Book contents
- Frontmatter
- Contents
- Preface
- A summary of the book in a nutshell
- PART A WEAK WIN AND STRONG DRAW
- PART B BASIC POTENTIAL TECHNIQUE – GAME-THEORETIC FIRST AND SECOND MOMENTS
- PART C ADVANCED WEAK WIN – GAME-THEORETIC HIGHER MOMENT
- PART D ADVANCED STRONG DRAW – GAME-THEORETIC INDEPENDENCE
- Appendix A Ramsey Numbers
- Appendix B Hales–Jewett Theorem: Shelah's proof
- Appendix C A formal treatment of Positional Games
- Appendix D An informal introduction to game theory
- Complete list of the Open Problems
- What kinds of games? A dictionary
- Dictionary of the phrases and concepts
- References
Preface
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- A summary of the book in a nutshell
- PART A WEAK WIN AND STRONG DRAW
- PART B BASIC POTENTIAL TECHNIQUE – GAME-THEORETIC FIRST AND SECOND MOMENTS
- PART C ADVANCED WEAK WIN – GAME-THEORETIC HIGHER MOMENT
- PART D ADVANCED STRONG DRAW – GAME-THEORETIC INDEPENDENCE
- Appendix A Ramsey Numbers
- Appendix B Hales–Jewett Theorem: Shelah's proof
- Appendix C A formal treatment of Positional Games
- Appendix D An informal introduction to game theory
- Complete list of the Open Problems
- What kinds of games? A dictionary
- Dictionary of the phrases and concepts
- References
Summary
There is an old story about the inventor of Chess, which goes something like this. When the King learned the new game, he quickly fell in love with it, and invited the inventor to his palace. “I love your game,” said the King, “and to express my appreciation, I decided to grant your wish.” “Oh, thank you, Your Majesty,” began the inventor, “I am a humble man with a modest wish: just put one piece of rice on the first little square of the chess board, 2 pieces of rice on the second square, 4 pieces on the third square, 8 pieces on the fourth square, and so on; you double in each step.” “Oh, sure,” said the King, and immediately called for his servants, who started to bring in rice from the huge storage room of the palace. It didn't take too long, however, to realize that the rice in the palace was not enough; in fact, as the court mathematician pointed out, even the rice produced by the whole world in the last thousand years wouldn't be enough to fulfill the inventor's wish (264 – 1 pieces of rice). Then the King became so angry that he gave the order to execute the inventor. This is how the King discovered Combinatorial Chaos.
Of course, there is a less violent way to discover Combinatorial Chaos.
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- Combinatorial GamesTic-Tac-Toe Theory, pp. xi - xivPublisher: Cambridge University PressPrint publication year: 2008