\begin{definition}[Definition:Maximin Strategy]
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 '''maxi'''mise $A$'s '''min'''imum 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.''
\end{definition}