The standard mathematical theory of probability is based on measure theory ("Kolmogorov's axioms of probability"); in this talk I will argue that the theory of perfect-information games can serve as an alternative foundation. Game-theoretic versions of standard limit theorems (I will state a game-theoretic law of large numbers, law of the iterated logarithm and central limit theorem) are more powerful than their measure-theoretic counterparts; but what is even more important, the game-theoretic approach appears better suited to several areas of application of probability theory. In finance, for example, game-theoretic ideas make it possible either to relax the stochastic assumptions needed or to replace them with completely different (and more natural) assumptions. This talk will be based on the book by Glenn Shafer and Vladimir Vovk "Probability and Finance: It's Only a Game!" (New York: Wiley, 2001).