Journal of Integer Sequences, Vol. 21 (2018), Article 18.6.3

A Probabilistic Take-Away Game

Tony W. H. Wong and Jiao Xu
Department of Mathematics
Kutztown University of Pennsylvania
Kutztown, PA 19530


Alice and Bob are playing a very simple game. Each of them starts with a pile of n chips, and they take turns to remove 1 or 2 chips from their own pile randomly and independently with equal probability. The first player who removes all chips from their pile is the winner. In this paper, we find the winning probability for Bob and analyze a new integer sequence. We also show that this game is highly disadvantageous to the second player, which is counter-intuitive. Furthermore, we study several variations of this game and determine the winning probability for Bob in each case.

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(Concerned with sequences A265919 A265920.)

Received May 11 2016; revised versions received May 30 2017; January 21 2018. Published in Journal of Integer Sequences, August 22 2018.

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