Dr. Z’s place & show racetrack betting system at the first Breeders’ Cup

This chapter recalls a memorable day on November 10, 1984 when Ed Thorp and I attended, with my Vancouver colleague Bruce Fauman, the first Breeders’ Cup day at Hollywood Park. The purpose of the day in addition to fun, was to test my Dr. Z system co-developed with Donald Hausch with some early help from Mark Rubinstein. The idea of the system is simple: use the data from a simple market, in this case the win probabilities to fairly price bets in the more complex markets, such as place and show. For example, with ten horses, there are 720 possible finishes for show. Then one searches for mispriced place and show opportunities. This is a weak form violation of the efficient market hypothesis based solely on prices. How much to bet depends on how much the wager is out of whack and it is a good application of the Kelly betting system. The formulation below shows such an optimization. There is a lot of data here on all the horses and not much time at the track. So a simplified approach is suggested. Don and I solved thousands of such models with real data and estimated approximation regression equations that only involve four numbers, namely, the amounts bet to win in the total pool and the horse under consideration for a bet. Plus the total place or show pool and the place or show bet on the horse under consideration…