How Do Odds Work in Betting?

Did you know there is a 2.44 percent probability (40/1 odds) that Dwayne "The Rock" Johnson will win the next U.S. Presidential Election in 2020, according to one of the well-known betting websites?

If you are planning to start betting, be it casino gambling, sports betting, or any other type, it's important to understand the odds. It would be preposterous and absurd to think about placing bets without having a good grip on the main types of betting odds and the ability to read and interpret the various associated formats.

The three main types of betting odds are fractional (British) odds, decimal (European) odds, and American (moneyline) odds. These are simply different ways of presenting the same thing, and hold no difference in terms of payouts. This means that a chance (percentage probability) of an event occurring can be converted and presented in any of the aforementioned types of odds.

Fractional odds (aka British odds, UK odds or traditional odds) are popular among British and Irish bookies. These are typically written with a “slash (/)” or a “hyphen (-),” e.g. 6/1 or 6-1 and announced as “six-to-one.” Fractional odds are used by some of the world’s largest bookmakers, making them the most preferred odds across the globe.

A fractional listing of 6/1 (six-to-one) odds would mean that you win $6 against every $1 you wager (in addition to receiving your dollar back, i.e. $1 – the amount you wagered). In other words, this is the ratio of the amount (profit) won to the initial bet, which means that you will receive your stake ($1) in addition to the profit ($6), resulting in a total return of $7. Therefore, if you stake $10 at 6/1, you get a total return of $70 ($60 profit + $10 stake).

Therefore, the total (potential) return on a stake can be stated as:

Total Return = [Stake x (Numerator/Denominator)] + Stake
where numerator/denominator is the fractional odd, e.g. 28/6.

For instance, one of the major sports betting websites lists the following fractional odds for futures betting on the team to win the 2017-18 NBA Championship. Below is a selection of the three teams with the lowest odds.

Golden State Warriors: 10/11
Houston Rockets: 9/4
Cleveland Cavaliers: 7/1

It can quickly be determined that the Golden State Warriors are the favorites while the odds on Houston and Cleveland winning are longer. That is, one wins only $10 against every $11 wagered on Golden State to be the champions. Meanwhile, one wins $9 against each $4 (i.e. 3.25 times) put at stake for Houston to win, which is a bit less probable. For Cleveland, one wins $7 against each $1 bet. 

In the above example, if I bet $100 on Golden State to win, I could make a $90.91 profit [$100 x (10/11)], and could get back my initial stake of $100, resulting in a total return of $190.91. However, if I wager $100 on Houston to win, I could receive a profit of $225 [$100 x (9/4)], in addition to the $100 initial stake leading to a total payout of $325. The potential profit for a Cleveland win would be even higher, as I could make a profit of $700 [$100 x (7/1)]. Plus with the initial stake of $100 being returned, it would make for a total payout of $800.

(For related reading, see: A Quick and Dirty Look at Sports Gambling.)

Decimal odds (aka European odds, digital odds, continental odds) are popular in continental Europe, Australia, New Zealand, and Canada. These are a bit easier to understand and work with. The favorites and underdogs can be spotted instantaneously by looking at the numbers.

The decimal odds number represents the amount one wins for every $1 wagered. For decimal odds, the number represents the total return, rather than the profit. In other words, your stake is already included in the decimal number (no need to add back your stake), which makes its total return calculation easier.

The total (potential) return on a stake can be calculated as:

Total Return = Stake x Decimal Odd Number

For instance, one of the renowned betting websites prices several candidates to win the 2020 U.S. Presidential Election. Here, we list the decimal odds for the top three candidates and the biggest long shot among the candidates listed by the bookmaker as of March 21, 2018.

Donald Trump: 3.00
Bernie Sanders: 11.00
Elizabeth Warren: 13.00
and American media personality and sports businessman LaVar Ball: 251.00 (yes, you read that right, it's the Big Baller himself!)

These numbers merely represent the amount one could win against each $1 put at stake. Therefore, if one bets $100 on Donald Trump to be re-elected as President, this person could make a total return of $300 ($100 x 3.00). This amount includes the initial stake of $100, giving a net profit of $200.

Similarly, a bettor could make a total return of $1,100 ($100 x 11.00) if they successfully bet $100 on Bernie Sanders or $1,300 ($100 x 13.00) if a bettor gambles on Elizabeth Warren. Deducting $100 from these returns gives the bettor the net profit earned.

Reviewing the prices that the bookmaker has set for each candidate, it can be determined that according to the bookmaker, the probability of Donald Trump (favorite) wining the election is higher than that for any other candidate. The higher the total payout (i.e. the higher the decimal odd), the less probable (and more risky) it is for the listed candidate to win.

American odds (aka moneyline odds or US odds) are popular in the United States. The odds for favorites are accompanied by a minus (-) sign, indicating the amount you need to stake to win $100. Meanwhile, the odds for underdogs are accompanied by a positive (+) sign, indicating the amount won for every $100 staked. In both cases, you get your initial wager back, in addition to the amount won. The difference between the odds for the favorite and the underdog widens as the probability of winning for the favorite increases.

Let’s understand this with the help of an example:

One of the popular betting websites prices the NCAA "Sweet 16" men's basketball game between Duke and Syracuse on March 23, 2018 with the following moneyline odds.

Syracuse: +585
Duke: -760

The bookmaker has offered odds of +585 for Syracuse, which indicates that the bookmaker has placed a much lower probability (about 15 percent) of Syracuse winning the game. One needs to risk $100 on Syracuse to make a potential win of $585. If Syracuse can pull off the upset, one gets back their initial stake of $100, in addition to the $585 won, giving a total payout of $685.

If you decide to bet Duke who is listed as the favorite, which has a higher implied probability of winning the game according to the bookmaker, one would need to bet $760 to win $100. If Duke is victorious, one wins $100 with a total payout of $860 (initial stake $760 + profit won $100).

In this matchup, there is a big difference between the two odds, indicating a much higher probability of Duke winning the game and advancing to the next round of the NCAA Tournament.

Betting odds are expressed in three popular formats: fractional (British), decimal (European) and American (moneyline). These formats hold no difference in terms of final payoffs. Fractional odds are the ratio of the amount (profit) won to the stake; Decimal odds represent the amount one wins for every $1 wagered; and American odds, depending on the negative or positive sign, either indicate the amount one needs to wager to win $100 or the amount one would win for every $100 staked. So, if you are planning to enter the betting or the gambling world, it is important to understand and interpret these types of odds well.

Once you have mastered the three popular types of odds (fractional, decimal and American), you can move towards a more detailed read on this topic and find out how the house always wins. Please refer to Understanding the Math Behind Betting Odds & Gambling for the conversion between the different formats of odds, the conversion of odds into implied probabilities, and the differences between the true chances of an outcome as well as the odds on display.