What Are The Odds?

A philosopher’s guide to betting on the Derby


By Steve Humphrey


Last year for the April Derby Issue, I wrote a column on probability, but that was scientific, or logical, probability. This time, I decided to write about something far more important: probability in horse racing. In that last column, I distinguished two kinds of probability, Classical and Relative Frequency. Briefly, classical probability applies to cases where there are a finite number of possible outcomes, each equally likely, like flipping a coin or rolling a die. Relative frequencies are those cases in which there are many trials, and we count how often a particular outcome occurs. 

Clearly, neither of these work in the case of horse racing. If we used the classical approach, each horse in a race would be assigned the same odds, but we do not believe that every horse has the same chance of winning. And we cannot run the same race many times over to determine how often Olivia wins. 

So, what do the odds in a horse race mean? This kind of probability is called “Subjective” and reflects the beliefs of the people setting the odds. The track handicapper sets the “morning line” based upon his or her subjective, though educated, judgment as to who is most likely to win. This can be based on past performance, past races against common opponents, workouts in the weeks preceding the race, how the horses look, etc. But the morning line are not the odds when the race is run. The odds change as bettors weigh in with their judgments. I know horseplayers who like to bet on “value.” They figure that the handicapper knows more than the bettors, and if the bettors change the odds significantly from the morning line, there is a chance to make some money.

Another fact about wagering at the track is that it is “Pari-mutuel” betting. The horseplayer is not betting against the track, as a roulette player does in a casino, but against other bettors. The money bet all goes into pools of win, place and show, and that money is distributed to the winning bets, according to the odds at race time, minus a percentage that goes to the track. The track cannot lose money on the races. The track only loses money if the “handle” is too light to cover costs, so the track has a vested interest in getting more people to bet more money.

Now, what about betting strategies? If all you want to do is cash tickets, and not lose too much, bet the favorite in each race. If you want big, though infrequent, payouts, bet the longshot in each race. My favorite bets are exactas and trifectas. If I think there are two clear favorites in a race, I will bet them in an “exacta box,” which is two exacta bets. (A $2 exacta box costs $4). In an exacta, you are betting that two horses will come in first and second in a particular order. In an exacta box, those two only need to come in first and second, in any order. The same applies to trifecta boxes, in which you bet that three chosen horses will finish first, second and third. 

But above all, try to avoid a “Dutch Book,” which is a bet in which you are guaranteed to lose money. I see this a lot on the Derby. There are so many horses running, and so much time before the race, that people make multiple bets which end up contradicting each other. My wife grew so tired of not cashing any tickets one day that she bet all the horses in one race to win. Sure enough, she cashed a ticket, but she lost money. Enjoy the Derby and happy betting!

Steve Humphrey has a Ph.D. in the history and philosophy of science, with a specialty in the philosophy of physics. He teaches courses in these subjects at the University of California, Santa Barbara and has taught them at the University of Louisville.