Mathematics of Horse Race Gambling

Anyone have an interest in horse racing? If even for the mathematics behind it?

 

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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.

 

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I see how the vigourish makes it so that even if you were betting on a rather exceptional horse in a race of flops at 1-1 odds and it comes in first, you still wouldn't be breaking even.

 

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A friend of mine gambled on the ponies for his entire life. He even kept a record of when he won and lost throughout the years. After over 50 years of gambling he said he was at a loss overall. He also said when he needed money at times he would lose and when he didn't need money at other times , he'd win!

 

A dinosaur thread :crazy:, I know (pun not intended), and although I know nothing about horse betting...
@Dinosaur

Regarding the first race example, are those bets arbitrary, aside from getting a consistent payout? And what is this "average loss"... in comparison to the take?

Regarding the second race example, is this like poker, where you compare your probability against the pot odds? (Although after using your numbers, I was looking at the booking pct).

 

I've looked into the mathematics of gambling, and I've done a bit myself. My userid "Farsight" is one I adopted in about 2002 on a shares website called ADVFN, the idea being that I was a farsighted stockpicker.

You know what I found? That there's this psychology that overrides the mathematics. When you win it's great, and you don't want to stop gambling. So you keep on gambling, and you raise the stakes. And in the end, you only stop gambling when you've lost. I should have known this, because when I was about 20 I worked as a croupier in a casino for a summer. Me and my mate Nessie were students, and we told porkies to get the job, saying we'd packing in our courses. I used to deal American roulette, and you'd see the pattern. Some guy would come in with say £100 to punt, he'd win £500, then it would be excitement all round and £5 chips plastered all over the table, his gorgeous blonde girlfriend squealing and egging him on. Then he'd lose it all, and get £200 from the cashier, and then keep playing until he lost it. Then he'd go home with his tail between his legs.

It was a bit like that for me and shares. I'd make a few grand, because I was quite a good stock-picker, but then I'd get all excited and lose it fast. In the end I blew twenty grand before I realised I just liked gambling too much. So take care.

Something else I should mention: there were some guys at the casino who had the self-control to quit when they were ahead. They'd do that a few times, then they'd get banned.

 

Everyone I know who gambles on horses says that they break even.
So where do bookies get their Rolls Royces from?

 

@Captain
from their local dealer? j/k

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Not too sure myself, but I think they make their profits via fees and/or by setting all payout odds lower than the perceived probabilities (similar to Dino's second example). Even if they have no idea what these probabilities were, it wouldn't matter since the payout odds are in their favor, i.e. the overround (kinda like the take in Dino's first example). But I imagine a bookie can't set his rates too high, since folks will just go elsewhere in a hurry.

 

By going to sites such as oddschecker, you can find the best odds on each horse from every bookmaker.
I have heard that occasionally you can back all the horses and win, but I am sceptical.
http://www.oddschecker.com/

One way in which you can win is to take advantage of every sign-up offer,
and never bet again.
They all have loss leaders to get you hooked.
http://www.oddschecker.com/free-bets.html

If you live in the USA they will not let you join any of them,

 

Captain Kremmen: The following could only be true at a track with old style Hand books.

There might still be Hand Books in England. In the USA, there used to be races run by wealthy folks. Example: In Pennsylvania there is an area called the Main Line (Near Bryn Mawr, Haverford, Villanova) which had races run by Country club types.

Aside from places like the above, all betting is paramutual. The track take in paramutual betting is circa 17-22% (if you include breakage). If you make the same bet on all the horses in a race, you can only win money if the winner is a long shot. If you bet on all the horses using Booking Percentages, you will lose 17-22 percent of your money.

BTW: If you intend to bet on two or more (but not all horses in a race), it is best to use booking percentages to decide how much to bet on each horse.

FarSight: I have never heard of a winner being banned from a casino.

There just are not any consistent winners.

Blackjack is the only game that can be beaten due to the probabilities changing as cards in the shoe are dealt. A counter can get a small edge on the casino. The casino pretty much ignores those who bet small amounts. As mentioned in a previous post of mine, those who bet large amounts are watched carefully by casino personnel.

Both winners & losers are comped to encourage them to continue playing. Winners are comped because the casino does not expect them to win consistently enough to stay ahead of the casino.

Winners are watched to make sure that the dealer is not a partner in the action.

Big bettors are also scrutinized to check for card counting. Frequent shuffling thwarts a counter.


​

The only players I have ever known to be banned were ousted due to obnoxious behavior. The author of a book on Blackjack was deliberately obnoxious so that he would be banned & mentioned being banned in his book, implying that he won so much that a casino banned him to avoid further losses.


BTW: There is a reason that people believe in beginner's luck. It is due to an obvious selection process.

Consider 100 first time gamblers. Those who lost badly tend not to be regular gamblers. Those who won in their first experience, tend to become regular gamblers.

It amuses me that many gamblers have very little (or erroneous) knowledge of the games they play. For example: In Evian France on Lake Geneva, I noticed that a table advertising American roulette was crowded. American roulette has a zero & a double zero, while European roulette has only a zero. American roulette thus has worse odds that European roulette.Both games pay off 35 to one on a winning number. American roulette odds are 37 to one against the bettor, while European roulette odds are only 36 to one.

 

There is one case that I know for a fact, Dr. Richard Jarecki made 1.20 million dollars at the roulette tables in the casinos on the Riviera in the early 70's before being banned. He did not cheat, he was able to determine the roulette "bias" from the sequence of numbers coming up via a model of the bearing wear and tear he had created (a true mechanical engineer genius).
Many years later, I walked into a large casino in Monte Carlo to find a couple of players with a laptop at the roulette table. Knowing the Jarecki story, I figured that there was no way the management would let them play if their program was any good, so I tailored my bets to be exactly the opposite of theirs. One hour later I left with an extra 800 EUR in my pocket.

 

A length (one full stride of a horse in full flight) is roughly equivalent to one second or one pound of weight carried.

 

If your lucky number is 00 that is the only place to bet.

Re fixed odds betting.
You can get ahead of the bookmaker if you know that something will change the odds.
For example, if a horse is running in a race and performs better than expected,
you can sometimes bet on that horse to win a later race in which it is entered.
You would need to move quickly, before the bookie changes the odds.
Sometimes the difference can be huge.

Q. Anyone have an interest in horse racing? If even for the mathematics behind it?

It is like the stock market. Pure chance and speculation, unless you know which horse is going to win by nefarious means.

 

Tach: I have heard stories like the following, but do not believe any of them.

Casinos check their equipment regularly. No wheel would be so biased that a player could beat the house edge by even a small amount.

You might have been lucky, but I suspect your account of the 800 Euro win. No matter what bets you make, the house edge for an American wheel is circa 5% & half of that for a European wheel.

BTW: If their program was so bad, why did they continue to use it?

Furthermore, the effectiveness of their program is not really an issue. Their method being incapable of overcoming the house edge does not imply that a reverse strategy would result in winning. The house edge applies to every bet.

In Las Vegas, there are shops which sell forms for use in recording roulette wheel results. No casino worries about their use. I have noticed them being used in casinos.

I have seen newspaper articles about players winning at roulette due to some system. I suspect that casino Public Relations people plant such stories when they notice that there are not many system players at their wheels.

 

I think that you will find out that your claim is wrong. Here is the detailed account of what happened. It is quite fascinating.

I have no idea what you are talking about but I sense that you are calling me a liar.

I do not know and I was never interested in finding out.

While this is true, I simply had a sequence of wins by choosing the appropriate color. The house got their share, I got mine. What is so difficult to comprehend?

Did you consider that the casinos learned from the Jarecki experience? If you read the reference to the end, you will see how they fixed the issue.

Possible, I was never interested in playing roulette after my experience in Monte Carlo.

 

Q, If their program was so bad, why did they continue to use it?

Madness perhaps. Persistence in folly.
Success with the opposite numbers must have annoyed them no end.

A computer program using information from a video camera can tell in which part of the wheel a ball will drop.
With success rate greater than chance, and enough to give you an edge.
It uses simple mechanics. Given a location and speed, the program will work out statistically how much further the ball will travel.

Regarding biases. I believe wheels are checked fairly regularly,
but if you were fortunate enough to spot a wheel that had gone out of true, you could gain an advantage.

Here's an article giving people tips on roulette success,
NONE of which would work. All hokum. (though it does say, correctly, to avoid American tables)
http://www.wikihow.com/Win-at-Roulette

It amazes me how people can believe in such rubbish.
What is in their heads instead of brains?

 

Don't kid yourself. Put a big bet on a horse, and the jockey will fall off. The stock market isn't "pure chance and speculation" either.

 

Are you suggesting everything in the stock market is not above board?

 

Yep.

 

Hardly. There are big .. very big bets put on horses all the time. Hardly any jockeys falling off, though.

No the stock market isn't chance and speculation. It is driven by the two age old forces that drive mankind - greed and fear, particulalry, especially, in times of high volatility.