A theorem of de Finetti states that if odds are posted on each set in a finite partition of a probability space, then either the odds are consistent with a finitely additive probability measure or a sure win is possible. A generalization of this result is proved which in turn implies a generalization of Von Neumann's theorem on the existence of the value of a game. Also, two horse race examples are considered.
"On a Theorem of De Finetti, Oddsmaking, and Game Theory." Ann. Math. Statist. 43 (6) 2072 - 2077, December, 1972. https://doi.org/10.1214/aoms/1177690887