The Combinatorics of Mancala-Type Games: Ayo, Tchoukaillon, and l/Pie

Around the world, hundreds of different kinds of mancala games have been observed [Deshayes et al. 1976; Murray 1978; Russ 19841, with some dating back to the Empire Age of ancient Egypt. Their common features involve cupshaped depressions called pits filled with seeds or stones. Players take turns harvesting stones by moving them around the board according to various rules. In this paper, we study two variants: The two-player game ayo, played by the Yoruba of western Nigeria, and the solitaire game Tchoukaillon, created by Deledicq and Popova [1977,1801 as a variant of the game Tchouka played in central Europe and in the East Indies.