International Journal of Game Theory

, Volume 47, Issue 2, pp 695–705 | Cite as

Impartial poker nim

  • Craig TennenhouseEmail author
Original Paper


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 \(\mathcal {P}\)-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.


Combinatorial game Nim Geography 

Mathematics Subject Classification

91A46 05C 


  1. Albert MH, Nowakowski RJ, Wolfe D (2007) Lessons in play: an introduction to combinatorial game theory. Taylor & Francis/CRC Press, Boca RatonGoogle Scholar
  2. Berlekamp ER, Conway JH, Guy RK (2001) Winning ways for your mathematical plays, vol 2. AK Peters, Natick, MAGoogle Scholar
  3. Bouton CL (1901–1902) Nim, a game with a complete mathematical theory. Ann Math 3(14):35–39Google Scholar
  4. Fraenkel AS, Scheinerman ER, Ullman D (1993) Undirected edge geography. Theor Comput Sci 112:371–381CrossRefGoogle Scholar
  5. Fraenkel AS, Simonson S (1993) Geography. Theor Comput Sci 11o:197–214CrossRefGoogle Scholar
  6. Grundy PM (1939) Mathematics and games. Eureka 2:6–8Google Scholar
  7. Schaefer T (1978) On the complexity of some two-person perfect-information games. J Comput Sys Sci 16(2):185–225CrossRefGoogle Scholar
  8. Sprague R (1936) Uber mathematische Kampfspiele. Tohoku Math J 41:438–444Google Scholar
  9. Wythoff WA (1907/1909) A modification of the game of nim. Nieuw Arch Wisk 8:199–202Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of New EnglandBiddefordUSA

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