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
 |
where 
is called the value of the game
and 
and 
are called the solutions. It also turns out that if there is more than one optimal
mixed strategy, there are infinitely many.
In the Season 4 opening episode "Trust Metric" (2007) of the television crime drama NUMB3RS, math genius Charlie Eppes mentions that he used the minimax theorem in an attempt to derive an equation describing friendship.
