I want to have a measure of the "synergy" between two players in a game. Each player has its own win ratio (won/played), which I'm modeling as two binomial distributed random variables X and Y. A third binomial distributed variable Z models the win ratio of both players as a team. The three variables are clearly dependent. The trouble I have is that, AFAIK, the joint distribution of the variables is needed to calculate the joint entropy of the variables, and I have no idea how to get around this.
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$\begingroup$ You are talking about distributions, but I think you simply mean that there are three numbers. $\endgroup$– Douglas ZareCommented Nov 6, 2015 at 21:35
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$\begingroup$ Thanks for the answer Douglas. Actually, yes there are three numbers, but I'm assuming they are drawn from three binomial distributions. So if $b(k; n, p) = \binom{n}{k}p^k(1-p)^{n-k} $ I'm estimating $p$ with the win ratio, $n$ is the number of matches played, and $k$ the number of matches won. $\endgroup$– Mario TambosCommented Nov 8, 2015 at 11:59
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