Playing Konane mathematically: A combinatorial game-theoretic analysis

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“Playing Konane mathematically: A combinatorial game-theoretic analysis” by Michael D. Ernst. UMAP Journal, vol. 16, no. 2, Spring 1995, pp. 95-121.
A previous version appeared as Microsoft Research technical report MSR-TR-95-24, (Redmond, WA), August 7, 1995.
A previous version appeared as “Playing Konane mathematically” by Michael D. Ernst and Elwyn Berlekamp. In Articles in Tribute to Martin Gardner, (Scott Kim, ed.), January 16, 1993, pp. 6-15, Atlanta International Museum of Art and Design.

Abstract

This article presents a combinatorial game-theoretic analysis of Konane, an ancient Hawaiian stone-jumping game. Combinatorial game theory [Berlekamp et al. 1982] applies particularly well to Konane because the first player unable to move loses and because a game often can be divided into independent subgames whose outcomes can be combined to determine the outcome of the entire game. By contrast, most popular modern games violate the assumptions of combinatorial game-theoretic analysis. This article describes the game of Konane and the ideas of combinatorial game theory, derives values for a number of interesting positions, shows how to determine when a game can be divided into noninteracting subgames, and provides anthropological details about Konane.

Download: PDF, PostScript, talk slides (PowerPoint, 1/17/2001), implementation.

BibTeX entry:

@article{Ernst95:Konane,
   author = {Michael D. Ernst},
   title = {Playing {Konane} mathematically: A combinatorial
	game-theoretic analysis},
   journal = {UMAP Journal},
   volume = {16},
   number = {2},
   pages = {95--121},
   month = {Spring},
   year = {1995}
}

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