From 2082ab2b32a9e78a2f923d919178a8ef331cf773 Mon Sep 17 00:00:00 2001
From: Jeff Burdges <burdges@gnunet.org>
Date: Wed, 25 Apr 2018 23:07:03 +0200
Subject: blank lines

---
 games/games.tex | 7 -------
 1 file changed, 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
 %%% $L - w' \over (L - w') + (w - s)$
-- 
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