Definition:Maximin Strategy

Definition
Let $G$ be a two-person game between players $A$ and $B$.

A minimax strategy for $A$ is one in which:
 * $(1): \quad A$ assumes that $B$ will make that move which makes $A$'s payoff (or average payoff, in the case of a random element) as small as possible.
 * $(2): \quad A$ then makes the move which makes this smallest gain the largest possible.

Hence it is the strategy that will maximise $A$'s minimum payoff.

The reasoning is:
 * I fear that my opponent will make the move which makes my payoff the smallest possible. Hence I make my move so as to make this smallest payoff as large as possible.