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Generalized genus sequences for misère octal games

Author

Listed:
  • D. T. Allemang

    (Department of Computer Science, Boston University, Boston, MA 02215, USA)

Abstract

Two approaches have been used to solve impartial games with misère play; genus theory, which has resulted in a number of results summarized in [2], and Sibert-Conway decomposition [9], which has been used to solve the octal game 0.77 (known as Kayles). The main aim of this paper is to publish (for the first time) the results archived in [1], extending genus theory beyond the applications to which it has previously been applied. In addition, we extend a result from [6] to misère play by adapting it to use the extended genus theory. The resulting theorems require extensive calculations to verify that their preconditions hold for any particular games. These calculations have been carried out by computer for all two-digit octal games. For many of these games, this has resulted in complete solutions. Complete solutions are presented for four games listed in [8] as unsolved.

Suggested Citation

  • D. T. Allemang, 2002. "Generalized genus sequences for misère octal games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 539-556.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:4:p:539-556
    Note: Received: September 2001
    as

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