  We show that for any countable amenable group action, along F{\o}lner
sequences that have for any $c>1$ a two sided $c$-tempered tail, one have
universal estimate for the probability that there are $n$ fluctuations in the
ergodic averages of $L^{\infty}$ functions, and this estimate gives exponential
decay in $n$. Any two-sided F{\o}lner sequence can be thinned out to satisfy
the above property, and in particular, any countable amenble group admits such
a sequence. This extends results of S. Kalikow and B. Weiss for
$\mathbb{Z}^{d}$ actions and of N. Moriakov for actions of groups with
polynomial growth.
