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Endgames in Fog of War Chess

Authors Matthias Gehnen , Julius Stannat

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LIPIcs.FUN.2026.21.pdf
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  • 20 pages

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Subject Classification

ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
Keywords
  • Chess
  • Endgame
  • King
  • Queen
  • Rook

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Abstract

Fog of War chess is a popular variant of classical chess, in which both players have only partial information about the position of the opponent’s pieces. This study provides the first theoretical analysis of endgames in Fog of War chess. In particular, we analyze the setups king and queen versus king, king and rook versus king, and king and two rooks versus king. We show that a king and queen can always guarantee a win against a lone king. In contrast to classical chess, a king and a rook cannot guarantee a win against a lone king. However, adding one more rook guarantees a win.

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Matthias Gehnen and Julius Stannat. Endgames in Fog of War Chess. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.21

Author Details

Matthias Gehnen
  • RWTH Aachen University, Germany
Julius Stannat
  • RWTH Aachen University, Germany

References

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  7. MIT Hardness Group, Della Hendrickson, and Andy Tockman. Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants. In FUN 2024, 2024. Google Scholar
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  9. Jens Bæk Nielsen. Darkness chess. https://www.chessvariants.com/incinf.dir/darkness.html, 1997. Accessed: 2026-01-06.
  10. Brian Hu Zhang and Tuomas Sandholm. General search techniques without common knowledge for imperfect-information games, and application to superhuman fog of war chess. arXiv preprint arXiv:2506.01242, 2025. URL: https://doi.org/10.48550/arXiv.2506.01242.
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