WEAK WIN AND STRONG DRAW
József Beck · Cambridge University Press eBooks · 2008
Games belong to the oldest experiences of mankind, well before the appearance of any kind of serious mathematics. (“Serious mathematics” is in fact very young: Euclid's Elements is less than three-thousand years old.) The playing of games has long been a natural instinct of all humans, and is why the solving of games is a natural instinct of mathematicians. Recreational mathematics is a vast collection of all kinds of clever observations (“pre-theorems”) about games and puzzles, the perfect empirical background for a mathematical theory. It is well-known that games of chance played an absolutely crucial role in the early development of Probability Theory. Similarly, Graph Theory grew out of puzzles (i.e. 1-player games) such as the famous Königsberg bridge problem, solved by Euler (“Euler trail”), or Hamilton's roundtrip puzzle on the graph of the dodecahedron (“Hamilton cycle problem”). Unlike these two very successful theories, we still do not have a really satisfying quantitative theory of games of pure skill with complete information, or as they are usually called nowadays: Combinatorial Games. Using technical terms, Combinatorial Games are 2-player zero-sum games, mostly finite, with complete information and no chance moves, and the payoff function has three values ±1, 0 as the first player wins or loses the play, or it ends in a draw.