Games of No Chance 3

by Edited by Michael H. Albert , Richard J. Nowakowski

• ISBN13: 9780521861342
• ISBN10: 0521861349
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-05-29
• Publisher: Cambridge University Press

Summary

This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.

Table of Contents

Preface	p. ix
Surveys	p. 1
Playing games with algorithms: Algorithmic combinatorial game theory	p. 3
Advances in losing	p. 57
Coping with cycles	p. 91
On day n	p. 125
Standards	p. 133
Goal threats, temperature, and Monte-Carlo Go	p. 135
A puzzling Hex primer	p. 151
Tigers and Goats is a draw	p. 163
Counting liberties in Go capturing races	p. 177
Backsliding Toads and Frogs	p. 197
Loopy games	p. 215
A library of eyes in Go, I: A life-and-death definition consistent with bent-4	p. 233
A library of eyes in Go, II: Monolithic eyes	p. 249
Complexity	p. 269
The complexity of Dyson Telescopes	p. 271
Amazons, Konane, and Cross Purposes are PSPACE-complete	p. 287
Impartial	p. 307
Monotonic sequence games	p. 309
The game of End-Wythoff	p. 329
On the geometry of combinatorial games: A renormalization approach	p. 349
More on the Sprague-Grundy function for Wythoff's game	p. 377
Theory of the small	p. 411
Yellow-Brown Hackenbush	p. 413
Ordinal partizan End Nim	p. 419
Reductions of partizan games	p. 437
Partizan Splittles	p. 457
Columns	p. 473
Unsolved problems in Combinatorial Games	p. 475
Bibliography of Combinatorial Games	p. 501
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