Combinatorial games

 Content: pt. A. Weak win and strong draw --
 ch. I. Win vs. weak win --
 Illustration : every finite point set in the plane is a weak winner --
 Analyzing the proof of theorem 1.1 --
 Examples : tic-tac-toe games --
 More examples : tic-tac-toe like games --
 Games on hypergraphs, and the combinatorial chaos --
 ch. II. The main result : exact solutions for infinite classes of games --
 Ramsey theory and clique games --
 Arithmetic progressions --
 Two-dimensional arithmetic progressions --
 Explaining the exact solutions : a meta-conjecture --
 Potentials and the Erdős-Selfridge theorem --
 Local vs. global --
 Ramsey theory and hypercube tic-tac-toe --
 pt. B. Basic potential technique : game-theoretic first and second moments --
 ch. III. Simple applications --
 Easy building via theorem 1.2 --
 Games beyond Ramsey theory --
 A generalization of Kaplansky\'s game --
 ch. IV. Games and randomness --
 Discrepancy games and the variance --
 Biased discrepancy games : when the extension from fair to biased works! --
 A simple illustration of \'\'randomness\'\' (I) --
 A simple illustration of \'\'randomness\'\' (II) --
 Another illustration of \'\'randomness\'\' in games. pt. C. Advanced weak win : game-theoretic higher moment --
 ch. V. Self-improving potentials --
 Motivating the probabilistic approach --
 Game-theoretic second moment : application to the picker-choose game --
 Weak win in the lattice games --
 Game-theoretic higher moments --
 Exact solution of the clique game (I) --
 More applications --
 Who-scores-more games --
 ch. VI. What is the biased meta-conjecture, and why is it so difficult? --
 Discrepancy games (I) --
 Discrepancy games (II) --
 Biased games (I) : biased meta-conjecture --
 Biased games (II) : sacrificing the probabilistic intuition to force negativity --
 Biased games (III) : sporadic results --
 Biased games (IV) : more sporadic results --
 pt. D. Advanced strong draw : game-theoretic independence --
 ch. VII. BigGame-SmallGame decomposition --
 The Hales-Jewett conjecture --
 Reinforcing the Erdős-Selfridge technique (I) --
 Reinforcing the Erdős-Selfridge technique (II) --
 Almost disjoint hypergraphs --
 Exact solution of the clique game (II). ch. VIII. Advanced decomposition --
 Proof of the second ugly theorem --
 Breaking the \'\'square-root barrier\'\' (I) --
 Breaking the \'\'square-root barrier\'\' (II) --
 Van der Waerden game and the RELARIN technique --
 ch. IX. Game-theoretic lattice-numbers --
 Winning planes : exact solution --
 Winning lattices : exact solution --
 I-can-you-can\'t games --
 second player\'s moral victory --
 ch. X. Conclusion --
 More exact solutions and more partial results --
 Miscellany (I) --
 Miscellany (II) --
 Concluding remarks --
 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.
 Abstract:             
              A comprehensive and unique volume by the master of combinatorial game theory.                 Read more...