Combinatorial games: tic-tac-toe theory

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 Erdos̋-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 Erdos̋-Selfridge technique (I)

Reinforcing the Erdos̋-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.

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.