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A summary of the book in a nutshell 1
Pt. A Weak Win and Strong Draw 15
Ch. I Win vs. Weak Win 17
1 Illustration: every finite pointset in the plane is a Weak Winner 19
2 Analyzing the proof of Theorem 1.1 32
3 Examples: Tic-Tac-Toe games 42
4 More examples: Tic-Tac-Toe like games 59
5 Games on hypergraphs, and the combinatorial chaos 72
Ch. II The main result: exact solutions for infinite classes of games 91
6 Ramsey Theory and Clique Games 92
7 Arithmetic progressions 106
8 Two-dimensional arithmetic progressions 118
9 Explaining the exact solutions: a Meta-Conjecture 131
10 Potentials and the Erdos-Selfridge Theorem 146
11 Local vs. Global 163
12 Ramsey Theory and Hypercube Tic-Tac-Toe 172
Pt. B Basic Potential Technique - Game-Theoretic First and Second Moments 193
Ch. III Simple applications 195
13 Easy building via Theorem 1.2 196
14 Games beyond Ramsey Theory 204
15 A generalization of Kaplansky's game 216
Ch. IV Games and randomness 230
16 Discrepancy Games and the variance 231
17 Biased Discrepancy Games: when the extension from fair to biased works! 245
18 A simple illustration of "randomness" (I) 260
19 A simple illustration of "randomness" (II) 270
20 Another illustration of "randomness" in games 286
Pt. C Advanced Weak Win - Game-Theoretic Higher Moment 305
Ch. V Self-improving potentials 307
21 Motivating the probabilistic approach 308
22 Game-theoretic second moment: application to the Picker-Chooser game 320
23 Weak Win in the Lattice Games 329
24 Game-theoretic higher moments 340
25 Exact solution of the Clique Game (I) 352
26 More applications 362
27 Who-scores-more games372
Ch. VI What is the Biased Meta-Conjecture, and why is it so difficult? 380
28 Discrepancy games (I) 381
29 Discrepancy games (II) 392
30 Biased Games (I): Biased Meta-Conjecture 400
31 Biased games (II): Sacrificing the probabilistic intuition to force negativity 418
32 Biased games (III): Sporadic results 430
33 Biased games (IV): More sporadic results 439
Pt. D Advanced Strong Draw - Game-Theoretic Independence 459
Ch. VII BigGame-SmallGame Decomposition 461
34 The Hales-Jewett Conjecture 462
35 Reinforcing the Erdos-Selfridge technique (I) 470
36 Reinforcing the Erdos-Selfridge technique (II) 479
37 Almost Disjoint hypergraphs 485
38 Exact solution of the Clique Game (II) 492
Ch. VII I Advanced decomposition 504
39 Proof of the second Ugly Theorem 505
40 Breaking the "square-root barrier" (I) 525
41 Brea king the "square-root barrier" (II) 536
42 Van der Waerden Game and the RELARIN technique 545
Ch. IX Game-theoretic lattice-numbers 552
43 Winning planes: exact solution 553
44 Winning lattices: exact solution 575
45 I-Can-You-Can't Games - Second Player's Moral Victory 592
Ch. X Conclusion 610
46 More exact solutions and more partial results 611
47 Miscellany (I) 620
48 Miscellany (II) 634
49 Concluding remarks 644
Appendix A Ramsey Numbers 658
Appendix B Hales-Jewett Theorem: Shelah's proof 669
Appendix C A formal treatment of Positional Games 677
Appendix D An informal introduction to game theory 705
Complete list of the Open Problems 716
What kinds of games? A dictionary 724
Dictionary of the phrases and concepts 727
References 730
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Add Combinatorial Games: Tic-Tac-Toe Theory, Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solita, Combinatorial Games: Tic-Tac-Toe Theory to the inventory that you are selling on WonderClubX
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Add Combinatorial Games: Tic-Tac-Toe Theory, Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solita, Combinatorial Games: Tic-Tac-Toe Theory to your collection on WonderClub |