A Day at the Races: Optimal Betting Strategies for Novice Bettors

A Day at the Races: Optimal Betting Strategies for Novice Bettors

Background

Why do people gamble in general, and on horse racing in particular? The most apparent and easily understood reason is the desire and opportunity for monetary gain (Roby and Lumley, 1995). Race tracks, like most commercial gambling operations (casinos and lotteries), are designed by their very nature to be losing propositions for the bettor; if not, the racetracks would not be in business for very long. The "take" for racetracks in the U.S. varies by state and ranges between 14% and 20%, with the average being around 17%. From an economic standpoint, a guaranteed average loss of 17% does not seem like a good opportunity for monetary gain. Yet, despite this fact, in 2010, Americans wagered $11.4 billion at racetracks (Beyer, 2011).

Whereas winning or losing in lotteries and most casino games are strictly based on probabilities, betting on horses includes a perceived element of skill (Burger and Smith, 1985). Additionally, horse race betting is pari-mutuel system in which the bettors are betting against one another in a market-based odds system, as opposed to betting against the "house" in lotteries or casinos. Bettors believing they possess this skill may feel that they have a greater chance of winning and therefore an opportunity for monetary gain that compensates for the track take. As this line of reasoning may be valid only for the very skilled, there is another reason for gambling.

A second, and widely studied, reason people gamble is the emotional effects associated with gambling (Leary and Dickerson, 1985). In fact, the excitement and thrill of gambling may be the major reinforcing factor (Anderson and Brown, 1984) that leads to compulsive and addictive gambling behaviors. These gamblers can be called "sensation seekers". Sensation seeking is a personality trait characterized by both the need for a variety of complex experiences and the willingness to engage in risky behavior strictly for the sake of these experiences (Zuckerman, 1979). These bettors gamble not for the possibility of monetary reward, but the emotional high they receive while gambling. This heightened state of arousal has been shown to be similar to that achieved from cocaine use (Rosenthal and Lesieur, 1992).

Beyond the psychological aspects, a significant amount of academic research has focused on the economics of horse racing, in particular the existence of market inefficiencies within the betting pools at racetracks (Figlewski, 1979; Asch, Malkiel and Quandt, 1982/1986; Swidler and Shaw, 1995; Gramm and Owens, 2006). Several betting strategies have been proposed to take advantage of the identified inefficiencies, particularly in the place and show betting pools (Hausch, Ziemba and Rubenstein, 1981; Asch, et al., 1986). These strategies, however, are rather complicated, especially for an inexperienced bettor. To calculate the estimated returns for place and show pools, all possible combinations of finishes must be analyzed. In a race with 10 horses, there are 18 possible combinations of horses in which a particular horse finishes first or second. This number jumps to 216 for a particular horse finishing in-the-money (first, second or third.)

In addition to other variables, the large number of combinations makes it difficult for an inexperienced bettor to identify the existing inefficiencies, and therefore the most attractive bets. Additional difficulty is due to the fluid nature of odds leading up to the race; the bettors do not know the final odds until after the race begins. In previous studies, win results for the favorite horse have been shown to occur between 29.3% (Swidler and Shaw, 1995) and 36.3% (Gramm and Owens, 2006). This study will examine a narrowly defined set of racing data first, to determine is the morning line odds are an accurate predictor of race winner and second, to determine the optimal, simple betting strategy which will deliver the best results for a novice bettor.

Odds and Probability

One aspect of horse racing that may confuse the novice bettor is the odds system. The odds for a horse to win are not the same as the probability of a horse winning. Probability is determined by the following equation:

(Chances for)

P(x) = ---------------------

(Total chances)

For example, the probability of rolling a 6 on a fair die is 1 side out of 6 total sides = 1/6 or 16.7%. Odds in horse racing do not directly indicate the probability of a horse to win the race. Instead, they reflect a relationship between the chances for and chances against a horse, expressed as

(Chances against) : (Chances for)

For the same die example above, the odds of rolling a 6 would be expressed as 5:1.

The odds are used to calculate payouts, another area of confusion for novice bettors. In the die example, if you bet $1 that you would roll a 6 and were successful, the payout would be $6 (the $5 that would have been bet by those guessing other numbers plus the return of your initial $1 bet). However, if this case, due to equal odds, it would be expected for there to be the same number of people betting on each number. In this case, all money taken in would be paid out to the winners. As stated above, there is a track take. We can see this take by converting morning lines into subjective probabilities seen in Table 1. The sum of the subjective probabilities is greater than 100%, in this case, 120.55%. This indicates that based on the morning line odds, the track's take is estimated to be 20.55%.

Table 1. Odds and determination of subjective probabilities

Methodology

The data set for this study is limited to races with a total of six horses running. To increase the sample size, races scheduled with 7 horses but having one horse scratch (pulled from the race prior to post-time) were included. A concern arises regarding the changes to the odds of the remaining horses resulting from a scratch. The removal of a horse from the field will have an impact on the betting odds of the remaining horses, in most cases slightly increasing the odds of winning for each remaining horse. Since this study only looks at the ranks of the horses based upon the morning line odds, the removal of a horse (and the associated changes in odds)