deletions | additions       diff --git a/subsection_MI_based_metric_According__.tex b/subsection_MI_based_metric_According__.tex  index 8e80bd4..505a399 100644  --- a/subsection_MI_based_metric_According__.tex  +++ b/subsection_MI_based_metric_According__.tex 
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\[d_{MI}(X,Y) = 1 - \frac{2MI(X,Y)}{S(X) + S(Y)} \]  Where $X$ and $Y$ are the positions of the two players.  This quantity may be interpreted as to the proportion of uncertainty that is not shared between $X$ and $Y$.  Indeed it comes from the previous section that:  \begin{enumerate}  \item $d_{MI}$ is symmetric. 
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\item $d_{MI}(X,Y) = 0$ iff $X$ and $Y$ have the same probability law.  \item in particular $d_{MI}(X,X) = 0$ for any trajectory.  \item $d_{MI}(X,Y) = 1$ iff $X$ and $Y$ are independent.  \end{enumerate} This quantity may be interpreted as to the proportion of uncertainty that is not shared between $X$ and $Y$.