**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.)

Read more about this topic: Strategy (game Theory)

### 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)

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—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

Avail: I am fain for to water the plain.

Downward, the voices of Duty call—

Downward, to toil and be *mixed* with the main,

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And a myriad flowers mortally yearn,

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)