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Full Description
This book considers a specific problem-generally a game or game fragment, and introduces the mathematical methods. It contains a section on the historical development of the theories of games of chance, and combinatorial and strategic games.
Contents
Preface -- I Games of Chance -- 1 Dice and Probability -- 2 Waiting for a Double 6 -- 3 Tips on Playing the Lottery: More Equal Than Equal? -- 4 A Fair Division: But How? -- 5 The Red and the Black: The Law of Large Numbers -- 6 Asymmetric Dice: Are They Worth Anything? -- 7 Probability and Geometry -- 8 Chance and Mathematical Certainty: Are They Reconcilable? -- 9 In Quest of the Equiprobable -- 10 Winning the Game: Probability and Value -- 11 Which Die Is Best? -- 12 A Die Is Tested -- 13 The Normal Distribution: A Race to the Finish! -- 14 And Not Only at Roulette: The Poisson Distribution -- 15 When Formulas Become Too Complex: -- The Monte Carlo Method -- 16 Markov Chains and the Game Monopoly -- 17 Blackjack: A Las Vegas Fairy Tale -- II Combinatorial Games -- 18 Which Move Is Best? -- 19 Chances of Winning and Symmetry -- 20 A Game for Three -- 2 1 Nim: The Easy Winner! -- 22 Lasker Nim: Winning Along a Secret Path -- 23 Black-and-White Nim: To Each His (or Her) Own -- 24 A Game with Dominoes: Have We Run Out of Space Yet? -- 25 Go: A Classical Game with a Modern Theory -- 26 Misere Games: Loser Wins! -- 27 The Computer as Game Partner -- 28 Can Winning Prospects Always Be Determined? -- 29 Games and Complexity: When Calculations Take Too Long -- 30 A Good Memory and Luck: And Nothing Else? -- 3 1 Backgammon: To Double or Not to Double? -- 32 Mastermind: Playing It Safe III Strategic Games -- 33 Rock-Paper-Scissors: The Enemy's Unknown Plan -- 34 Minimax Versus Psychology: Even in Poker? -- 35 Bluffing in Poker: Can It Be Done Without Psychology? -- 36 Symmetric Games: Disadvantages Are Avoidable, but How? -- 37 Minimax and Linear Optimization: As Simple as Can Be -- 38 Play It Again, Sam: Does Experience Make Us Wiser? -- 39 Le Her: Should I Exchange? -- 40 Deciding at Random: But How? -- 41 Optimal Play: Planning Efficiently -- 42 Baccarat: Draw from a Five? -- 43 Three-Person Poker: Is It a Matter of Trust? -- 44 QUAAK! Child's Play? -- 45 Mastermind: Color Codes and Minimax -- Index.
