One‐pile misère Nim for three or more players
Annela R. Kelly · International Journal of Mathematics and Mathematical Sciences · 2006
The analysis of the classical game of Nim relies on binary representation of numbers as shown in the books of Berlekamp and Gardener. There is considerable interest in generalizations and modifications of the game. We will consider one‐pile misère Nim for more than two players. In the case of three or more players, the impartial game theory results rarely apply. In this note, we analyze the game in a variety of cases where alliances are formed among the players.