The Kelly criterion for spread bets

摘要

The optimal betting strategy for a gambler betting on a discrete number of outcomes was determined by Kelly (1956, A new interpretation of information rate. J. Oper. Res. Soc., 57, 975–985). Here, the corresponding problem is examined for spread betting, which may be considered to have a continuous distribution of possible outcomes. Since the formulae for individual events are complicated, the asymptotic limit in which the gamblers edge is small is examined, which results in universal formulae for the optimal fraction of the bank to wager, the probability of bankruptcy and the distribution function of the gamblers total capital.