..PURE AND MIXED STRATEGY..GAME THEORY..

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 .)
Mixed strategy Illustration
A B
A 1, 1 0, 0
B 0, 0 1, 1
Pure coordination game
Consider the payoff matrix pictured to the right (known as a coordination game ). Here one player chooses the row and the other chooses a column. The row player receives the first payoff, the column player the second. If row opts to play A with probability 1(i.e. play A for sure), then he is said to be playing a pure strategy. If column opts to flip a coin and play A if the coinlands heads and B if the coin lands tails, then she is said to be playing a mixed strategy, and not a pure strategy.
Significance...
In his famous paper, John Forbes Nash proved that there is an equilibrium for every finite game. One can divide Nash equilibria into two types. Pure strategy Nash equilibria are Nash equilibria where all players are playing pure strategies. Mixed strategy Nash equilibria are equilibria where at least one player is playing a mixed strategy. While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. Foran example of a game that does not have a Nash equilibrium in pure strategies, see Matching pennies . However, many games do have pure strategy Nash equilibria (e.g. the Coordination game , the Prisoner's dilemma , the Stag hunt ). Further, games can have both pure strategy and mixed strategy equilibria.