  We study the behavior of the capital process of a continuous Bayesian mixture
of fixed proportion betting strategies in the one-sided unbounded forecasting
game in game-theoretic probability. We establish the relation between the rate
of convergence of the strong law of large numbers in the self-normalized form
and the rate of divergence to infinity of the prior density around the origin.
In particular we present prior densities ensuring the validity of
Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm.
