One can, instead, interpret mixed strategies in zero-sum games as a means of introducing continuity of strategies into a discrete-strategy game that has no pure-strategy saddle point, thereby converting it into a game that does have a saddle point. In this interpretation the role of mixed strategies in zero-sum games is not so different from their role in the nonzero-sum games. One can flip a coin to keep an opponent from guessing with confidence whether it will come up heads or tails; or one may flip a coin to “average” heads and tails, to create (in an expected-value sense) a strategy halfway between heads and tails. Both interpretations are useful. If the second is somewhat more sophisticated, the first may better catch the spirit of the problem as it presents itself to a game player. And the first reminds us that the problem, even with randomization, is still to prevent the opponent’s anticipation of our actual strategy choice, and that the machinery of choice, the procedures for recording and communicating a choice, and any advance preparations required by the outcome of the random process, must remain inaccessible to his intelligence system.

DEFINE: Clarifies two interpretations of mixed strategies: averaging creates a halfway strategy, and randomization prevents opponent anticipation.

Thomas C. Schelling, The Strategy of Conflict, loc. 800