Betting Odds and Implied Probability: American, Decimal, and Fractional Formats
October 29, 2026
Odds express the price of a bet. Implied probability is the chance that the odds suggest. Decimal odds D: probability = 1 ÷ D. Fractional odds a/b: probability = b ÷ (a + b). American odds: for positive odds +X, probability = 100 ÷ (X + 100); for negative odds −X, probability = X ÷ (X + 100).
Examples: decimal 2.50 → 1 ÷ 2.5 = 40%. Fractional 3/2 → 2 ÷ 5 = 40%. American +150 → 100 ÷ 250 = 40%. American −200 → 200 ÷ 300 = 66.7%.
Skip the math and get your answer instantly:
Open the Percentage Calculator →The Bookmaker Margin
A fair two-outcome market would have implied probabilities summing to 100%. Bookmakers build in a margin (overround or vig). For a coin-flip game priced at −110 on both sides, each side has an implied probability of 110 ÷ 210 = 52.38%, and the total is 104.76%. The overround of 4.76% means that the bookmaker keeps about 4.5% of the money wagered in the long run if bets are balanced (1 − 1 ÷ 1.0476 = 4.55%). To find the fair probability, divide each implied probability by the total: 52.38 ÷ 104.76 = 50%. A bettor must win 52.38% of the time at −110 just to break even.
| American | Decimal | Fractional | Implied probability |
|---|---|---|---|
| +100 | 2.00 | 1/1 | 50.0% |
| +150 | 2.50 | 3/2 | 40.0% |
| -110 | 1.91 | 10/11 | 52.4% |
| -200 | 1.50 | 1/2 | 66.7% |
| +400 | 5.00 | 4/1 | 20.0% |
Expected Value
The expected value of a bet = (probability of winning × profit) − (probability of losing × stake). A $100 bet at +150 (profit $150) with a true winning probability of 45% has an EV of 0.45 × 150 − 0.55 × 100 = 67.5 − 55 = +$12.50. If the true probability were only 35%, the EV would be 52.5 − 65 = −$12.50. The odds suggest 40%, so the bet is valuable only if you believe the probability is higher than that, and you are right. Most bettors lose money over time because of the margin and imperfect estimates.
Parlays Multiply the Margin
A parlay combines bets, multiplying the odds: three legs at −110 each pay about +596. The fair payout for three 50% events is +700 (7-to-1). The true probability of winning is 12.5% (0.5³), and the break-even probability at +596 is 100 ÷ 696 = 14.4%, so the bettor starts at a larger disadvantage than on a single bet. The more legs, the bigger the house edge.
A Note on Gambling
Gambling involves risk of loss and can be addictive. Only wager what you can afford to lose, set limits, and seek help if gambling causes problems (in the US, the National Problem Gambling Helpline is 1-800-GAMBLER). This article explains the mathematics and does not encourage betting.
Frequently Asked Questions
How do I convert decimal odds to probability?
Divide 1 by the decimal odds.
What does -110 imply?
A 52.4% implied probability.
What is the bookmaker's margin?
The amount by which implied probabilities exceed 100% in a market.
What is expected value in betting?
Win probability × profit minus loss probability × stake.
Why are parlays worse for bettors?
Each leg's margin compounds.