Impartial poker nim

摘要

The combinatorial game of nim is well-studied, along with many impartial and partizan modifications. We develop a new impartial modification using the idea of bogus nim heaps and preventing loops. We completely characterize the $$mathcal {P}$$ P -positions for the two-heap version, and solve the problem for a larger number of heaps dependent on counting integer partitions of a fixed size.