Game-theoretic probability

In 1939, the French mathematician Jean Ville demonstrated the inadequacy of Richard von Mises's frequency theory of probability. For von Mises, a sequence of 0s and 1s was random if the frequency of 1s converged to one-half on (1) the sequence as a whole and (2) any reasonably chosen subsequence. Convergence on subsequences is needed, he said, to keep a gambler from beating the odds by choosing when to bet. Ville pointed out that more is needed. The gambler can also vary the amount he bets and the side on which he bets. Since 2001, Vladimir and Vovk and I have sought to revive Ville's idea of basing probability on game theory. In this talk, I explain how the game-theoretic approach leads to a new understanding of classical probability and finance and a new method of prediction. I also discuss why Ville's ideas were forgotten by statisticians and philosophers for 60 years. Because he wrote in French? Because he was a prisoner of war? Because of his bohemian lifestyle? Because he spent too much time teaching and consulting to pay for it? Because he was a dilettante? Or was he just too far ahead of his time?