A game-theoretic proof of Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair-coin tossing

TL;DR

This paper presents a game-theoretic proof of the Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair coin tossing, providing an explicit Bayesian strategy alternative to traditional probabilistic proofs.

Contribution

It introduces a novel, explicit Bayesian game-theoretic approach to prove a fundamental law in probability theory, expanding the toolkit for such proofs.

Findings

Provides a new game-theoretic proof of the law

Uses an explicit Bayesian strategy

Offers insights into probabilistic laws through game theory

Abstract

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.