Explanation needed on mathematics in horse racing betting?

Question

Horse racing betting beyond doubt is one of the most profitable sports betting. I am unable to understand the mathematics involved in horse racing betting. Can you help me understand the mathematical aspects in horse racing betting?

Answer 1

At the end of this post, the correct methodology is described for winning money versus a parimutuel system. It follows a methodology for beating a hand book. It is not likely to result in finding a winning system, but is the best known approach to the problem short of fixing races.

If anyone has specific questions, I might be able to provide answers. Sorry for the use of some jargon, the meanings of which I think should be obvious from context.

As a teenager, a friend & I had a lot of luck the first time we went to a race track. We won about $2000 in 4-5 days & thought we knew what we were doing.

In about a week, we had lost it all & were never ahead again. I never became addicted, only going to a track on rare occasions when friends wanted to go. My friend who was from a wealthy family lost millions over his life time, never realizing that our initial winnings were due to luck, not skill at handicapping horses.

I know a lot about handicapping horses, calculating payoffs, the track take, et cetera. I was involved in writing the first programs for calculating payoffs, which is not difficult but a bit more complex than most people imagine. I prefer Blackjack, which I have played a lot over a period of 50 or so years.

Until the late 1950's, payoffs were computed by men who had a knack for doing arithmetic very fast. I forget the numbers, but there is some estimate that many thousands of dollars are not bet on the next race for every minute that payoffs are delayed. Track owners want to pay off the winners as soon as possible, in order to increase the handle on the next race.

In theory, a parimutuel system is beatable. The odds are determined by the way people at the track bet. If most of them lose their minds & bet on hopeless horses, a knowledgeable person can win money by betting at good odds on horses who are likely to win.

In practice, there are not enough stupid bettors to result in odds skewed enough to allow a good handicapper to beat the track take. There are touts, tip sheets, & other sources of advice to help the really stupid bettors.

When I first went to the track, the take was about 17% counting breakage. It rose to 22% & I have no idea whether it is higher or lower now. You can get an indication of the track take by computing 1/(odds +1) for each horse & adding up the fractions. Then subtract one. The result indicates the take. Example using a 4-horse race

    * Assume odds on the horses are on the horses are 1 to 1, 2 to 1, 3 to 1 & 4 to 1.

    * Compute booking percentages as 1/2, 1/3, 1/4, 1/5

    * Approximate booking percentages: .50, .33, .25, .20, totaling 1.28

    * If you bet on all 4 horses using ratios of the above, you would bet $50, $33, $25 & $20, totaling $128

    * No matter which horse won, you would receive $100 & be out $28.

100/128 = .78, indicating that you would get back about 78% of the money you bet. This approximates the average loss to the overall betting public at the track.

At society horse shows & races, there used to be hand books instead of a parimutuel machine. Old time bookies would give you a slip of paper showing that you had bet say $10 at 3 to 1 on horse number three. You would be paid off at those odds no matter what final odds were assigned to the horse. As more bets were made, the bookie would adjust the odds to balance the book. I do not think that there are any old time bookies in United States, but they might exist in the UK.

When I was in college, there were bookies who ran hand books at these society events for nostalgia, not to make money. They had no idea of which horses were the best. In a 5-horse race, they would usually start out giving 3 to 1 odds on each horse (total booking percentages: 1.25) & adjust as the bets indicated which horses should have higher or lower odds.

Some of my college friends knew horse owners & could give advice on which horses should be favored. I would make early bets on the better horses & later bet on the other horses at high odds (as the bookie dropped the odds on the better horses, the odds on the other horses would rise).

The above allowed me to win a small amount of money 3-4 times a year. What I did was called Dutching the book. The term was due to a Dutchman who made money off of hand bookies circa 1900-1930.

I did not invent the above system on my own. I happened to be the friend of a childless bookie in the neighborhood where I grew up. I ran errands for him & he told me a lot about the gambling industry. I felt closer to him than to some of my uncles & he was very fond of me. We kept in touch until he died when I was about 40 years old.

Most attempts to beat a parimutuel system are based on attempts to handicap horses & decide which horse is going to win. Some handicapping systems advise betting on more than one horse in a race. In the latter case, ratios of booking percentages (see above) should be used to determine how much to beat on each horse. The emphasis on trying to determine a winner is an incorrect approach to the problem. Another bad idea is to make Place or Show bets (will describe why if asked).

The correct methodology for beating a parimutuel system is to use a computer to analyze past performance data & compare with the known results of past races. If you can determine an algorithm which accurately estimates the probability of a horse winning, you have the basis for a winning methodology. For example consider the following imaginary situation, using the above 4-horse race.

    * Your supposedly accurate algorithm is supplies the following probabilities (assume bets of $1.00).

    * Horse 1: odds 1 to 1 & probability of winning is .40, resulting in a return of $80 for one hundred $1.00 bets. Net loss:$20.00

    * Horse 2: odds 2 to 1 & probability of winning is .30, resulting in a return of $90 for one hundred $1.00 bets. Net loss:$10.00

    * Horse 3: odds 3 to 1 & probability of winning is .28, resulting in a return of $112 for one hundred $1.00 bets. Net gain:$12.00

    * Horse 4: odds 4 to 1 & probability of winning is .02, resulting in a return of $10 for one hundred $1.00 bets. Net loss:$90.00

Horses 1 & 2 are more likely to win, but will result in net losses over 100 bets. Horse 3 is less likely to win, but will result in a gain over 100 bets.

There are many types of races: Maiden (virgin) races, Claiming races, Allowance races, Handicap races, Stakes races, Stakes races with added purse money, and I am not sure what other types. Within each type there are different ratings. For example: A horse entered in a Claiming race can be bought for the Claiming price. A horse can be bought for $1000 in a low rated race, while I think there are races with claiming prices of as much as $100,000

BTW: A Maiden race is for horses who have never won. Nobody in their right mind attempts to pick a winner from a bunch of losers, but there are many who bet on such races.

The quest for a winning methodology attempts to find some type of race for which accurate probabilities of winning can be determined for at least a few of the horses. Given accurate probabilities, one then checks the parimutuel display to determine if some horse’s payoff will show a profit in the long run (EG: Horse 3 in the above hypothetical example).

I think it is possible, but unlikely, that a suitable algorithm can be found. It is futile to attempt to find an algorithm applicable to all (or even many) different types/classes of races. It is probably futile to attempt to find more than a few algorithms, each applicable to a particular type/class of race.

BTW: The history of my teenage friend indicates that there is some rationale behind the belief in beginner’s luck. Suppose you pick (for example) 100 individuals who try gambling for the first time. Perhaps 1 or 2 will win big, 20 will win some money & the rest will break even or lose. Those who initially win (especially the ones who won big) are more likely to become regular gamblers, while those who lose the first time they try are less likely to become regulars. Hence, a group of regular gamblers is likely to include many who were winners the first time they gambled.