Luck, Logic, and White Lies: The Mathematics of Games

ISBN-13: 9780367552961 / Angielski / Twarda / 2021 / 548 str.

J?rg Bewersdorff

Opis

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.

 

 

Spis treści

I. Games of Chance. 1. Dice and Probability. 2. Waiting for a Double. 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. 21. 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? 31. 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. 46. A Car, Two Goats–and a Quizmaster. IV. Epilogue: Chance, Skill, and Symmetry. 47. A Player's Inuence and Its Limits. 48. Games of Chance and Games of Skill. 49. In Quest of a Measure. 50. Measuring the Proportion of Skill. 51. Poker: The Hotly Debated Issue.