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On the distribution of winning moves in random game trees

Published online by Cambridge University Press:  17 April 2009

J. A. Flanigan
J. A. Flanigan
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90024, USA.
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Abstract

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In a natural way, associated with each rooted tree there exists a pair of two-person games, each game possessing the root as initial position. When a rooted tree is selected at random from the set of all rooted trees which possess {1, 2, …, n} as vertex set, the number of winning moves available to the first player to move in each of the associated games is a random variable. For fixed n, we determine the distribution of this random variable. As an immediate consequence, we find the probability that the first player to move has no winning move at all. The “saddlepoint method” is applied to a certain contour integral to obtain the asymptotic distribution of the number of winning moves as n → ∞.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 2 , October 1981 , pp. 227 - 237
Copyright
Copyright © Australian Mathematical Society 1981

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