Analysis of One Pile Misére NIM for Two Alliances
The traditional game of Nim is an impartial game for two players that plays a central role in combinatorial game theory. The analysis of the two-player game relies on binary representations of numbers, see [1,2]. However, the game for three or more players has not been studied extensively. In this paper, we will consider a one-pile Nim misére version for more than two players. Typically, the strategy for the game of one-pile Nim with three or more players cannot be completely determined without considering alliances. The paper  establishes the basic terminology and certain fundamental results for the game with three or more players. The current paper expands it to a general result.
Kelly, A.R. (2011). Analysis of One Pile Misére NIM for Two Alliances. Rocky Mountain Journal of Mathematics, 41(6), pp. 895-1906. https://doi.org/10.1216/RMJ-2011-41-6-1895
Virtual Commons Citation
Kelly, Annela (2011). Analysis of One Pile Misére NIM for Two Alliances. In Mathematics Faculty Publications. Paper 62.
Available at: http://vc.bridgew.edu/math_fac/62