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Let A be an $m\times n$ payoff matrix of a two person zero sum game. If the avg entry in a column$\ge 5$. Show that the row player's expected winnings $\ge 5$

I'm assuming the proof has to do with the fact that every index in the column has an avg of 5 or more so that probably means the rows have an average of 5 or more. So regardless of the what row player 1 chooses the avg expected reward will be at least 5 as well, but I'm not sure that's a complete proof.

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