Betting Strategies in Horse Races

In this paper we consider the strategies a gambler may employ in situations such as horse races. We assume that the gambler knows which horses have odds which are favourable to him, that he wants to bet in such a way as to have a given positive expectation of win on a race, and that he wishes to minimise the probability of loss of his finite capital. We show that the best strategy is to bet on all the horses whose odds are favourable so as to minimise the probability of loss on a race. We further show that in order to achieve the last objective it is advisable to have a bet on a horse with fair odds, and at times on a horse with unfavourable odds, in addition to a bet on a horse with favourable odds.