Zugzwang

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 passing the turn, if this were allowed, would be the best move.[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] 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] Katai, 9th century abcdefgh8877665544332211abcdefghWhite 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 abilities) 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. Kf4puts 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]

Polerio, 1585 abcdefgh8877665544332211abcdefghWhite to move and win

Philidor, 1777 abcdefgh8877665544332211abcdefghAfter 36.Kc3, Black is in zugzwang, since they must move their rook away from their king.

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? abcdefgh8877665544332211abcdefghWhite 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] 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]

Hooper & Whyld 1992, p. 458 abcdefgh8877665544332211abcdefghWhite to move draws; Black to move loses.

Flear 2004, p. 11 abcdefgh8877665544332211abcdefghBlack to move. Black is in zugzwang; any Black move allows White's king to create a passed pawn and win.

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 KQ v KR Philidor position. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies. Examples from games[edit]Fischer vs. Taimanov, second match game[edit]Fischer vs. Taimanov, 1971, game 2 abcdefgh8877665544332211abcdefghPosition 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. Kg6and 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 1–0Fischer vs. Taimanov, fourth match game[edit]Fischer vs. Taimanov, 1971, game 4 abcdefgh8877665544332211abcdefghPosition 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 Ne7Now the bishop is able to make a waiting move. It is able to do so while maintaining access to f7, so that it can reach e8 safely, where it attacks the pawn on g6 and restricts the black king from c6. 59. Bc4! Nc6 60. Bf7 Ne7 61. Be8and 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. Kxc5and 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 abcdefgh8877665544332211abcdefghPosition after 86.Ke5.