Parlay calculator
Combined odds across any number of legs, in any odds format, with the number most parlay calculators leave out: how much margin compounds as you add selections.
| Legs | 3 |
|---|---|
| Combined decimal odds | 9.000 |
| Total returns | 450.00 |
| Profit | 400.00 |
| Implied probability | 11.11% |
| Fair odds with no margin | 10.270 |
The margin compounds across legs. On these 3 selections you are giving up about 12.4% against a no-margin price, against 4.3% on a single bet at the same margin.
Why margin compounds and the payout does not keep up
A parlay multiplies the decimal odds of each leg. It also multiplies the margin baked into each of those prices, and that is the part the payout figure hides. A four percent margin on a single bet becomes roughly sixteen percent across four legs, because the margins compound in exactly the same way the odds do.
The fair-odds row in this calculator strips the margin out and shows what the combined price would be without it. The gap between that number and the offered price is the cost of the parlay, expressed in the only terms that matter.
This is why parlays are the most heavily promoted product in any sportsbook and the most profitable one. Nothing about them is dishonest. The arithmetic is public and the promotion is simply pointed at the product with the highest margin, which is what promotion is for.
Correlation, and why some parlays are refused
Legs are assumed independent. Where they are not, the true combined probability differs from the product of the individual probabilities, sometimes enormously. A bet on a team to win and the same team’s striker to score is positively correlated, and multiplying the two prices overstates the true odds against.
Books know this, which is why correlated legs are frequently blocked, repriced as a single market, or quietly voided after the fact. Same-game parlays are priced with correlation models instead of simple multiplication, and their effective margin is usually well above a standard accumulator.
Where correlation runs the other way, against you, nobody blocks anything. A parlay of legs that tend not to occur together is worse than the price suggests and will be accepted without comment.
What a parlay is actually good for
Variance. A parlay converts a small stake into a small chance of a large return, and if that is what you want, the margin is the price of it. Stated that way it is a clear transaction and not a mistake.
It stops being a clear transaction when a parlay is presented as a way to increase expected return. It cannot be. Each added leg lowers expected value while raising variance, and the only case where a parlay beats separate bets is when every leg individually carries positive expected value, which is rare and does not survive contact with a book that limits winners.
If you are placing parlays for the return profile, size them as entertainment and use the fair-odds row to know what the entertainment costs. That is a defensible position. Believing the payout figure is the whole story is not.