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Enter a positive denominator.
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Enter a stake to see payout and profit
📊 Quick reference: Fractional 5/1 = Decimal 6.0 = American +500 = Implied probability 16.67%.
Implied Probability
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Sources & Methodology
Odds conversion formulas verified against standard probability mathematics and the UK Gambling Commission reference materials. All conversion formulas are mathematically exact.
UK Gambling Commission — Understanding Betting Odds
Regulatory reference for fractional, decimal, and American odds formats and implied probability
Khan Academy — Probability Library
Probability theory and odds-to-probability conversion concepts used in this calculator
Methodology: Fractional N/D: prob = D/(N+D); decimal = N/D+1; American = (N/D)x100 if N/D>=1 else -D/N x100. Decimal D: prob = 1/D; fractional = (D-1)/1; American = (D-1)x100 if D>=2 else -100/(D-1). American A: if A>0 prob=100/(A+100) else prob=|A|/(|A|+100). Payout = stake x decimal odds. Profit = payout - stake.
⏱ Last reviewed: April 2026
How Odds Are Calculated and Converted in 2026
Odds represent the ratio of probability to its complement — how likely an event is to occur versus not occur. Three formats are in common use globally: fractional (used primarily in the UK and Ireland), decimal (standard in Europe, Australia, and Canada), and American or moneyline (standard in the United States). All three formats express the same underlying probability; the conversion between them is purely mathematical.
Conversion Formulas
Fractional N/D: Implied Prob = D / (N + D)
To decimal: (N/D) + 1 | To American: if N/D ≥ 1, then (N/D) x 100; if N/D < 1, then -D/N x 100
Decimal D: Implied Prob = 1 / D
To fractional: (D-1)/1 simplified | To American: if D ≥ 2, then (D-1) x 100; if D < 2, then -100/(D-1)
American A: Prob = 100/(A+100) if positive, or |A|/(|A|+100) if negative
To decimal: if A > 0, then (A/100)+1; if A < 0, then (100/|A|)+1
Common Odds Conversion Reference Table
| Fractional | Decimal | American | Implied Prob |
|---|---|---|---|
| 1/10 | 1.10 | -1000 | 90.91% |
| 1/4 | 1.25 | -400 | 80.00% |
| 1/2 | 1.50 | -200 | 66.67% |
| 1/1 (Evens) | 2.00 | +100 | 50.00% |
| 2/1 | 3.00 | +200 | 33.33% |
| 5/1 | 6.00 | +500 | 16.67% |
| 10/1 | 11.00 | +1000 | 9.09% |
| 100/1 | 101.00 | +10000 | 0.99% |
What Is Implied Probability?
Implied probability is the probability of an outcome as baked into the odds. If decimal odds are 4.0, the implied probability is 1/4 = 25%. Bookmakers set odds so all implied probabilities sum to more than 100% — typically 102-108% — creating the bookmaker margin (overround or vig). This is why the house always has a mathematical edge over time.
Expected Value (EV) in Probability
Expected Value is the average outcome of a bet repeated many times. EV = (probability of winning x profit) - (probability of losing x stake). For a $100 bet at 3/1 (decimal 4.0) where the true probability is 30%: EV = (0.30 x $300) - (0.70 x $100) = $90 - $70 = +$20. Positive EV bets have long-run value; negative EV bets (where implied probability exceeds true probability) lose money over time.
💡 Key insight: Odds of 5/1 do NOT mean "5 to 1 chance against." They mean the bookmaker is implying a 1/6 = 16.67% probability. The fair odds would be 5/1 only if the true probability is exactly 16.67%. If you believe the true probability is 25%, the odds have positive expected value for you.
Frequently Asked Questions
Implied probability = denominator / (numerator + denominator). For 3/1: 1 / (3+1) = 25%. For 5/2: 2 / (5+2) = 28.57%. For evens (1/1): 1/2 = 50%.
Implied probability = 1 / decimal odds. For 4.0: 1/4 = 25%. For 1.50: 1/1.50 = 66.67%. Decimal odds always include the return of your stake, so decimal 2.0 = evens (1/1 fractional).
Positive odds: 100 / (odds + 100). For +300: 100/400 = 25%. Negative odds: |odds| / (|odds| + 100). For -150: 150/250 = 60%.
Fractional odds show profit per unit staked. 5/1 means you win 5 units profit for every 1 unit staked, plus your stake back (total return 6). 5/2 means 5 units profit for every 2 staked. Common in UK and Ireland betting markets.
Decimal odds show total return per unit staked, including your original stake. Decimal 6.0 means a 1 unit bet returns 6 units total (5 profit + 1 stake). Standard in Europe, Canada, and Australia.
American odds use a +/- format relative to 100. +300 means a 100 unit bet wins 300 units profit. -150 means you must stake 150 to win 100 profit. Positive odds = underdog. Negative odds = favourite.
Evens (1/1 fractional, 2.0 decimal, +100 American) means a 50% implied probability. A 10 dollar bet at evens wins 10 dollars profit and returns 20 dollars total. Both outcomes are implied as equally likely.
EV = (probability of winning x profit) - (probability of losing x stake). For 100 dollar bet at 3/1 where true probability is 30%: EV = (0.30 x 300) - (0.70 x 100) = 90 - 70 = +20 dollars. Positive EV = long-run value. Negative EV = long-run loss.
The overround is the bookmaker margin. Add up all implied probabilities for an event: if they total more than 100%, the difference is the overround. A market at 104% means the bookmaker holds a 4% edge. Most sports betting markets run at 102-108% overround.
Decimal = (numerator / denominator) + 1. For 3/1: (3/1) + 1 = 4.0. For 5/2: (5/2) + 1 = 3.5. For 1/4: (1/4) + 1 = 1.25.
Probability = 1/6 = 16.67%. In fractional odds: 5/1 (5 ways to fail vs 1 success). In decimal: 6.0. In American: +500.
Payout = stake x decimal odds. For 50 dollar stake at decimal 3.5: payout = 50 x 3.5 = 175 dollars. Profit = payout - stake = 125 dollars. At fractional 5/2: profit = stake x numerator / denominator = 50 x 5/2 = 125 dollars.
Probability is a number between 0 and 1 (or 0 to 100%). Odds are the ratio of success to failure. A 25% probability equals 3 to 1 odds against. Odds can be expressed as fractional (3/1), decimal (4.0), or American (+300), all conveying the same 25% probability.
Implied probability is baked into the odds by the bookmaker. True probability is your own assessment of how likely an event is. If implied probability is 25% but you believe the true probability is 35%, the bet has positive expected value. Finding discrepancies between the two is the basis of value betting.
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