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The combinatorics of Mancala-type games: Ayo, Tchoukaitlon, and 1/pi

Duane M. Broline·Daniel E. Loeb
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Abstract

Certain endgame considerations in the two-player Nigerian Mancala-type game Ayo can be identified with the problem of finding winning positions in the solitaire game Tchoukaitlon. The periodicity of the pit occupancies in $s$ stone winning positions is determined. Given $n$ pits, the number of stones in a winning position is found to be asymptotically bounded by $n^{2}/π$.

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Duane M. Broline, Daniel E. Loeb. 1995-02-09. The combinatorics of Mancala-type games: Ayo, Tchoukaitlon, and 1/pi. https://arxiv.org/abs/math/9502225

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