Optimal Mixed Strategies? I'm trying to understand how I would find the optimal mixed strategies in zero sum games. For example... given the following zero sum game in standard strategic form...
\begin{array}{r|r|}
       +8 & -2 \\
       -4 & +20\\
\end{array}
How would I find the optimal mixed strategy for the given player?

Suppose hero chooses first strategy (payoffs +8/-2) with probability $p$. We want to have the same expectation independent of which strategy the other player chooses. So
$$ 8p -4(1-p) = -2p + 20(1-p) \Rightarrow p = \frac{12}{17}.$$
gives the optimal mixed strategy.
