Methods of Representing Odds

Keywords you should know :

American odds ( US odds ) = Odds specification used in the US.

Decimal odds ( European odds ) = Standard odds specification.

Fractional odds ( UK odds ) = Odds specification used in the UK.

Odds-on = Odds of the favorite (winnings are less than stakes).

Odds-against = Odds of the underdog (winnings are more than stakes).

Payout = The total amount of money paid when a bet is won.

Stakes ( wager ) = The amount of money you risk.

Winning(s) = The amount won in a bet.

Odds may be specified in three different ways: Decimal Odds, Fractional odds, and American odds. In order to introduce you to these different representations of odds, let's see a a list of two games where you can bet on either the point spreads or the total points(over/under) or both. This is a simple interactive example the purpose of which is only to show you what values of the same odds would look like in the three representations. Initially, they are shown in the Decimal form. To see how the same odds are shown in the other two methods, just click on (mark) the radio buttons. You can see that a 1.90 odds is represented as 9/10 in fraction and -111 in American odds. Similarly an 8.5 odds is 15/2 in fraction and +750 in American.

If your browser is not Internet Explorer 4 or higher, the following table may not show and respond properly!!

Decimal Fractional American

Game	Point Spread	Game Totals	Money Line
MIA Dolphins NE Patriots	+12.5 1.90 -12.5 1.90	O 34.5 1.90 U 34.5 1.90	8.5 1.08
CLE Browns PIT Steelers	+6.0 1.90 -6.0 1.90	O 37.0 1.90 U 37.0 1.90	3.2 1.37

Quiz : Using only this table, how is a 1.37 decimal odds expressed in fraction and American methods ?
Answer

The definitions of each are listed below together with how to calculate the winnings and the payouts of a bet. Winnings are what the bettor wins with a certain stake (wager), while payouts are the total amount paid to the winner. Obviously, payouts are winnings plus stakes.

Fractional odds (UK):
The fractions here represent that a stake equal to the denominator will result in a winning equal to the numerator. E.g., odds of 10/11 mean that 10 units will be won with a stake of 11 units, or, for every $11 wagered, the winning will be $10.

Winning = Stake * Fraction Odds
Payout = Stake * (Fraction Odds + 1)
= Winning + Stake

See also the detailed description of Fractional odds.
American odds (US):
US odds are denoted by numbers always greater than or equal to 100 preceded by a '+' or '-' sign. These signs are not mathematical signs; they are simply symbols that point out whether your winnings are more than or less than your stakes. The positive sign is used to indicate that winnings are greater than stakes; and the negative sign vise versa.

Negative odds represent how much to wager in order to win $100. E.g., odds of -110 mean that in order to win $100, the wager must be $110.

Winning = Stake * 100/negative American Odds
Payout   = Stake * (100/negative American Odds + 1)
              = Winning + Stake

Positive odds represent how much the winnings will be when $100 are wagered. E.g., odds of +110 mean that $110 will be won, when $100 are wagered.

Winning = Stake * positive American Odds/100
Payout   = Stake * (positive American Odds/100 + 1)
              = Winning + Stake

See also the detailed description of American odds.
Decimal odds (European):
These are simply a factor that indicate how many times the stake will the payout be. E.g., odds of 2.50 mean that the payout will be two and a half times the stake, or, for each dollar wagered, the payout will be $2.50.

Payout = Stake * Decimal Odds
Winning = Stake * (Decimal Odds - 1)
= Payout - Stake

See also the detailed description of Decimal odds.

Let's state some outstanding features of these odds.

Decimal odds are always greater than 1.0 since '1' represents the stake.
American odds are always greater than or equal to 100 (+ and - are just symbols, not mathematical signs).
Fractional and American odds are indicative of winnings, while decimal odds indicate payouts.
Even odds, with respect to a fair bet, are when you win exactly the same amount as your stake. So, evens are represented by 2.0 in decimal, by 1/1 in fraction odds, and by 100 in US odds(-100 and +100 are the same).
In cases of odds-on, that is, when winnings are less than stakes, which is normally the case of a favorite team,
- the decimal odds fall between 1.0 and 2.0,
- In fraction odds they are identified by the fact that the numerator (winning) is less than the denominator (the stake), and
- In US odds they are the negative odds.
In cases of odds-against, that is, when winnings are greater than stakes, which is normally the case of an underdog team,
- the decimal odds will be greater than 2.0,
- the numerator will be greater than the denominator in fraction odds, and
- they are the positive odds in US odds.