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Mathematical Go: Chilling Gets the Last Point »

Authors: Elwyn R. Berlekamp, David Wolfe
ISBN-13: 9781568810324, ISBN-10: 1568810326
Format: Hardcover
Publisher: CRC Press
Date Published: January 1994
Edition: (Non-applicable)

Author Biography: Elwyn R. Berlekamp

Book Synopsis

The ancient game of Go is one of the less obvious candidates for mathematical analysis. With the development of new concepts in combinatorial game theory, the authors have been able to analyze Go games and find solutions to real endgame problems that have stumped professional Go players. Go players with an interest in mathematics and mathematicians who work in game theory will not want to miss this book because it describes substantial connections between the two subjects that have been, until now, largely unrecognized.

Booknews

Presents mathematical techniques for solving late-stage endgame problems. Uses combinational game theory, which Berlekamp (mathematics, UC Berkeley) helped develop, to solve Go-related problems. The theory presented assigns each active area on the board an abstract value and shows how to compare them to select the optimum move or add them up to determine the ideal outcome. Values can be familiar numbers and fractions, or other abstractions. Includes an overview of the mathematics of games, Go rules and history, and a glossary. Annotation c. Book News, Inc., Portland, OR (booknews.com)

	Foreword
	Preface
	List of Figures
1	Introduction	1
1.1	Why study Go	2
1.2	Easy (?) endgame problem	3
1.3	Teaser	7
1.4	Useful programs	7
2	An Overview	9
2.1	Fractions	9
2.2	Chilling	13
2.3	The need for more than just numbers	14
2.4	Ups, downs and stars	16
2.5	Tinies and minies	22
2.6	Multiple invasions	26
3	Mathematics of Games	31
3.1	Common concerns	31
3.2	Sums of games	34
3.3	Difference games	38
3.4	Simplifying games	40
3.5	Combinatorial game theory	45
3.6	Warming	52
4	Go Positions	57
4.1	Conventions	57
4.2	A problem	58
4.3	Corridors	65
4.4	Sums of corridors	68
4.5	Rooms	70
4.6	Proofs	79
4.7	Group invading many corridors	80
4.8	Another problem	85
4.9	9-dan stumping problem	88
4.10	Multiple sockets	93
4.11	Infinitesimals generalizing up-second	102
5	Further Research	105
5.1	Applying the theory earlier in the game	105
5.2	Approximate results	105
5.3	Kos	106
5.4	Life and death	107
5.5	The last play	108
5.6	Extensions of current results	108
5.7	Hardness results	109
	A Rules of Go - A Top-down Overview	113
A.1	Rulesets can (rarely) yield differing results	114
A.2	Who has used these different rulesets?	114
A.3	Top-down view of rule options	116
A.4	Interpretations of territories	121
A.5	Loopy play and hung outcomes	121
A.6	Protocol	122
A.7	References to official rules	124
A.8	Overview	124
	B Foundations of the Rules of Go	127
B.1	Abstract	127
B.2	Ancient Go	129
B.3	Local versions of the ancient rules	137
B.4	Modeling by mathematical rules	145
B.5	Traditional basic shapes	152
	C Problems	169
	D Solutions to Problems	179
	E Summary of Games	189
	Examples of Go positions with simple values	189
	Combinatorial game theory summary	193
	Summary of incentives	194
	Generalized corridor invasions	196
	Summary of rooms	202
F	Glossary	207
	Bibliography	219
	Index	223

Subjects

Game Books

Go
Entertainment