Zugzwang

Zugzwang (German for "compulsion to move", ) is a situation found usually in chess, but also in various other games, where one player is put at a disadvantage because he has to make a move when he would prefer 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 was his opponent's turn to move.

The term finds its formal definition in combinatorial game theory, where 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, i.e., 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). Putting the opponent in zugzwang is a common way to help the superior side win a game. In some cases 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 his position is said to be in zugzwang (Soltis 2003a:78). Thus every move would make his position worse, and he would be better off if he 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).

The term zugzwang was used in German-language chess literature in 1858 (or earlier) (Winter 1997). The first known use of the term in English was by World Champion Emanuel Lasker in 1905 (Winter 2008). The concept of zugzwang (as distinguished from the word) must have been known to players many centuries earlier, since it is necessary to win the elementary king and rook versus king endgame, among others. The concept is also seen in an endgame study published in 1604 by Alessandro Salvio, one of the first writers on the game. It also appeared in Shatranj studies dating back to the early 9th century, over 1000 years before the first known use of the term zugzwang.

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 (Károlyi & Aplin 2007:358). National Master Alex Angos wrote an entire book about zugzwang, You Move ... I Win! (Angos 2005). According to John Nunn, positions of reciprocal zugzwang (see below) are surprisingly important in the analysis of endgames (Nunn 1995:6), (Nunn 1999:7).