Every price a bookmaker offers is a statement about probability in disguise. Odds of 4/1 are not just “you win four for every one you stake”; they also say “this outcome has roughly a 20% chance”. Being able to translate freely between odds and percentages is the foundation of understanding value, comparing bookmakers, and seeing through promotional prices. It takes a few minutes to learn and pays off on every bet.
Decimal odds to probability
Divide 100 by the decimal odds.
| Decimal odds | Calculation | Implied probability |
| 1.25 | 100 ÷ 1.25 | 80.0% |
| 1.50 | 100 ÷ 1.50 | 66.7% |
| 2.00 | 100 ÷ 2.00 | 50.0% |
| 3.00 | 100 ÷ 3.00 | 33.3% |
| 4.00 | 100 ÷ 4.00 | 25.0% |
| 6.00 | 100 ÷ 6.00 | 16.7% |
| 11.00 | 100 ÷ 11.00 | 9.1% |
| 21.00 | 100 ÷ 21.00 | 4.8% |
| 101.00 | 100 ÷ 101.00 | 1.0% |
Fractional odds to probability
Take the denominator, divide by the sum of numerator and denominator, and multiply by 100.
| Fractional odds | Calculation | Implied probability |
| 1/4 | 4 ÷ 5 | 80.0% |
| 1/2 | 2 ÷ 3 | 66.7% |
| 4/6 | 6 ÷ 10 | 60.0% |
| Evens (1/1) | 1 ÷ 2 | 50.0% |
| 2/1 | 1 ÷ 3 | 33.3% |
| 3/1 | 1 ÷ 4 | 25.0% |
| 5/1 | 1 ÷ 6 | 16.7% |
| 10/1 | 1 ÷ 11 | 9.1% |
| 20/1 | 1 ÷ 21 | 4.8% |
| 100/1 | 1 ÷ 101 | 1.0% |
A quick conversion between the two formats: decimal = (numerator ÷ denominator) + 1. So 7/2 = 3.5 + 1 = 4.50.
Probability to odds
Divide 100 by the percentage to get decimal odds; subtract one and express as a fraction for fractional.
- 40% → 100 ÷ 40 = 2.50 decimal → 6/4 fractional.
- 15% → 100 ÷ 15 = 6.67 decimal → roughly 11/2 fractional.
Why a market adds up to more than 100%
Add the implied probabilities of every outcome in a market and you will get more than 100%. That excess is the bookmaker’s overround, covered earlier in this series. A three-way football market might total 105%; a 16-runner race might total 130%.
To estimate the bookmaker’s “true” opinion of each outcome, divide each implied probability by the market total:
| Selection | Odds | Implied % | ÷ 105% | “Fair” % |
| Home | 2.10 | 47.6 | 45.3 | |
| Draw | 3.40 | 29.4 | 28.0 | |
| Away | 3.60 | 27.8 | 26.5 | |
| Total | 104.8 | ~100 |
Using implied probability to think about value
The concept of a “value bet” is simple to state: if you believe an outcome is more likely than the odds imply, the price is value. If you think a team has a 50% chance and the odds imply 45%, you would — if your estimate is right — profit over many such bets. If the odds imply 55%, you would not.
The difficulty lies in the phrase “if your estimate is right”. Bookmakers employ analysts, use large datasets and adjust to market money. Consistently forming a more accurate probability estimate than the market is difficult, and short-term results tell you almost nothing about whether you are managing it — a run of winning bets is entirely consistent with poor estimates and good luck.
Price boosts and anchoring
Promotional prices — “was 3/1, now 4/1” — are best evaluated by converting both to probability. 3/1 implies 25%; 4/1 implies 20%. The boost is meaningful only if you believe the true probability is below 20%. The “was” price is an anchor, not a benchmark; the question is whether the boosted price is below your own honest estimate, not whether it is better than the original.
Comparing bookmakers
This is the most practical everyday use. For the same selection, a bookmaker at 2.10 implies 47.6%; one at 2.20 implies 45.5%. The second is offering a better price. Over hundreds of bets, consistently taking the best available price is a concrete, low-effort improvement that does not depend on being right about the outcome.
Accumulators
Multiply the implied probabilities of each leg to get the combined probability. Four legs at 60% each: 0.6 × 0.6 × 0.6 × 0.6 = 13%. The accumulator’s decimal odds should therefore be around 7.7 if fair — and a bookmaker’s price will be lower, because each leg carries margin. The combined probability is usually far smaller than intuition suggests.
A reference table
| Probability | Decimal | Fractional |
| 90% | 1.11 | 1/9 |
| 75% | 1.33 | 1/3 |
| 60% | 1.67 | 4/6 |
| 50% | 2.00 | Evens |
| 40% | 2.50 | 6/4 |
| 33% | 3.00 | 2/1 |
| 25% | 4.00 | 3/1 |
| 20% | 5.00 | 4/1 |
| 10% | 10.00 | 9/1 |
| 5% | 20.00 | 19/1 |
| 2% | 50.00 | 49/1 |
Related reading on site: “How Betting Odds Work”; Bookie Guide; “What is an Accumulator Bet?”
Understanding odds does not make an outcome more likely. Bet only with money set aside for the purpose.
