NDLI: Building Nim

Content Provider	Springer Nature Link
Author	Larsson, Urban Duchêne, Eric Heubach, Silvia Dufour, Matthieu
Copyright Year	2015
Abstract	The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games as e.g. nine-men’s morris): first building, where players alternate to put one token on one of the, initially empty, stacks until all tokens have been used. Then, the players play nim. Of course, because the solution for the game of nim is known, the goal of the player who starts nim play is a placement of the tokens so that the Nim-sum of the stack heights at the end of building is different from 0. This game is trivial if the total number of tokens is odd as the Nim-sum could never be 0, or if both the number of tokens and the number of stacks are even, since a simple mimicking strategy results in a Nim-sum of 0 after each of the second player’s moves. We present the solution for this game for some non-trivial cases and state a general conjecture.
Ending Page	873
Page Count	15
Starting Page	859
File Format	PDF
ISSN	00207276
e-ISSN	14321270
Journal	International Journal of Game Theory
Issue Number	4
Volume Number	45
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-08-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Combinatorial games Behavioral/Experimental Economics Nim 2-person games Combinatorial game Economic Theory/Quantitative Economics/Mathematical Methods Operation Research/Decision Theory Game Theory, Economics, Social and Behav. Sciences
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Social Sciences Economics and Econometrics Statistics, Probability and Uncertainty

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