Betting odds converter and overround calculator
Implied probabilities from a bookmaker always sum to more than one. The excess is the margin, and it is where the profit comes from.
Implied probability
40.0000%
- Fractional odds, to 1
- 1.5000
- American odds
- 150.0
- Profit if it wins
- 30.00
- Total return
- 50.00
- Book total
- 95.238 %
- Bookmaker margin
- -4.762 % An arbitrage: the book is under 100%
- Margin-free probability of outcome A
- 50.000 %
Show the working
- Decimal odds = 2.5
- Stake = 20
- Price on outcome A = 2.1
- Price on outcome B = 2.1
- Price on outcome C = 0
- Implied probability = 100 / 2.5 = 40
- Fractional odds, to 1 = 2.5 - 1 = 1.5
- American odds = 2.5 >= 2 ? (2.5 - 1) * 100 : -100 / (2.5 - 1) = 150
- Profit if it wins = 20 * (2.5 - 1) = 30
- Total return = 20 * 2.5 = 50
- book_a = 100 / 2.1 = 47.619
- book_b = 100 / 2.1 = 47.619
- book_c = 0 > 1 ? 100 / 0 : 0 = 0
- Book total = 47.619 + 47.619 + 0 = 95.2381
- Bookmaker margin = 95.2381 - 100 = -4.7619
- Margin-free probability of outcome A = 95.2381 > 0 ? 47.619 / 95.2381 * 100 : 0 = 50
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- implied probability = 1 / decimal odds
- overround = sum of implied probabilities
- margin-free probability = implied / overround
A book summing to under 100% is an arbitrage. They exist, briefly, and are usually voided or limited.