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How to calculate implied probability in betting

Learning how to calculate implied probability from betting odds is key to assessing the potential value in a betting market.

Implied probability is a conversion of betting odds into a percentage. It takes into account the bookmaker margin to express the expected probability of an outcome occurring.

Knowing how to convert betting odds into implied probabilities is fundamental for betting as it helps you assess the potential value on a particular market. Once converted, if the implied probability is less than your assessment, then it represents betting value.

The most common odds formats are decimal, American and fractional. The formulas below explain how to convert odds to implied probabilities.

For the examples below we will use Smarkets odds for the 2016 Australian Open final between Andy Murray and Novak Djokovic:

Player Decimal odds Fractional odds American odds Implied probability
Djokovic 1.20 1/5 - 500 83.3%
Murray 5.50 9/2 +450 18.1%


Converting decimal odds to implied probability

To calculate the implied probability from decimal odds the equation is:

(1/ decimal odds) * 100 = implied probability

So to find out the probability of a Murray win would be:

(1 / 5.50) * 100 = 18.1%

Therefore, according to the decimal odds of 5.50, Andy Murray had an 18.1% chance of winning.

Converting fractional odds to implied probability

To calculate the implied probability from fractional odds the equation is:

denominator / (denominator + numerator) * 100 = implied probability

Therefore to find out the probability of a Murray win would simply be:

2 / (2 + 9) * 100 = 18.1%

As you can see this is the same probability as with the decimal odds. Why? Because odds in any format are just a different display of the same chance.

Converting American odds to implied probability

There are two instances of American odds (positive and negative) which require separate calculations.

Converting negative American odds

The equation to convert negative American odds is:

Negative American odds / (Negative American odds + 100) * 100 = implied probability

To find out the probability of a Djokovic win:

500 / (500+100) * 100 = 83.3%

Converting positive American odds

The equation to convert positive American odds is:

100 / (positive American odds + 100) * 100 = implied probability

To calculate the probability of a Murray win would be:

100 / (450 + 100) * 100 = 18.1%

Apply this to betting

Now you understand how to calculate the implied probability behind the odds, you can identify potential value in a betting market. If the bookmaker/exchange implied probability is less than your own assessed probability, that outcome represents a value betting opportunity.

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