Let the elements in a payoff matrix be denoted , where the s are player A's strategies and the s are player B's strategies. Player A can get at least
(1)

for strategy . Player B can force player A to get no more than for a strategy . The best strategy for player A is therefore
(2)

and the best strategy for player B is
(3)

In general,
(4)

Equality holds only if a game saddle point is present, in which case the quantity is called the value of the game.