Stochastic Programming and Optimization in Horserace Betting

Abstract

AbstractRacetrack betting is simply an application of portfolio theory. The racetrack offers many bets that involve the results of one to about ten horses. Each race is a special financial market with betting, then a race that takes one or a few minutes. Unlike the financial markets, one cannot stop the race when one is ahead, or have the market going almost 24/7. There is a well-defined end point. Like standard portfolio theory, the key issues are to get the means right. In this case, it is the probabilities of, say, two, three or more horses finishing first, second, third, etc., in a given order, and to bet well. For the latter, the Kelly capital growth criterion is widely used and that maximizes the expected logarithm of final wealth. Transaction and price pressure odds changes fit well into the stochastic programming models.Professional syndicates or teams have been successful as hedge funds with gains approaching one billion over several years for the most successful. In the modern era, there are two features used extensively. First, there are rebates for large bettors of the track take similar to discounts at Costco. So instead of facing a 13–30% transaction cost, it's more like 10%. So to win, the bettors must make back this 10% disadvantage before profits ensue. And this is not easy as the markets are quite efficient. Also over half the betting is not recorded in the pools until the race is being run. This is because monies are bet near the start of the race and come from many off track sites which are combined with the on-track bets into the track pool. All this takes time. So estimates of future prices are crucial. Secondly, betting exchanges such as Betfair in London allow short as well as standard long bets. This allows for more arbitrage and the ability to take advantage of known biases. I have been involved in this research since the late 1970s with six books and a number of articles.In this paper I relate the theory, computations and examples of real races and experiences for various bets such as win, place and show, exactas, triactors, superfectas, super hi five, place pick all, double, pick 3, 4, 5 and 6. In the Halifax presentation I showed two of the greatest races ever by two undefeated female horses, one that was still then running (Zenyatta) and one retired (Personal Ensign) in 1988. The previous US undefeated horse was Colin in 1907! These and other great races can be seen free on the website chef-de-race.com.