The combinatorics of Mancala-type games: Ayo, Tchoukaitlon, and 1/pi
Duane M. Broline, Daniel E. Loeb
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 n2/π.
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