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 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.
  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. ^ Cite error: The named reference winter97 was invoked but never defined (see the help page).
  9. ^ Cite error: The named reference winter08 was invoked but never defined (see the help page).
  10. ^ Cite error: The named reference nunn95p6 was invoked but never defined (see the help page).
  11. ^ Nunn 1999, p. 7