Editing Strategy (game theory) (section)

==Pure and mixed strategies==
A '''pure strategy''' provides a complete and deterministic plan for how a player will act in every possible situation in a game. It specifies exactly what action the player will take at each decision point, given any information they may have. A player's '''strategy set''' consists of all the pure strategies available to them.

A '''mixed strategy''' is a probability distribution over the set of pure strategies. Rather than committing to a single course of action, the player randomizes among pure strategies according to specified probabilities. Mixed strategies are particularly useful in games where no pure strategy constitutes a best response, allowing players to avoid being predictable. Since the outcomes depend on probabilities, we refer to the resulting payoffs as '''expected payoffs'''.

A pure strategy can be viewed as a special case of a mixed strategy—one in which a single pure strategy is chosen with probability 1, and all others with probability 0.

A '''totally mixed strategy''' is a mixed strategy in which ''every'' pure strategy in the player's strategy set is assigned a strictly positive probability—that is, no pure strategy is excluded or played with zero probability. This means the player randomizes across ''all'' of their options, never fully ruling any one out. Totally mixed strategies are important in some advanced game theory concepts like [[trembling hand perfect equilibrium]], where the idea is to model players as occasionally making small mistakes. In that context, assigning positive probability to every strategy—even suboptimal ones—helps capture how players might still end up choosing them due to small "trembles" in decision-making.