Implied probability & margin calculatorHERMES TOOLS · Odds math
Implied probability, overround, payout rate and margin-free fair probability for a full market.
Result
How it works: formula and examples
Each outcome's implied probability is 1 ÷ decimal odds. Enter all mutually exclusive outcomes that cover every result, such as home win, draw and away win in football.
The amount by which total implied probability S exceeds 100% is the overround: S−1. The theoretical payout rate is 1/S and the theoretical hold is 1−1/S; the three use different denominators and are not interchangeable.
Example: both sides at 1.90 give 52.63% each and 105.26% in total; the overround is 5.26 percentage points, the payout rate 95% and the hold 5%. After proportional removal both sides are 50%, fair odds 2.00.
Another example: 2.00, 3.00 and 4.00 total 108.33%; proportional removal gives 46.15%, 30.77% and 23.08%. The additive method subtracts the excess equally; the power method finds the exponent that makes the probabilities sum to 1. These are only models and prove nothing about real chances.
FAQ
Can I get the margin from the home-win odds alone?
No. The margin needs every mutually exclusive outcome in the same market.
What if the total is below 100%?
A negative overround probably means missing outcomes or a typo; it does not guarantee a profitable opportunity.
Is the fair probability always accurate?
Not necessarily. Each method makes different assumptions and uses no team information or check against real results.
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All tools ›This tool is for math and data reference only and offers no betting services. Do not buy sports lottery tickets if you are under 18.