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| -rw-r--r-- | games/games.tex | 7 |
1 files changed, 0 insertions, 7 deletions
diff --git a/games/games.tex b/games/games.tex index 365013f..fef4a3a 100644 --- a/games/games.tex +++ b/games/games.tex @@ -952,13 +952,6 @@ Now $p = {1\over\kappa |X|} \sum_{C \in X} p_C$ and $b = {1\over\kappa |X|} \sum_{C \in X} b_C$ so $E({p \over b + p} | X \neq \emptyset) = {1\over\kappa}$, which yields the inequality (\dag). - - - -induction on the length of the game now still produces disjoint groupings -$\mathbb{G}$ of optimal games in which - $\sum_{\mathbb{G}} {p \over b + p} = {1\over\kappa} |\mathbb{G}|$. -We conclude that $E({p \over b + p}) = {1\over\kappa}$, as desired. \end{proof} % https://math.stackexchange.com/questions/852890/expectation-of-random-variables-ratio %%% $L - w' \over (L - w') + (w - s)$ |