Interpretations of a mixed strategy

1.  The player tosses a (weighted) coin in order to choose the strategy to be played.

2.  The player J is playing against a population of opponents.  One part of the population of opponents always plays L, the other proportion of the population always plays R.  The proportions are such that J is indifferent between the pure strategy of L and the pure strategy of R.

3.  The players always use a pure strategy, but the payoffs from a strategic pair <L_Jay, R_Kay> are uncertain; payoffs are stochastic.

4. One or more players have a trembling hand.  That is, sometimes you know the strategy you mean to play, but make a mistake when it is time to implement.