Elwyn R. Berlekamp, John Horton Conway, Richard K. Guy1568811438, 9781568811437, 1568811306, 156881142X, 1568811446
In Volume 3, the authors examine Games played in Clubs, giving case studies for coing and paper-and-pencil games, such as Dots-and-Boxes and Nimstring.
Table of contents :
Title page……Page 1
Date-line……Page 2
Dedication……Page 3
Authors……Page 5
Contents……Page 7
Preface to the Second Edition……Page 15
Preface to the Original Edition……Page 16
Games in Clubs!……Page 19
Turning Turtles……Page 21
Odious and Evil Numbers……Page 23
The Mock Turtle Theorem……Page 24
Why Moebius?……Page 26
Mogul……Page 27
The Ruler Game……Page 29
Turnips (or Ternups)……Page 30
Grunt……Page 32
Turning Corners……Page 33
Nim-Multiplication……Page 35
Swirling Tartans……Page 36
The Tartan Theorem……Page 37
Rugs, Carpets, Windows and Doors……Page 38
Acrostic Games……Page 42
Uglification and Derision……Page 43
“Coins” (or Heaps) with Infinitely Many (or $2^{2^N}$) “Sides”……Page 48
References and Further Reading……Page 49
The Silver Dollar Game……Page 51
Profit from Gaming Tables……Page 52
Antonim……Page 53
Synonim……Page 54
Simonim……Page 56
Staircase Fives……Page 59
Twopins (pronounced “Tuppins”)……Page 60
Cram……Page 62
Welter’s Game……Page 66
The Congruence Modulo 16……Page 67
Frieze Patterns……Page 69
Inverting the Welter Function……Page 70
The Abacus Positions……Page 72
The Abacus Strategy……Page 73
The Misere Form of Welter’s Game……Page 74
Kotzig’s Nim……Page 75
More Generally Bounded Nim……Page 77
Epstein’s Put-or-Take-a-Square Game……Page 78
Third One Lucky……Page 80
D.U.D.E.N.E.Y……Page 81
Strings of Pearls……Page 82
Schuhstrings……Page 83
The Princess and the Roses……Page 84
More on Subtraction Games……Page 89
Smallest Nim, Largest Nim……Page 92
The More the Merrier……Page 93
Not with a Bang but a Whim……Page 94
Tribulations and Fibulations……Page 95
Our Code of Behavior for Princes……Page 97
References and Further Reading……Page 98
16 Dots-and-Boxes……Page 101
Double-Dealing Leads to Double-Crosses……Page 103
How Long Is “Long”?……Page 106
The 4-Box Game……Page 107
The 16-Box Game……Page 109
Dots-and-Boxes and Strings-and-Coins……Page 110
Nimstring……Page 112
Why Long Is Long……Page 114
To Take or Not to Take a Coin in Nimstring……Page 115
Sprague-Grundy Theory for Nimstring Graphs……Page 116
All Long Chains Are the Same……Page 121
Which Mutations Are Harmless?……Page 122
Vines……Page 124
Dots + Doublecrosses = Turns……Page 131
How Dodie Can Win the 4-Box Game……Page 132
When Is it Best to Lose Control?……Page 134
Computing the Values of Vines……Page 135
Loony Endgames Are NP-Hard……Page 137
Solutions to Dots-and-Boxes Problems……Page 138
Nimbers for Nimstring Arrays……Page 141
References and Further Reading……Page 144
Rims……Page 145
Loops-and-Branches……Page 146
Contours……Page 147
Lucasta……Page 148
A Child’s Guide to Normal Lucasta……Page 149
The Misere Form of Lucasta……Page 150
The Positions (7,3,1) and (11,1,1)……Page 154
Jocasta……Page 157
Sprouts……Page 158
Stars-and-Stripes……Page 163
Bushenhack……Page 164
Genetic Codes for Nim……Page 165
Von Neumann Hackenbush……Page 166
References and Further Reading……Page 167
18 The Emperor and His Money……Page 169
How Long Will It Last?……Page 170
Some Openings Are Bad……Page 171
Are All Openings Bad?……Page 173
Not All Openings Are Bad……Page 175
Strategy Stealing……Page 176
Quiet Ends……Page 177
Halving and Thirding?……Page 180
Finding the Right Combinations……Page 181
What Shall I do When $g$ is Two……Page 186
The Great Unknown……Page 189
Are Outcomes Computable?……Page 190
The Etiquette of Sylver Coinage……Page 191
Zig-Zag……Page 192
5-Pairs……Page 195
Sylver Coinage Has Infinite Nim-Values……Page 196
References and Further Reading……Page 200
Chessgo, Kinggo and Dukego……Page 201
Quadraphage……Page 202
Strategy and Tactics……Page 203
Dukego……Page 204
The Edge Attack……Page 206
The Edge Defence……Page 207
A Memoryless Edge Defence……Page 208
The Edge-Corner Attack……Page 210
Strategic and Tactical Stones……Page 212
Corner Tactics……Page 214
Defence on Large Square Boards……Page 217
Leaving the Central Region……Page 218
The Sidelined King……Page 221
How Chas. Can Win on a 34 x 34 Board……Page 223
Rectangular Boards……Page 224
Wolves-and-Sheep……Page 225
Saxon Hnefatafl……Page 226
King and Rook Versus King……Page 227
References and Further Reading……Page 228
20 Fox and Geese……Page 229
Some Properties of Our Strategy……Page 232
Towards Greater Precision……Page 233
The Indefinite Board……Page 234
How the Geese Survive Triumphantly……Page 235
Eight Exciting Escapades……Page 237
Tactics and Startegy for the Fox……Page 241
Fox’s Play on Definite Boards……Page 246
The Scrimmage Sequence……Page 247
Values of the Initial Positions……Page 248
Sophisticated New Software……Page 250
High Region……Page 252
Welton’s Region of Value 2over……Page 253
Parity in the High Scrimmage Region……Page 257
Early Values……Page 260
The aba’s to Trifurcate the Two-Ish Transition……Page 261
Early Values of Other Formations……Page 262
Resolving the Exceptions……Page 264
Museums……Page 265
Solutions to Problems……Page 269
References and Further Reading……Page 270
The French Military Hunt……Page 271
The Different Kinds of Place……Page 273
The Opposition……Page 274
When Has the Hare Escaped?……Page 275
Losing the Opposition……Page 276
A Strategy for the Hare……Page 278
On the Small Board……Page 281
On the Medium and Larger Boards……Page 282
All Is Found for the Small Board Hound……Page 285
References and Further Reading……Page 289
Tit-Tat-Toe, My First Go, Three Jolly Butcher Boys All in a Row……Page 291
Jam……Page 292
Analysis of Tic-Tac-Toe……Page 293
Ovid’s Game, Hopscotch, Les Pendus……Page 296
Four-in-a-Row……Page 297
Five-in-a-Row……Page 298
Six, Seven, Eight, Nine, …, in a Row……Page 300
$n$-Dimensional $k$-in-a-Row……Page 302
Strategy Stealing in Tic-Tac-Toe Games……Page 303
The Shannon Switching Game……Page 304
The Black Path Game……Page 306
Meander……Page 307
Winners and Losers……Page 308
Dodgem……Page 309
Dodgerydoo……Page 311
Philosopher’s Football……Page 312
Amazons……Page 316
Clobber……Page 317
Go……Page 318
Konane……Page 319
Shogi……Page 320
Answers to Problems……Page 321
References and Further Reading……Page 322
Index to Volumes 1-3……Page 330
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