ON MISERE GAMES
Ranan B. Banerji, CHARLES A. DUNNING · Cybernetics & Systems · 1992
Kayles is a nonpartizan two-person game. In such games the moves available to both the players are the same and either the player on move wins or the previous player wins. In the “normal form” of the game, the last player who can make a move is declared the winner. In the “misere form” of the game, the player who makes the last move is declared the loser. The complete analysis of the normal form of the game of Kayles has been described by Berlekamp, Conway, and Guy. This paper completes their analysis of the misere form of Kayles. This is done on the basis of certain properties of what have been called “wild” positions of misere games.