LibraryPhysical Science & MathMathematics

Some Notes on Game Bounds

by Silva Jorg

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Institution: University of California at Berkeley
Advisor(s): E. Berlekamp
Degree: Master of Arts, Mathematics
Year: 1991
Volume: 19 pages
ISBN-10: 1581120214
ISBN-13: 9781581120219

Abstract

Combinatorial Games are a generalization of real numbers. Each game has a recursively defined complexity (birthday). In this paper we establish some game bounds. We find some limit cases for how big and how small a game can be, based on its complexity. For each finite birthday, N, we find the smallest positive number and the greatest game born by day N, as well as the smallest and the largest positive infinitesimals. As for each particular birthday we provide the extreme values for those types of games, these results extend those in [1, page 214]. The main references in the theory of combinatorial games are ONAG [1] and WW [2]. We'll use the notation and some fundamental results from WW---mainly from its first six chapters---to establish some bounds to the size of the games.

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