P-positions in modular extensions to Nim

Tanya Khovanova () and Karan Sarkar

International Journal of Game Theory, 2017, vol. 46, issue 2, No 12, 547-561

Abstract: Abstract In this paper, we consider a modular extension to the game of Nim, which we call m-Modular Nim, and explore its optimal strategy. In m-Modular Nim, a player can either make a standard Nim move or remove a multiple of m tokens in total. We develop a winning strategy for all m with 2 heaps and for odd m with any number of heaps.

Keywords: Combinatorial games; Nim; P-positions; Modular arithmetic; Self-similarity (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00182-016-0545-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0545-7

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-016-0545-7

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().