A game-theoretic proof of Erdos-Feller-Kolmogorov-Petrowsky law of the   iterated logarithm for fair-coin tossing
  We give a game-theoretic proof of the celebrated Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair coin tossing. Our proof, based on Bayesian strategy, is explicit as many other game-theoretic proofs of the laws in probability theory. 
Takeyuki Sasai and Kenshi Miyabe and Akimichi Takemura
math.PR