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Queen reflections: a modification of Wythoff Nim

Author

Listed:
  • Robbert Fokkink

    (Delft University of Technology)

  • Dan Rust

    (The Open University)

Abstract

Wythoff Nim is a classical combinatorial game of queen moves on a chessboard. There are many ways to describe its P-positions (safe positions to move to). One way is to code them by the Fibonacci word 010010100100101..., which is the unique fixed point of the substitution of 0 by 01, and of 1 by 0. The coordinates of the n-th P-position are encoded by the location of the n-th zero and the n-th one in the Fibonacci word. We show that a minor modification of the rules of Wythoff Nim leads to a game with P-positions that are coded by 010010010010100100... This word can be derived by deleting all 2’s from the Tribonacci word, which is the unique fixed point of the substitution of 0 by 01, of 1 by 02, and of 2 by 0.

Suggested Citation

  • Robbert Fokkink & Dan Rust, 2024. "Queen reflections: a modification of Wythoff Nim," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(4), pages 1099-1117, December.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:4:d:10.1007_s00182-022-00824-1
    DOI: 10.1007/s00182-022-00824-1
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