# Eli5: How do betting odds work?

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Why is something 1/6 and something else 1/25? Why is something that was last week 1/5 is 1/15 this week? I’ve seen these “odds” change in the newspapers for horse racing, football, and other sports. I have never understood this. I watched some YouTube videos to try to make heads or tails from it but it’s left me in the same.

In: Mathematics

>Why is something 1/6 and something else 1/25?

For every \$1 you bet, you will win \$6 and \$25 respectively. Odds are set so the sportsbook can try to get equal amounts of money on both sides of the bet.

If you had people bet on David vs. Goliath, obviously there’s going to be a ton of people betting on Goliath. So you have to increase the payout for people betting David, and lower it for Goliath, or you’ll risk losing a lot of money should Goliath win. Odds are what the sportsbook/casino uses to encourage people to bet underdogs and discourage people from betting favorites. Setting a “point spread” is another way they do it.

Don’t think of it as “what do the betting companies think the odds should be” think of it as “what odds do the betting companies need to set to get bets placed evenly”

In an over/under scenario betting companies pay out 10/11 meaning you bet 11 and they pay out 10 to a winner. Their sole goal is to get as much money bet on both sides and they win.

As an example. Total points in a basketball game set at 210, \$2000 goes on the over. Betting company needs to get \$2000 on the under so moves to 220. The figure adjusts to make the under more attractive. \$3000 goes on the under and the line moves to 215. It is the betting patterns of the public that make the line.

For odds based gambling. A horse on even money gets \$10000 bet on it, if it wins \$10k gets paid out. They need the odds on the other horses to be attractive enough to get \$11k bet on them then they win.

Moral of the story, its the public betting patterns that make the changes

Sportsbooks have “odds makers” who basically use historical data to inform how likely they believe an event is to happen

Let’s take the Super Bowl today

Travis Kelce might have like 1:1 odds of getting a Touchdown, because the Odds Makers know that he scores about every other game, so it’s about a 50/50 shot

Conversely, someone like Kyle Juszczyk might have 5:1 odds of getting a Touchdown because he doesn’t get them nearly as often.

Lines can also move based off sentiment. The Odds Makers might set San Fransisco as the favourite, but if that causes people to bet overwhelmingly on Kansas City, then they’ll move the odds in KC’s favour to try to balance it out.

They could also move the lines based on news, if news came out that Patrick Mahomes is feeling sick, the odds might move more in favour of SF

So the thing is that betting odds don’t actually reflect the peobability that you will win. They reflect the amount you will win if you win the bet. There are three types of odds.

The first, the one you reference, is “fractional odds.” In this case, the odds are presented as winnings/bet. So if the odds are 6/1, then for every dollar you bet, you get six back on a win. If the odds are 1/6, then for every six dollars you bet you win 1 back . The closer the fraction is to 1, the more likely the bet is to win.

The second is “decimal odds.” This one is easier to understand. It is just take the bet, multiply it by the odds, and that’s your payout. If the decimal odds are 7.0, then whatever you bet is paid out seven times over. If the decimal odds are 1.167, then whatever you bet is paid out 1.167 times over. The closer to 1.0, the better the bet is, the more likely the bet is to win.

The third type is “money line,” and it is the most confusing. Money line odds are a positive or negative number, and they actually mean different things. A positive number is the amount of money you will win if you bet \$100, while a negative number is the amount of money you need to bet in order to win \$100. (But in either case, you get your original bet back if you win.) So if the odds are +600, then you would bet \$100 to win \$600 for a total payout of \$700. If the odds are -600 then that means you would bet \$600 to win \$100 for a total of \$700. The negative numbers are the ones that are most likely to win.

Now, if you are really math saavy, you may have noticed that all the odds I listed were the same. So why the difference? Well, all of them are made this way to obscure the actual odds. Because saying 6/1 or 6.0 or +500 sounds like a much more enticing deal than 14.29% and 1/6 or 1.167 or -600 or 85.71%. (These percentages are called the “implied odds and are found by dividing 1 by the decimal odds and multiplying it by 100%.)

Now you might also note something else here they add up to 0 in this case and 100%. But if you look at the moneyline odds for the two teams competing in the Superbowl today (February 11th, 2024) the 49ers are at -130 or a decimal odds of 1.77 and the Chiefs are at +110 or a decimal odds of 2.1. Those add up to a total of -20 and an implied odds of 56.52% and 47.62%, which is a total of 104.14%. Which doesn’t make sense? How can there be more than a 100% chance? Well, the answer is that they are skewing the odds to manipulate the expectation values.

So, the expectation value is how much money you can expect to get from a given bet. The equation for the expecation value is E=WP-C, where W is the winnings you get, P is the probability you win, C is the cost, and E is the amount you can expect to win from the average result. In other words, let’s say that the game was played 10,000 times, and each time you bet \$100 on the Chiefs. You would win 4762 of those bets and get \$210 for each of those 4762 victories. But would that offset the cost for the 5238 losses? Well E=210(0.4762)-100, which gives an expectation value of E=0.002, so you will actually win \$0.002 per game. For the 49ers, the expectation value is \$0.0404 per game. But this is only true if the odds are ACTUALLY the present odds. But they aren’t. If the odds that the 49ers will actually win is lower than 56.50% and the odds that the Chiefs will win is lower than 47.62% the. You will have a negative expectation value. So if the actual odds are 56% for the 49ers and 44% for the 49ers than the average better will lose money.