Combinatorial Games : Tic-Tac-Toe Theory (Paperback)

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.