Sources page biographical material

4.B.10. MU TORERE
This is a Maori game which can be found in several books on board games. I have included it because it has been completely analysed. There are eight (or 2n) points around a central area. Each player has four (or n) markers, originally placed on consecutive points. One can move from a point to an adjacent point or to the centre, or one can move from the centre to a point, provided the position moved to is empty. The first player who cannot move is the loser. To prevent the game becoming trivial, it is necessary to require that the first two (or one) moves of each player involve his end pieces, though other restrictions are sometimes given.
Marcia Ascher. Mu Torere: An analysis of a Maori game. MM 60 (1987) 90-100. Analyses the game with 2n points. For n = 1, there are 6 inequivalent positions (where equivalence is by rotation or reflection of the board) and play is trivially cyclic. For n = 2, there are 12 inequivalent positions, but there are no winning positions. For n = 3, there are 30 inequivalent positions, some of which are wins, but the game is a tie. Obtains the number of positions for general n. For the traditional version with n = 4, there are 92 inequivalent positions, some of which are wins, but the game is a tie, though this is not at all obvious to an inexperienced player. In 1856, it was reported that no foreigner could win against a Maori. For n = 5, there are 272 inequivalent positions, but the game is a easy win for the first player -- the constraints on first moves need to be revised. Ascher gives references to the ethnographic literature for descriptions of the game.

Marcia Ascher. Ethnomathematics. Brooks/Cole Publishing, Pacific Grove, California, 1991. Sections 4.4-4.7, pp. 95-109 & Notes 4-7, pp. 118-119. Amplified version of her MM article.