Paper titled From Coin Betting to Parameter-Free Online Learning by Francesco Orabona and Dávid Pál submitted to COLT 2016.
The paper describes how to use algorithms for repeated betting on outcomes of a coin to construct algorithms for online learning (learning with expert advice and online linear optimization over Hilbert space). As a coin betting algorithm one can use Krichevsky-Trofimov estimator, which is essentially optimal, from which we derive two simple online learning algorithms.