# Guest Post: Know Your Odds

And, We’re Back!

The great thing about horse racing is that it will take you all around the world, literally (because sometimes being in the last race at Wolverhampton on an icy January night can feel pretty outlandish). Traveling to the Middle East I became good friends with Arapahoe Park’s track announcer Jonathan Horowitz . I asked Jonathan to write a little something about how maths relate to horse racing being the racing enthusiast that he is. Et voila, it’s all yours.

## Know Your Odds

by Jonathan Horowitz

The “win odds” posted by bookmakers or on the tote board are essentially a measure of the probability that a horse will win in the opinion of the bookmakers setting the odds or, in the case of the tote, all those that are wagering on the race. For example, if the posted win odds are 7 to 1 (abbreviated: 7-1 or simply 7), then add these two numbers together to get 7 + 1 = 8 total. Now divide the second number 1 by this total to obtain the probability that this horse will win the race: probability of winning = 1/8 = 12.5%. Similarly, for a horse having odds of 8 to 5 (abbreviated: 8-5) first add 8 + 5 = 13. Then the probability of winning = 5/13 = 38.5%. In general, if the win odds are X to Y then the probably of winning = Y/(X + Y).

When placing a bet with bookmakers, the odds are “fixed,” meaning that the posted odds at which a bettor makes his or her wager will stay the same for him or her regardless of whether the bookmaker subsequently decides to change the posted odds. Betting on other sports and casino games also offers fixed odds.

In response to unscrupulous bookmakers, French horse racing introduced a system in the 1870s whereby bettors would wager against each other instead of with a bookmaker. The money would be pooled together, and, after the racetrack would take out a percentage for operating it, the pool would be divided amongst the winning bettors. The Paris mutuel system became known worldwide as the pari-mutuel system. Pari-mutuel odds are continuously changing as the wagering public places bets. Only after the start of the race are the payoff odds finally fixed.

Calculating the win odds using the pari-mutuel system involves two factors: (i) the amount of money bet to win on that particular horse, and (ii) the total amount of money bet to win on all the horses in the race (the “win pool”). The win odds are completely independent of any money that is bet to place or on any of the exotics (exacta, trifecta, etc.).

The horse with the lowest win odds is known as the “favorite,” or the “chalk” in homage to when bookmakers would have to adjust the most popular horse’s odds on their chalkboard. If a horse has relatively large win odds then it is deemed a “longshot.” Odds of 1 to 1 (abbreviated: 1-1 or simply 1) are called “even money.” A horse with odds of less than 1 (e.g. 1‑2 or 2-5) is said to be running “odds on.”

The payoff for a victorious win ticket is determined by the final win odds and the amount bet on that ticket:

PAYOFF = (AMOUNT BET) + (AMOUNT BET x WIN ODDS)

For example if $10.00 is wagered to win on a horse having win odds of 5-2, then if successful that ticket will pay:

PAYOFF = ($10.00) + ($10.00 x 5/2) = ($10.00) + ($25.00) = $35.00

And now for a money-making quiz…

PROBLEM #1. If the win odds on a horse are 2-1, what is the probability that this horse will win the race?

PROBLEM #2. If a horse has a 5% chance of winning the race, what are its win odds?

PROBLEM #3. If $20.00 is bet to win on a horse with odds of 7-2, what will be the payoff if it wins?

PROBLEM #4. If a $5.00 winning ticket had a payoff of $20.00, what were the win odds on this horse?

PROBLEM #5. A winning ticket on a horse at odds of 1-2 had a total payoff of $30.00. What was the amount bet on that ticket?

Answers to these problems will be posted in a future newsletter. The first reader to send in the correct answers wins an IGL baseball cap 🙂