Mathematical Go: chilling gets the last point
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wellesley, Mass.
Peters
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | paperback ed.: Mathematical Go endgames by Ishi Pr. Internat. |
| Beschreibung: | XX, 234 S. graph. Darst. |
| ISBN: | 9780923891367 0923891366 |
Internformat
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| 245 | 1 | 0 | |a Mathematical Go |b chilling gets the last point |c Elwyn Berlekamp ; David Wolfe |
| 264 | 1 | |a Wellesley, Mass. |b Peters |c 1994 | |
| 300 | |a XX, 234 S. |b graph. Darst. | ||
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| 500 | |a paperback ed.: Mathematical Go endgames by Ishi Pr. Internat. | ||
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Datensatz im Suchindex
| _version_ | 1804124548489019392 |
|---|---|
| adam_text | Contents
Foreword be
Preface xi
List of Figures xv
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
3.4.1 Deleting dominated options 40
3.4.2 Reversing reversible options 41
3.5 Combinatorial game theory 45
3.5.1 Definitions 45
3.5.2 Canonical forms 47
3.5.3 Examples of games 48
3.5.4 Cooling 50
v
vi CONTENTS
3.5.5 Incentives 51
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
4.10.1 Consistency check 97
4.10.2 Another example 99
4.10.3 A realistic example 100
4.10.4 The economist s view 100
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.I 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
CONTENTS vii
B Foundations of the Rules of Go 127
B.I Abstract 127
B.2 Ancient Go 129
B.2.1 The capturing rule 130
B.2.2 Ancient rules 131
B.2.3 Historical note 132
B.2.4 Greedy ancient Go 132
B.2.5 Groups of stones and topological configurations .... 133
B.2.6 Decomposition of a TGAP into a sum of configurations 135
B.2.7 Proof of completeness of the list of configurations . . . 136
B.2.8 Definitions of seki and independent life 137
B.3 Local versions of the ancient rules 137
B.3.1 Philosophical revision of the ancient rules 137
B.3.2 American score = Chinese score 138
B.3.3 Komi 139
B.3.4 Five variations on the ancient rules 139
B.3.5 Mathematized ancient rules 140
B.3.6 Parity 141
B.3.7 One point adjustments among C, J, and MU 142
B.3.8 The mathematized half integer komi 145
B.4 Modeling by mathematical rules 145
B.4.1 Foreseeing the terminal configurations 145
B.4.2 Dead stones in ancient territory 146
B.4.3 Modernized territory in living regions 149
B.4.4 Earned immortality 149
B.4.5 Ko playing, a la Conway 149
B.4.6 Ko playing, a la Japanese confirmation phase 150
B.4.7 Chinese komi 151
B.4.8 Mathematical rules which approximate the Japanese
ko scoring rule 151
B.4.9 Encore formally defined 151
B.5 Traditional basic shapes 152
B.5.1 False eyes and sockets 152
B.5.2 Sequences of sockets 153
B.5.3 Defective shapes in TGAP imposters 154
B.5.4 Semi terminal ancient positions 157
B.5.5 Other terminal ancient positions 158
B.5.6 Bent 4 in a corner 158
B.5.7 Positions which stress the fine print of Japanese rules 163
viii CONTENTS
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
|
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| isbn | 9780923891367 0923891366 |
| language | English |
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| spelling | Berlekamp, Elwyn R. 1940-2019 Verfasser (DE-588)123359732 aut Mathematical Go chilling gets the last point Elwyn Berlekamp ; David Wolfe Wellesley, Mass. Peters 1994 XX, 234 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier paperback ed.: Mathematical Go endgames by Ishi Pr. Internat. Go (Jeu) Go (Jeu) - Modèles mathématiques Go (spel) gtt Wiskundige modellen gtt Mathematisches Modell Go (Game) Go (Game) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Go Spiel (DE-588)4071909-1 gnd rswk-swf Go Spiel (DE-588)4071909-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Wolfe, David 1964- Verfasser (DE-588)1213530741 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006743696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berlekamp, Elwyn R. 1940-2019 Wolfe, David 1964- Mathematical Go chilling gets the last point Go (Jeu) Go (Jeu) - Modèles mathématiques Go (spel) gtt Wiskundige modellen gtt Mathematisches Modell Go (Game) Go (Game) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Go Spiel (DE-588)4071909-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4071909-1 |
| title | Mathematical Go chilling gets the last point |
| title_auth | Mathematical Go chilling gets the last point |
| title_exact_search | Mathematical Go chilling gets the last point |
| title_full | Mathematical Go chilling gets the last point Elwyn Berlekamp ; David Wolfe |
| title_fullStr | Mathematical Go chilling gets the last point Elwyn Berlekamp ; David Wolfe |
| title_full_unstemmed | Mathematical Go chilling gets the last point Elwyn Berlekamp ; David Wolfe |
| title_short | Mathematical Go |
| title_sort | mathematical go chilling gets the last point |
| title_sub | chilling gets the last point |
| topic | Go (Jeu) Go (Jeu) - Modèles mathématiques Go (spel) gtt Wiskundige modellen gtt Mathematisches Modell Go (Game) Go (Game) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Go Spiel (DE-588)4071909-1 gnd |
| topic_facet | Go (Jeu) Go (Jeu) - Modèles mathématiques Go (spel) Wiskundige modellen Mathematisches Modell Go (Game) Go (Game) Mathematical models Go Spiel |
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