Analysis of one pile misère Nim for two alliances
The traditional game of Nim is a two-player combinatorial game which has been well analyzed. The current paper deals with a one-pile game for three or more players that follows the rules for misère Nim for each player, and is called Survivor Nim. It is assumed that the players form two alliances, that each player is in exactly one alliance, and that each player will support the interests of his alliance as long as it benefits his own interests. The author introduced this game in the earlier paper [``One-pile Nim for three or more players'', Int. J. Math. Math. Sci. 2006, No. 16, Article ID 40796, 8 p. (2006; Zbl 1151.91379)] and established some fundamental results. The current paper extends the work to a general result. The main theorem shows that if the game starts with a sufficiently large pile of counters, the larger alliance will win, no matter how the alliance members are distributed.
scientific article; zbMATH DE number 5996730