Every “Theory” of Games concentrates on one aspect only, and pretty much neglects the rest. For example:

1. (I) Traditional Game Theory (J. von Neumann, J. Nash, etc.) focuses on the lack of complete information (for example, card games like Poker). Its main result is a minimax theorem about mixed strategies (“random choice”), and it is basically Linear Algebra. Games of complete information (like Chess, Go, Checkers, Nim, Tic-Tac-Toe) are (almost) completely ignored by the traditional theory.

2. (II) One successful theory for games of complete information is the “Theory of Nim like compound games” (Bouton, Sprague, Grundy, Berlekamp, Conway, Guy, etc. – see volume one of the Winning Ways). It focuses on “sum-games”, and it is basically Algebra (“addition theory”).

3. (III) In this book we are tackling something completely different: the focus is on “winning configurations,” in particular on “Tic-Tac-Toe like games,” and develop a “fake probabilistic method.” Note that “Tic-Tac-Toe like games” are often called Positional Games.

Here in Appendix D a very brief outline of (I) and (II) is given. The subject is games, so the very first question is: “What is a game?”. Well, this is a hard one; an easier question is: “How can one classify games?” One natural classification is the following:

1. (a) games of pure chance;

2. (b) games of mixed chance and skill;

3. (c) games of pure skill.