# Strategy (game Theory) - Pure and Mixed Strategies

Pure and Mixed Strategies

A pure strategy provides a complete definition of how a player will play a game. In particular, it determines the move a player will make for any situation he or she 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. This allows for a player to randomly select a pure strategy. Since probabilities are continuous, there are infinitely many mixed strategies available to a player, even if their strategy set is finite.

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.)

### Famous quotes containing the words pure and, strategies, pure and/or mixed:

The truth is rarely pure and never simple. Modern life would be very tedious if it were either, and modern literature a complete impossibility!
Oscar Wilde (1854–1900)

By intervening in the Vietnamese struggle the United States was attempting to fit its global strategies into a world of hillocks and hamlets, to reduce its majestic concerns for the containment of communism and the security of the Free World to a dimension where governments rose and fell as a result of arguments between two colonels’ wives.
Frances Fitzgerald (b. 1940)

Such pure and genuine and childlike love of Nature is hardly to be found in any poet.
Henry David Thoreau (1817–1862)

But oh, not the hills of Habersham,
And oh, not the valleys of Hall
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Downward, the voices of Duty call—
Downward, to toil and be mixed with the main,
The dry fields burn, and the mills are to turn,
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And the lordly main from beyond the plain
Calls o’er the hills of Habersham,
Calls through the valleys of Hall.
Sidney Lanier (1842–1881)