I've never once seen an application of the min-max Theorem to a question of military strategy that left me with a warm-and-fuzzy feeling that what I had just taken the time to digest would ever be actually repeated by a commander. My problem is mixed strategies.

Mixed strategies, where a player's strategy is expressed as a vector of probabilities (c.f. pure strategies), are central to min-max Theory, but don't seem like they would be very satisfying to a commander as a solution. The problem is that the optimal strategy predicted by min-max is only "optimal" in the probabilitic sense, i.e. over many runs it will tend not to be outperformed by any other strategy, and that much only if the other player also applies his optimal strategy with a suitable chance mechanism.

But what about one-off interactions like the kind we often face in the real world? What good is a vector of probabilities as a "solution" when a commander must choose a course of action exactly once and it is still possible to select the absolute worst course of action for any one specific interaction? Is min-max Theory not a tool that is used in Military Strategy?