Generalized genus sequences for misère octal games

D. T. Allemang ()
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D. T. Allemang: Department of Computer Science, Boston University, Boston, MA 02215, USA

International Journal of Game Theory, 2002, vol. 30, issue 4, 539-556

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.

Keywords: Impartial; games; ·; Genus; sequence; ·; misère; play. (search for similar items in EconPapers)
Date: 2002-05-27
Note: Received: September 2001
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