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authorJeff Burdges <burdges@gnunet.org>2018-04-25 23:19:15 +0200
committerJeff Burdges <burdges@gnunet.org>2018-04-25 23:19:15 +0200
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-
-We obtain a valid game run by terminating a game early of course,
-We may consider the adversaries ${\cal A}_n$ obtained by terminating
-$\cal A$ after the first $n$ refresh attempts $R_C$ with false planchets.
-Also ${\cal A}_n$ inherits optimality from $\cal A$.
-
-We shall now prove $E({p \over b + p} | X \neq \emptyset) = {1\over\kappa}$ for ${\cal A}_n$.
-
-We shall prove $E({p \over b + p} | X \neq \emptyset) = {1\over\kappa}$ (\dag)
-with the expectation taken over games with false planchets
- in which the adversary plays optimally
- in that no strictly simpler game run increases $p \over b + p$.
-
-
-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.
-