Chapter 15

Theory of Combinatorial Games

Aviezri S. Fraenkel*    * Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel Robert A. Hearn     H3 Labs LLC, Palo Alto, CA, USAAaron N. Siegel     Twitter, San Francisco, CA, USA

Abstract

Aim: To present a systematic development of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend from Nim to Chess and Go in small strides at a gradient that is not too steep. Presentation: Mostly informal; examples of combinatorial games sampled from various strategic viewing points ...

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