Random one-player games pit a decision against chance. In two-player games both decision-makers choose an action simultaneously, and the result depends on the pair of choices: this is the domain of game theory (von Neumann, Nash). This section introduces the fundamental tools — the payoff matrix, dominance between strategies, the Nash equilibrium and mixed strategies — and puts them to the test on three classic examples: a fantasy game solved with mixed strategies, the prisoner’s dilemma and the “odds or evens” zero-sum game.