The fundamental theorem of Game Theory which states that every Finite, Zero-Sum, two-person Game has optimal Mixed Strategies. It was proved by John von Neumann in 1928.
Formally, let and be Mixed
Strategies for players A and B. Let
be the Payoff Matrix. Then
See also Mixed Strategy
References
Willem, M. Minimax Theorem. Boston, MA: Birkhäuser, 1996.