Parlay calculator: odds, payout and EV

A parlay calculator works out what a parlay pays: multiply each leg's decimal odds together, then multiply by your stake. Every leg must win. Add your fair probability for each leg to see the parlay's expected value, and why the sportsbook's margin compounds with every leg you add.

Parlay calculator

Enter each leg's odds. Add your fair win probability for every leg to see the parlay's expected value.

Odds format

Stake

Leg 1 odds

Leg 1 fair probability

Optional

Leg 2 odds

Leg 2 fair probability

Optional

Leg 3 odds

Leg 3 fair probability

Optional

Parlay odds: +811; 9.11 decimal
Payout: $91.12; $81.12 profit
Implied probability: 11.0%; Win rate this price assumes
Expected value: —; Add fair probabilities to calculate

Assumptions and limitations

Parlay decimal odds = the product of each leg's decimal odds. Every leg must win.
The expected value multiplies your fair leg probabilities, which assumes the legs are independent. Correlated legs (e.g. from the same game) break that assumption.
Pushed or voided legs are usually removed and the parlay pays at the remaining legs' odds, but rules vary by sportsbook; check the house rules.
Nothing you enter is stored or sent anywhere.

How the parlay calculator works out the odds

A parlay's decimal odds are the product of its legs' decimal odds. American odds have to be converted first.

Leg	American	Decimal
1	-110	1.909
2	-110	1.909
3	+150	2.500
Parlay	+811	9.112

A $10 parlay on these three legs pays $91.12 if all three win, a profit of $81.12. If any leg loses, it pays nothing. Use the odds converter to check any conversion.

Why the margin compounds

Each leg's price includes the sportsbook's margin. In a parlay, those margins multiply. Take legs that are each a true 50/50, priced at -110 (see Implied probability and no-vig odds, explained for where that margin comes from):

Legs	Parlay odds	Fair odds	Expected value
1	-110	+100	−4.5%
2	+264	+300	−8.9%
3	+596	+700	−13.0%
4	+1228	+1500	−17.0%

The rule behind the table: if every leg has the same expected value per unit, e, and the legs are independent, a parlay of n legs has an expected value of (1 + e)ⁿ − 1. A small negative edge per leg becomes a large one.

The same rule works in your favour if every leg is genuinely +EV, but it only takes one overpriced leg to cancel the others.

Correlated legs

Multiplying probabilities assumes the legs are independent. When two legs depend on each other (for example, a team to win and that team's quarterback to throw for a high total), the true chance of both winning differs from the product, and the calculator's expected value no longer applies. The payout arithmetic is still correct.

To bet several smaller parlays from the same legs, use the round robin calculator.

Frequently asked questions

How are parlay payouts calculated?

Convert each leg to decimal odds, multiply them together, and multiply by your stake. Two -110 legs (1.909 each) give 3.645, so a $10 parlay pays $36.45 including the stake.

Why do parlays have worse expected value than single bets?

Because the margin compounds. If each leg is a fair 50/50 priced at -110, one bet has an expected value of -4.5%, a two-leg parlay -8.9%, and a four-leg parlay -17%.

Can a parlay be a +EV bet?

Yes, if every leg is +EV and the legs are independent: the parlay's expected return is then the product of the legs' expected returns. It only takes one -EV leg to drag the whole parlay down.

What happens to a parlay if one leg pushes?

That depends on the sportsbook's house rules, so check them. A common treatment is to drop the pushed leg and pay at the remaining legs' odds, which is what entering that leg at decimal 1.00 models.

Parlay calculator: odds, payout and expected value