What Are True Odds?
If an event had an objective probability of 50%, its true decimal odds would be 2.00. If the objective probability were 25%, its true decimal odds would be 4.00. The relationship is simply the reciprocal of probability.
True or fair odds formula
Decimal odds = 1 / probability
Example: 1 / 0.50 = 2.00.
The important limitation is that the actual pre-match probability is not directly observable. What analysts can calculate from bookmaker prices is a market estimate, not proof of the true probability.
Bookmaker Odds, Implied Probability, and True Probability
These terms describe different things. Bookmaker odds are quoted prices. Implied probability is the probability represented by those prices before margin adjustment. No-vig probability is the market-implied probability after a chosen margin-removal method. True probability is the actual underlying chance of the event.
The first three can be observed or calculated. The last one is the quantity the market is trying to estimate.
How to Calculate Implied Probability
For decimal odds, the conversion is straightforward:
Implied probability formula
Implied probability = 1 / decimal odds
Decimal odds of 2.50 imply 1 / 2.50 = 0.40, or 40%.
For a football 1X2 market, repeat the calculation for Home, Draw, and Away. Because bookmaker margin is embedded in the prices, those raw implied probabilities usually add up to more than 100%.
Bookmaker Margin and Overround
The amount by which the raw implied probabilities exceed 100% is commonly called the overround. It is one way to see the commercial margin embedded in a market.
1X2 example
Home: 2.10 → 47.62%
Draw: 3.40 → 29.41%
Away: 3.60 → 27.78%
Total implied probability: 104.81%
Overround: 4.81%
This is why raw implied probability should not be treated as a clean estimate of the event probabilities without accounting for margin.
How No-Vig or Fair Odds Are Calculated
A simple margin-removal method normalizes each raw implied probability by the total implied probability. Using the example above:
Normalization formula
Normalized probability = raw implied probability / sum of all implied probabilities
| Outcome | Quoted odds | Raw implied | Normalized | No-vig odds |
|---|
| Home | 2.10 | 47.62% | 45.43% | 2.20 |
| Draw | 3.40 | 29.41% | 28.06% | 3.56 |
| Away | 3.60 | 27.78% | 26.50% | 3.77 |
The normalized probabilities sum to 100%, and taking their reciprocals produces a no-vig or fair-odds representation of that same market.
Does Removing Bookmaker Margin Reveal the True Probability?
No. Removing margin corrects one known distortion in the quoted prices, but it does not prove that the remaining probabilities are objectively correct. The bookmaker may still be mispricing the event, information may be incomplete, and different margin-removal methods can produce slightly different estimates.
No-vig probability is best described as a margin-adjusted market estimate. It is not automatically the true probability.
True Odds vs Implied Odds
Implied odds or implied probability come directly from the bookmaker's quoted price. True odds would correspond to the event's actual underlying probability. Between those concepts sits the practical market estimate: margin-adjusted or no-vig odds.
- Quoted odds: the bookmaker's published price.
- Raw implied probability: reciprocal of the quoted decimal odds.
- No-vig probability: a margin-adjusted estimate derived from the market.
- True probability: the unknown underlying chance of the event.
- True odds: the reciprocal of that true probability.
Why Do Odds Differ Between Bookmakers?
Bookmakers can publish different odds for the same match because they do not necessarily use identical information, models, margin structures, risk controls, or market inputs. Prices also move as new information and trading activity enter the market.
Those differences are analytically useful. If operators systematically produce different probability errors over large samples, their forecasting quality can be compared rather than assumed to be equivalent.
How OddsAccuracy Uses Market Probabilities
OddsAccuracy converts Home, Draw, and Away decimal odds into implied probabilities and normalizes them to remove the bookmaker margin before evaluating forecast accuracy. The platform does not treat those normalized probabilities as guaranteed true probabilities.
Instead, OddsAccuracy tests how well those probability estimates align with actual match outcomes over time. The OA Score applies a three-outcome Brier framework to the normalized probabilities, so lower scores indicate smaller probability error.
See the Brier Score explanation for the scoring formula and the OddsAccuracy methodology for the full calculation process.
Bottom Line
Bookmaker odds are useful probability estimates, but they are not the same as objective true probability. Converting odds to implied probabilities and removing margin produces a cleaner market estimate. The remaining question is empirical: how accurate was that estimate? That is what probabilistic scoring is designed to measure.
Read the full football odds accuracy analysis
Frequently Asked Questions
What are true odds?
True odds are the odds that would correspond exactly to an event's actual underlying probability with no bookmaker margin. Because the true probability is unknown in advance, calculated fair or no-vig odds are estimates rather than guaranteed true odds.
What is true probability?
True probability is the actual underlying chance that an event occurs. Before the event, it is generally not directly observable and must be estimated.
Are true odds the same as fair odds?
The terms are often used as synonyms, but fair odds calculated by removing bookmaker margin remain market-derived estimates. They are not proof of the objective true probability.
How do you calculate implied probability?
For decimal odds, divide 1 by the quoted odds. Decimal odds of 2.00 imply 50%, while odds of 4.00 imply 25% before margin adjustment.
Does removing the bookmaker margin give true odds?
No. It gives a margin-adjusted or no-vig estimate derived from the quoted market. The bookmaker can still be wrong about the underlying event probability.
Why do odds differ between bookmakers?
Operators can use different information, pricing models, margins, market inputs, and risk decisions, so their prices do not have to be identical.