The Math of Odds Conversions

There are many ways in which sports betting providers display their odds. Odds are the probability of an event happening and each formatting system can be represented with the other. Going back and forth between these odds and/or understanding them naturally can help a gambler fully understand what they are betting. In this article we will show how to convert each of the major formats into a standardized percentage.

Decimal

Decimal odds are the most common type of odds in Europe and Asia. To convert decimal odds to a percentage, simply divide 1 by the odds.

% = [1/odds]

For example, odds of 2.00 would be converted to a probability of 1/2.00 or 50%.

Fractional

Fractional odds are the most common type of odds in the United Kingdom. To convert fractional odds to a percentage, divide the denominator by the sum of the numerator and denominator.

% = [denominator / (numerator + denominator)]

For example, odds of 3/1 would be converted to a probability of 1 / (1+3) = 1/4 or 25%.

American (Positive)

American odds are the most common type of odds in the United States. American odds are calculated differently depending on if they are positive or negative. To convert positive American odds to a percentage, add 100 to the odds and divide 100 by the new number.

% = 100 / (odds + 100)

For example, odds of +400 would be converted to a probability of 100 / (400 + 100) = 100/500 = 1/5 = 20%.

American (Negative)

To convert negative American odds to a percentage, subtract 100 from the odds, divide the odds by the new number.

% = [odds / (odds – 100)

For example, odds of -300 would be converted to a probability of -300 / (-300 – 100) = -300/-400 = 3/4 = 75%

Table

Here is a table that summarizes the methods:

Odds TypeFormula Example
Decimal[1/decimal_odds] 2.00 = 50%
Fractional[denom. / (num. + denom.)]3/1 = 25%
American (+)100 / (odds + 100)+400 = 20%
American (-)[odds / (odds – 100)-300 = 75%

It is important to note that gambling odds are only estimates of the probability of an event occurring offered by sportbooks. The actual probability of an event occurring may be higher or lower than the odds indicate and is impacted by many variables in real time.

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