Games of No Chance 6

Author: Urban Larsson Series: Mathematical Sciences Research Institute Publications

Hardcover

Discover the tools required to learn how to win (even more) games by seeing the underlying mathematical structure.

This edited volume surveys Richman bidding combinatorial games, classical subtraction games and absolute additive theory. The recurring list of open problems, updated and annotated, will interest all practitioners of CGT and related fields including algebra, computer science, combinatorics, number theory and classical game theory.

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Summary

Discover the tools required to learn how to win (even more) games by seeing the underlying mathematical structure.

Description

This collection of 22 research papers and state-of-the-art surveys extends the subseries 'Games of No Chance' pioneered in 1996. Survey topics include Richman bidding combinatorial games, classical subtraction games and absolute additive theory. Other topics discussed include extensions of normal play theory such as Absolute CGT and Affine normal play; additive theory; aspects of generic impartial games arising from the study of nim-values; dead-ending misère reduction theorems; Wythoff-type variations; complexity issues; and aspects of classical games including a rigorous justification of the celebrated result that king, bishop and knight can checkmate a lonely king on an arbitrarily large chessboard. The recurring list of open problems, updated and annotated, will interest all practitioners of CGT and related fields including algebra, computer science, combinatorics, number theory and classical game theory.

Critic Reviews

'Games of No Chance are games with perfect information like Chess (about which chapter 15 says something new). They were pioneered by the renowned mathematicians Berlekamp, Conway and Guy. This volume demonstrates how this original and playful but serious branch of mathematics flourishes and grows.' Bernhard von Stengel, London School of Economics and Political Science

About the Author

Urban Larsson is an associate professor at the Department of Industrial Engineering and Operations Research at the Indian Institute of Technology, Bombay, India. He is a worldwide researcher and teacher in combinatorial game theory, and organizes workshops and conferences on this subject. He has won awards such as the Killam Fellowship, and he is the editor of the volumes 'Games of No Chance 5' (2019), and IJGT's 'Special Issues on Combinatorial Game Theory' (2018 and 2025). He publishes regularly in the top journals of the field, with 24 accepted/published papers in the last five years, and he has more than 50 co-authors.