Strategy (game theory)
Pure and mixed strategies

A pure strategy provides a complete definition of how a player will play a game. Pure strategy can be thought about as a singular concrete plan subject to the observations they make during the course of the game of play. In particular, it determines the move a player will make for any situation they could face. A player's strategy set is the set of pure strategies available to that player.

A mixed strategy is an assignment of a probability to each pure strategy. When enlisting mixed strategy, it is often because the game does not allow for a rational description in specifying a pure strategy for the game. This allows for a player to randomly select a pure strategy. (See the following section for an illustration.) Since probabilities are continuous, there are infinitely many mixed strategies available to a player. Since probabilities are being assigned to strategies for a specific player when discussing the payoffs of certain scenarios the payoff must be referred to as "expected payoff".

Of course, one can regard a pure strategy as a degenerate case of a mixed strategy, in which that particular pure strategy is selected with probability 1 and every other strategy with probability 0.

A totally mixed strategy is a mixed strategy in which the player assigns a strictly positive probability to every pure strategy. (Totally mixed strategies are important for equilibrium refinement such as trembling hand perfect equilibrium.)
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