Combinatorial games: tic-tac-toe theory
Choice Reviews Online · 2008
Preface A summary of the book in a nutshell Part I. Weak Win and Strong Draw: 1. Win vs. weak win 2. The main result: exact solutions for infinite classes of games Part II. Basic Potential Technique - Game-Theoretic First and Second Moments: 3. Simple applications 4. Games and randomness Part III. Advanced Weak Win - Game-Theoretic Higher Moment: 5. Self-improving potentials 6. What is the Biased Meta-Conjecture, and why is it so difficult? Part IV. Advanced Strong Draw - Game-Theoretic Independence: 7. BigGame-SmallGame decomposition 8. Advanced decomposition 9. Game-theoretic lattice-numbers 10. Conclusion 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 Appendix E. New results Complete list of the open problems What kinds of games? A dictionary Dictionary of the phrases and concepts References.