# 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?

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Optimal in what sense? –  Chris Eagle Dec 12 '11 at 13:18

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
$$8p -4(1-p) = -2p + 20(1-p) \Rightarrow p = \frac{12}{17}.$$