Berlekamp E., Wolfe D. — Mathematical Go: Chilling Gets the Last Point :: Электронная библиотека попечительского совета мехмата МГУ

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Berlekamp E., Wolfe D. — Mathematical Go: Chilling Gets the Last Point

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Название: Mathematical Go: Chilling Gets the Last Point

Авторы: Berlekamp E., Wolfe D.

Аннотация:

Develops the mathematical techniques for solving late-stage endgame problems in the game Go. As a typical game of Go approaches its conclusion, the active areas of play become independent of one another and the overall board position may be regarded as a sum of disconnected partial board positions. The authors apply combinatorial game theory to solving Go-related problems with a bewildering choice of similar-looking moves and subtle priority relationships. The theory in this book assigns each active area on the board an abstract value and then shows how to compare them to select the optimum move or add them up to determine the ideal outcome. Some of the values are familiar numbers or fractions, but most are bizarre objects not seen before in Go literature. From these abstractions, the reader learns that positions seeming to have the same numerical value can be crucially different, while positions that appear completely different can be mathematically identical.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 235

Добавлена в каталог: 16.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$G^{n}$       102 193
$G^{\to n}$       102 193
$G_{1}$       193
$n \cdot \uparrow *$       50
$n \cdot \uparrow$       50
$\bar{(K)}$       70
$\downarrow$       19 50 193
$\epsilon$       96
$\ge$       47
$\hat{\Delta}$ , $\hat{\Delta}^{L}$ , $\hat{\Delta}^{R}$       79
$\int$       9 13 52 193 217
$\int_{s}^{t}$       52 214
$\le$       47
$\leftrightarrow$       22—25 50
$\leftrightarrow$ , $\leftrightarrow_{x} | 0^{n}$       23 58
$\leftrightarrow$ , $\leftrightarrow_{x} | 0^{n}$ , approximation of      68
$\mathcal{G}^{L}$ and $\mathcal{G}^{R}$       45
$\not {^{>}_{<}}$       47
$\uparrow *$       50 193
$\Uparrow |$       193
$\uparrow$       18 50 193
$\|$       47
(K)      70
*      16—18 50
+      22—25 50
+, $0^{n} | +_{x}$       23 58
0 (zero game)      48 193
9-dan      88
9-dan stumping problem      88
<      47
=      47
>      47
Active ko      119
Adjournments      123
Adjustments, one-point      142
Aesthetic goals of rules      118
Alive      see "Life"
Alternating sum      110
Ancient rules      115 116 123—125 128 131 207
Ancient rules, American      139
Ancient rules, Chinese      139
Anti-seki, official Japanese      165
Approximations      105
Approximations of $\leftrightarrow_{x} | 0^{n}$       68
Approximations, exploding error      106
artificial intelligence      2
Associate and sever phase      94
Atari      129 207
Atomic weight (uppitiness)      69 90 203 207
b or $b_{i}$ (blocked corridor values)      26 81
b-value      208
Bar: |      18 45
Bar: |, $\|$ , |||, ...      23 46
Basic shapes, traditional      152
Baum, Eric      xiii
Belle Black      3 57 208
Bent four in a corner      158—163
Bent four in a corner, maxim      160
Berlekamp, Elwyn      xi 33 45 48 50—52 52 102 115 127 150 208 213 214
Bichromatic, cyclic      136
Bichromatic, linear      136
Bichromatic, linear seki      135
Bidding phase      101
Big eye      115 129 156 157 208
Big eye, big eye-like      159
Big eye, central point      155
Big eye, invasion      155
Big opening move      108
black      57
Black, first move      117 138 141
Blockbusting      xii 52
Blocked corridor      9—13 26 65 81 197
Blocked corridor, general      196
Board size      117
bounds      105
Bounds on subgames      106
Bounds, exploding approximation error      106
Bouton, Charles      xi
Bozulich, Richard      xiii 124 164 165 207
Bulls      132
C programming language      7
Canonical form      7 40 43 47 49 54 106 128 193 208
Canonical incentives      51
Canonical players      166
Canonical resignation      141
Cantor, Georg      49
Capacity      100
Captives, removal      148
Captives, used to fill territory      148
Capturing rule      117 130 131 208
Catalog of rooms      70 202
Central point of big eye      155
Chen, Raymond      xiii 7 169
Chess      2 122
Chilled corridor      13
Chilled incentive      99
Chilled ko: (k)      70
Chilled marked value      71
Chilled value      13
Chilled, playing the chilled game      14 17 58
Chilling: $G_{1}$       xii 13 57 193 208
Chilling: $G_{1}$ , inverts warming      54
Chilling: $G_{1}$ , tax      13
Chinese komi      151
Chinese rules      115 116
Chinese territory      121
Cho Chikun 9-dan      162
Clipping      17 58
Cold game      50 208
Colors reversed      38
Combinatorial game theory      45 128
Combinatorial game theory, definitions      45
Combinatorial game theory, history      xi
Comparing games, four outcome classes      40 47
Competent player      152 208
Competitor      101
Complex kos      107
Complex scoring rules      124 125
Computer Go      3
Computer programs      7 33 45 105 169
Computer science      1—3
Condensed topological graph      135
Conditions of play      122
Configuration      135
Confirmation phase      123 150 208
Confirmation phase, Japanese      152
Consistency check      97
Consumer      100
Conway, Conway ko rule      149
Conway, Conway loops      150
Conway, John H.      xi 18 22 33 45 47 48 49 50—52 102 115 127 150 208 213
Conway, surreal numbers      49
Cooling: $G_{1}$       13 50 55 57 209
Cooling: $G_{1}$ , properties      51
Corner involvement      88
Corridor      9—12 65—68
Corridor, blocked      9—13 26 65 81 197
Corridor, blocked, general      196
Corridor, mated      94
Corridor, others      19 67
Corridor, sums of      68
Corridor, table of incentives      24 194
Corridor, unblocked      12 66
Corridor, unblocked, general      198
Corridor, unblocked, shortest      26 81
Cost      100
Count (of score)      xii
Dame      55 209
Dame in seki      119
Dan (Go ranking)      209

Dashed boundary lines      58
Davies, James      xiii
dead      115 146
Dead group      197
Dead stones      129 209
Dead stones along corridor      108
Dead stones in ancient territory      146—149
Dead stones, removal      148
Dead, Japanese      150
Dead, Japanese, official      164
Decomposition into configurations      135
Dedekind, Richard      49
Defective monochromatic configuration      156
Defective shape      154 209
Definitions, glossary      207—217
Definitions, summary of games      193
Difference game      2 7 38—40
Difference game, four outcome classes      40 47
Distribution contracts      100
Dominant move      209
Dominated option      40 47 209
Dominating purported incentives      79
Domineering      xii 52
Dots (markings)      10 65
Dots and Boxes      xi
Double-up-star: $\Uparrow *$       193
Double-up: $\Uparrow$       18 50 193
Down: $\downarrow$       19 50 193
draw      122
Dyadic rational      48 210
Earlier in the game      105
Earned immortality      149
Economist's view      100
Edge of board rooms      109
Effective independence      64
Elementary position      52 52—55 210
Encore      146 151 210
Equality of games      79 210
Erbach, David      3
Eternal life      120
Even position      52 210
Exploding approximation error      106
EXPTIME-complete      109
eye      115 129
Eye, big      129 156 157
Eye, big eye-like      159
Eye, false      129
Eye, fractional      107
Eye, living space      156
Eye, pair of      156
Eye, point      210
Eye, single      153 155
Fairbairn, John      117 132
False eye      129 153 210
False eye in seki      119
First move      117 138 141
Follower      46 210
Formal incentives      51
Foundations      128
Four in a corner      158—163
Four in a corner, maxim      160
Four in a line      156
Fractional eyes      107
Fractions      9—12
Freeze      51
Fujisawa, Kazunari      xiii
Full graph      133
G + H (sum)      46
Game      45 128 210
Game, combinatorial game theory      45
Game, game tree      23 210
Game, summary of definitions      193
Gardner, Martin      52
General blocked corridor      196
General unblocked corridor      198
Getting the last move      5
Glossary      207—217
Go playing programs      1—3 105
Gote      1—2 6 14 67 210
Gote, x point gote      67
Graph, condensed topological      135
Graph, full      133
Graveyard play      140
Greater-equals      210
Greedy      125 129 210
Greedy, ancient rules      124 125 128 129 132
Greedy, pass restriction      132
Grid of numbers      70
Group      129 211
Group of stones      133 135
Group, independently alive      118 129
Group, invading many corridors      80—84
Group, mathematical group      1 47
Group, unconnected      80
Grundy, Patrick      xi
Guru      128 152 166 211
Guy, Richard      xi 33 45 48 50—52 102 115 127 150 208 213
h-value      100
Hackenbush      xii
Half-integer komi      145
Handicap      117 211
Hane-seki      158
Hanner, Olaf      xi
Hardness results      109
Harmless (dead)      146
Haruyama Isamu 9-dan      122
Heating      211
High, Rob      xiii
History of combinatorial game theory      xi
History of Go      115
Honimbo Dosaku      7
Hoshi points      57
Hot game      50 211
Hot game, chilled rooms      204
Hot game, rooms      204
Hung outcome      121 150 211
IDLE      101
Ikeda, Toshio      116 163 164
Immortality      57 63 211
Immortality, bulls      132
Immortality, earned      149
Immortality, promotion to      149
Immortality, Tibetan initial conditions      132
Impartial games      xi
Implicit problem goal      150
Incentive      19—20 51 212
Incentive, canonical      51
Incentive, chilled      99
Incentive, formal      51
Incentive, left      51
Incentive, partial order of      69
Incentive, purported: $\hat{\delta}$ and $\hat{\Delta}$       79 214
Incentive, right      51
Incentive, table of      24 194
Incomparable      18 19 20 212
Independent life      115 118 129 137 156 212
Independent regions      19 61—64
Infinitesimal      14—26 49 68 88 108
Infinitesimal, $\epsilon$       96
Infinitesimal, chilled rooms      203
Infinitesimal, generalizing up-second      102—104
Infinitesimal, playing sums of      24—25 26 68 194
Ing Chang-Ki, Ing cup      115
Ing Chang-Ki, Ing Foundation      114
Ing Chang-Ki, Ing rules      115 116 124
Initial conditions      117 131 139
Initialize phase      101
Integer game      48 193
Integer-valued score      128
Intrusions into rooms/territories      70 202

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