Mathematical Go endgames: nightmare for the professional Go player
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Jose [u.a.]
Ishi Press International
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | hardcover ed.: Mathematical Go by Peters Publ. |
| Beschreibung: | XX, 234 Seiten Illustrationen, Diagramme |
| ISBN: | 9780923891367 0923891366 |
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| adam_text | Contents Foreword ix Preface x* List of Figures xv 1 2 Introduction 1 1.1 Why studyGo ............................. 1.2 Easy (?) endgame problem ......................... 1.3 Teaser............................................................................................... 1.4 Useful programs ........................................................................... 2 3 7 7 An Overview 9 2.1 2.2 2.3 2.4 2.5 2.6 3 Fractions ................ Chilling............................................................................................ The need for more than just numbers . ................................... Ups, downs and stars............................. Tinies and minies .................................................................. Multiple invasions . ........................................................................ Mathematics of Games 9 13 14 16 22 26 31 Common concerns...................................... 31 Sums of games............................... 34 Difference games..................................................... 38 Simplifying games ...................... 40 3.4.1 Deleting dominated options.......................... 40 3.4.2 Reversing reversibleoptions . ........................ 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 3.1 3.2 3.3 3.4 v
CONTENTS vi 3.5.5 Incentives........................................................................... 3.6 Warming , . ................................................. 4 Go Positions 51 52 57 Conventions............................................. 57 A problem.............................. 58 Corridors....................................... 65 Sums of corridors........................................................................ . 68 Rooms . .......................... 70 Proofs ............ ................................................................... 79 Group invading many corridors.................................. .............. 80 Another problem........... ................................. 85 9-dan stumping problem ................................................. ............ 88 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 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 5 Further Research 105 5.1 Applying the theory earlier in the game ............ 5.2 Approximate results............................... 5.3 Kos ........................................... 5.4 Life and death . ......................... 5.5 The last play .....................................................
5.6 Extensions of current results...................... ... ...................... ... . 5.7 Hardness results..................................... 105 105 106 107 108 108 109 A Rules of Go — A Top-down Overview A.l A.2 A.3 A.4 A.5 A.6 A.7 A.8 113 Rulesets can (rarely) yield differing results ......................... ... . 114 Who has used these different rulesets?.........................................114 Top-down view of rule options........................................................ 116 Interpretations of territories........................................... 121 Loopy play and hung outcomes..................................................... 121 Protocol..................... 122 References to official rules........................ 124 Overview .............................................................................. 124
CONTENTS B Foundations of the Rules of Go vìi 127 B.l 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 ín a corner......................... 158 B.5.7 Positions which stress the fine print, of Japanese rules 163
viii C CONTENTS Problems 169 D Solutions to Problems 179 E 189 Summary of Games 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
|
| adam_txt |
Contents Foreword ix Preface x* List of Figures xv 1 2 Introduction 1 1.1 Why studyGo . 1.2 Easy (?) endgame problem . 1.3 Teaser. 1.4 Useful programs . 2 3 7 7 An Overview 9 2.1 2.2 2.3 2.4 2.5 2.6 3 Fractions . Chilling. The need for more than just numbers . . Ups, downs and stars. Tinies and minies . Multiple invasions . . Mathematics of Games 9 13 14 16 22 26 31 Common concerns. 31 Sums of games. 34 Difference games. 38 Simplifying games . 40 3.4.1 Deleting dominated options. 40 3.4.2 Reversing reversibleoptions . . 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 3.1 3.2 3.3 3.4 v
CONTENTS vi 3.5.5 Incentives. 3.6 Warming , . . 4 Go Positions 51 52 57 Conventions. 57 A problem. 58 Corridors. 65 Sums of corridors. . 68 Rooms . . 70 Proofs . . 79 Group invading many corridors. '. 80 Another problem. . 85 9-dan stumping problem . . 88 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 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 5 Further Research 105 5.1 Applying the theory earlier in the game . 5.2 Approximate results. 5.3 Kos . 5.4 Life and death . . 5.5 The last play .
5.6 Extensions of current results. . . . . 5.7 Hardness results. 105 105 106 107 108 108 109 A Rules of Go — A Top-down Overview A.l A.2 A.3 A.4 A.5 A.6 A.7 A.8 113 Rulesets can (rarely) yield differing results . . . 114 Who has used these different rulesets?.114 Top-down view of rule options. 116 Interpretations of territories. 121 Loopy play and hung outcomes. 121 Protocol. 122 References to official rules. 124 Overview . 124
CONTENTS B Foundations of the Rules of Go vìi 127 B.l 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 ín a corner. 158 B.5.7 Positions which stress the fine print, of Japanese rules 163
viii C CONTENTS Problems 169 D Solutions to Problems 179 E 189 Summary of Games 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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| spelling | Berlekamp, Elwyn R. 1940-2019 Verfasser (DE-588)123359732 aut Mathematical Go endgames nightmare for the professional Go player Elwyn Berlekamp ; David Wolfe San Jose [u.a.] Ishi Press International 1994 XX, 234 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier hardcover ed.: Mathematical Go by Peters Publ. 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 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034046767&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berlekamp, Elwyn R. 1940-2019 Wolfe, David 1964- Mathematical Go endgames nightmare for the professional Go player 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 |
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| title | Mathematical Go endgames nightmare for the professional Go player |
| title_auth | Mathematical Go endgames nightmare for the professional Go player |
| title_exact_search | Mathematical Go endgames nightmare for the professional Go player |
| title_exact_search_txtP | Mathematical Go endgames nightmare for the professional Go player |
| title_full | Mathematical Go endgames nightmare for the professional Go player Elwyn Berlekamp ; David Wolfe |
| title_fullStr | Mathematical Go endgames nightmare for the professional Go player Elwyn Berlekamp ; David Wolfe |
| title_full_unstemmed | Mathematical Go endgames nightmare for the professional Go player Elwyn Berlekamp ; David Wolfe |
| title_short | Mathematical Go endgames |
| title_sort | mathematical go endgames nightmare for the professional go player |
| title_sub | nightmare for the professional Go player |
| 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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