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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?2011-12-12

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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.

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    Thanks for the answer, this video http://www.youtube.com/watch?v=YRECCg7B_L0 and your answer helped enlighten me :)2011-12-13