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A mixed strategy in game theory is a choice by a player of a probability distribution over all the possible pure strategies. After selecting the probability distribution, the player lets chance do the work.

That's in theory. In practice, you often don't have chance waiting to do your bidding, so you just try to act randomly. The benefits of acting randomly are demonstrated by the Simpsons playing rock, paper, scissors:

Lisa: (thinking) Poor Bart. He can never resist Rock
Bart: (thinking) Good ole rock. Nuthin' beats rock.

In fact, the strategy of playing each of rock, paper, and scissors with probability 1/3 is the only Nash equilibrium of the game. Experiments show that in even moderately complicated environments, people don't really play mixed-strategy equilibria, though.

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