseshkovsky vs. Flear, 1988
  37. ^ Stiller 1996, p. 175
  38. ^ Müller & Pajeken 2008, p. 179
  39. ^ Hooper 1970, p. 21
  40. ^ Averbakh 1993, p. 35
  41. ^ Nunn 2002, p. 4
  42. ^ Flear 2004, p. 13
  43. ^ Dvoretsky 2003, p. 87
  44. ^ Dvoretsky 2006, p. 19
  45. ^ Müller & Pajeken 2008, pp. 179–80
  46. ^ Angos 2005, p. 178
  47. ^ Angos 2005, p. 183
  48. ^ Sämisch vs. Nimzowitsch
  49. ^ Reinfeld 1958, p. 90
  50. ^ Angos 2005, p. 180
  51. ^ Nunn 1981, p. 86
  52. ^ Horowitz 1971, p. 182
  53. ^ Golombek 1977
  54. ^ "Steinitz vs. Lasker, World Championship Match 1896–97". Retrieved 2008-12-24.
  55. ^ a b Reinfeld & Fine 1965, p. 71
  56. ^ Whyld 1967
  57. ^ Soltis 2005, pp. 89–90
  58. ^ Soltis 2005, p. 90
  59. ^ Crouch 2000, pp. 36–37
  60. ^ Soltis 1978, pp. 55–56
  61. ^ Fischer vs. Rossetto
  62. ^ Soltis 2003b, p. 34
  63. ^ Giddins 2007, p. 108
  64. ^ Fischer 2008, p. 42
  65. ^ Rowson 2005, p. 245
  66. ^ a b Andrew Soltis, "Going Ape", Chess Life, February 2008, pp. 10–11.
  67. ^ "Portisch vs. Tal, Candidates Match 1965". ChessGames.com. Retrieved 2009-03-30.
  68. ^ Soltis 2003a, pp. 78–79

Bibliography

Further reading

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