Zugzwang (; ) 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.
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. 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. 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.
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 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.
Etymology The word comes from German 'move' + 'compulsion', so that means 'being forced to make a move'. Originally the term was used interchangeably with the term 'obligation to make a move' as a general game rule. Games like chess and checkers have "zugzwang" (or "zugpflicht"): a player 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.
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.
History
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 abilities) have been chess pieces since the earliest versions of the game.
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.
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 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 , 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 (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".
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#.
Zugzwang in chess 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.
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".
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 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. 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 vs. KR Philidor position. Zugzwang is a mainstay of chess compositions and occurs frequently in endgame studies.
Examples from games
Fischer vs. 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 and Black is again in zugzwang. The game ended shortly (because the pawn will slip through and promote): 87... Nf3 88. h7 Ne5+ 89. Kf6
Fischer vs. Taimanov, fourth match game
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 Now 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. Be8 and Black is in zugzwang. Knights are unable to lose a tempo, so moving the knight would allow the bishop to capture the 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 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 vs. 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.
Reciprocal zugzwang
A special case of zugzwang is reciprocal zugzwang (also known as mutual zugzwang): a position that is in zugzwang regardless of which player's turn it is to move. The study of reciprocal zugzwang positions is considered part of endgame theory. In combinatorial game theory, a mutual zugzwang position is closely related to John Conway's concept of a zero game – one in which the player to move automatically loses.
In practice, a reciprocal zugzwang position must have been reached by a previous move by one of the players, so only the player to move is actually in zugzwang. However, the other player must play carefully because one inaccurate move can often result in zugzwang themselves, for example by returning to the same position but on the other player's turn. That is unlike regular zugzwang, in which the superior side usually has a or can triangulate to put the opponent in zugzwang.
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 because White must either stalemate Black with 1.Kc6 or allow Black to the pawn. Because each side would be in zugzwang if it were their move, it is a reciprocal zugzwang.
Trébuchet
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. 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.
Mined squares
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 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.
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 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.
Zugzwang in middlegames and complex endgames Alex Angos notes that, "As the number of pieces on the board increases, the probability for zugzwang to occur decreases." As such, zugzwang is very rarely seen in the middlegame.
Sämisch vs. Nimzowitsch