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Implied probability calculator

Enter the odds for a 2-way market (moneyline, totals) or a 3-way market (1X2) to see the implied probability of each outcome, how much margin the bookmaker builds in and the fair odds without it.

Implied prob.Fair prob.Fair odds
Outcome 147.62%45.43%6/5
Outcome 229.41%28.06%41/16
Outcome 327.78%26.50%25/9
Total probability
104.81%
Bookmaker margin (overround)
4.81%
Payout (return to player)
95.41%

How it works

Each decimal price converts to probability as 1 ÷ odds. If the bookmaker took nothing, the probabilities of every outcome would add up to exactly 100%. They always add up to a little more: that excess is the overround, the bookmaker’s margin.

The payout is 1 ÷ total: the share of stakes the book returns on average if its prices are accurate.

Fair odds come from removing the margin proportionally, dividing each probability by the total. It is the simplest method; others (Shin, power) put more of the margin on the less likely outcome.

It is useful for comparing books: on the same game, the one with the lower margin offers better prices overall. A price that beats another book’s fair odds is a sign of value.

Formulas

  • Implied probability = 1 ÷ decimal odds
  • Total = p₁ + p₂ (+ p₃)
  • Margin (overround) = total − 1
  • Payout = 1 ÷ total
  • Fair probability = pᵢ ÷ total
  • Fair odds = odds × total

Worked example

A 1X2 market at 11/10 / 12/5 / 13/5: the implied probabilities are 47.62%, 29.41%, 27.78%. They add up to 104.81%, so the overround is 4.81% and the payout 95.41%. Without the margin, the fair prices would be 6/5, 41/16, 25/9.

FAQ

What margin is normal?

It depends on the sport, the market and the book. Main markets in high-volume leagues usually carry less margin than props, specials or smaller leagues. The practical move is to compare the same market across books.

What are fair odds used for?

They are the price without margin. If another book pays more than those fair odds, the bet has value according to the first book’s estimate.

Does it work for handicaps and over/under?

Yes, for any market with two mutually exclusive outcomes. On whole-number lines that can push, the result is an approximation.

What is the difference between overround and payout?

They measure the same thing from two sides: overround is how far total probability exceeds 100%; payout is the share of stakes that goes back to bettors.

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