The formulas
Positive odds → probability = 100 ÷ (odds + 100)
Decimal odds = 1 ÷ probability
Overround = sum of both sides − 100%
Hold = 1 − 1 ÷ sum of both sides
No-vig probability = implied ÷ sum of both sides
Expected value = p × profit − (1 − p) × stake
Worked examples
Implied probability
−110 means risking $110 to win $100, so you need to win 110 ÷ 210 = 52.38% of the time. +150 means risking $100 to win $150, which needs 100 ÷ 250 = 40%.
No-vig odds
A moneyline of −150 and +130 implies 60.00% and 43.48%, a total of 103.48%. Divide each by the total and the fair probabilities are 57.98% and 42.02%, or about −138 and +138. The book’s hold on that market is 3.36%.
Expected value
Say you think an NBA player goes over his points line 55% of the time, and the price is −110. A $100 bet wins $90.91. Expected value is 0.55 × $90.91 − 0.45 × $100 = +$5.00 per $100. At −125 the same opinion is worth only about −$1.00.
Using it well
- Compare with the fair price, not the posted one. The posted price includes the vig; the no-vig number is the market’s actual estimate.
- Shop the price. The same opinion can be a good bet at one book and a bad one at another. The synthetic hold calculator finds the best price on each side across books.
- Be skeptical of huge edges. If your number disagrees with every sportsbook by ten points, the likelier explanation is an error in your number.
- Track the close. The closing line value calculator checks whether your price beat the market’s final estimate.
Frequently asked questions
How do you convert American odds to implied probability?
For negative odds, divide the odds by the odds plus 100: −150 is 150 ÷ 250 = 60%. For positive odds, divide 100 by the odds plus 100: +130 is 100 ÷ 230 = 43.48%.
How do you calculate no-vig odds?
Convert both sides to implied probabilities, add them, and divide each side by the total. −150 and +130 imply 60.00% and 43.48%, a total of 103.48%, so the no-vig probabilities are 57.98% and 42.02%, or about −138 and +138.
How do you calculate expected value on a bet?
Multiply your win probability by the profit if you win, and subtract the loss probability times your stake. A 55% bet at −110 risking $100: 0.55 × $90.91 − 0.45 × $100 = +$5.00.