Parlay calculator
Put your legs in and get the combined price, what it pays on your stake, and — if you have a view on the legs — the true expected value of the ticket. Below the calculator are the two tables most parlay pages leave out: what the vig actually costs you as legs pile up, and the win rate you need per leg to break even.
Your combined edge survives the multiplication — this parlay is priced in your favor.
How parlay odds are combined
American odds do not add and they do not average. To combine them you convert each leg to decimal — the multiplier on your stake including the stake itself — then multiply the decimals together and convert back.
A favourite at −110 becomes 1 + 100 ÷ 110 = 1.9091. An underdog at +150 becomes 1 + 150 ÷ 100 = 2.50. The reason multiplication is the right operation is that your stake genuinely rides: leg one turns $100 into $190.91, and leg two puts all of that at risk again.
Worked example: three legs at −110
Decimal 1.9091 × 1.9091 × 1.9091 = 6.9579, which is +596 in American odds. A $100 stake returns $595.79 in profit, or $695.79 back in total.
If your honest read on each leg is 52.4% — exactly what −110 implies — the ticket cashes 14.4% of the time and the expected value is 0.0% before the book's margin. Give each leg a real 55% instead and the same ticket becomes +15.8%. Parlays do not create edge. They multiply whatever edge — or deficit — the legs already carry.
Worked example: mixing a favourite and an underdog
Legs at −250, −110 and +180 convert to 1.40, 1.9091 and 2.80. Multiplied that is 7.4836, or +648 — a $100 stake profits $648.36. Note what the heavy favourite does: it barely moves the price while still carrying real risk of busting the ticket. That asymmetry is why short legs are the most expensive thing you can add to a parlay.
Worked example: the same parlay at two books
This is the part that actually moves money, and it is why the multiplication matters. Take three legs. Shop each one and you get −105, −108 and +105. Take all three at whichever single book you happened to open and you might get −115, −118 and +98. Every one of those gaps is small on its own — a cent or two.
Multiplied out, the shopped ticket prices at +671 and the unshopped one at +584. On a $100 stake that is $670.83 against $583.88 — $86.95 more for the identical three bets, on the same night, with the same risk.
Per-leg price differences compound exactly the way the margin does. That makes shopping worth more on a parlay than on any single bet, and it is the one edge on this page available to everybody, with no view on the games required at all.
The reference table: −110 legs
Everything below assumes the standard −110 leg. The last column is the one worth staring at: it is the expected value of the ticket when you hold no edge and are simply paying the margin.
| Legs | Price | $100 pays | Cashes | EV with no edge |
|---|---|---|---|---|
| 2 | +264 | $264.46 | 27.4% | −8.9% |
| 3 | +596 | $595.79 | 14.4% | −13.0% |
| 4 | +1228 | $1228.33 | 7.5% | −17.0% |
| 5 | +2436 | $2435.91 | 3.9% | −20.8% |
| 6 | +4741 | $4741.27 | 2.1% | −24.4% |
| 8 | +17545 | $17544.64 | 0.6% | −31.1% |
| 10 | +64208 | $64208.16 | 0.2% | −37.2% |
Cashing chance is the −110 implied rate of 52.38% raised to the number of legs. EV with no edge is 0.9545 — what an edgeless −110 leg returns per dollar — raised to the same power, minus one.
Why the vig compounds
A two-sided market at −110 both ways is fair at 50% a side, so an edgeless leg returns 0.50 × 1.9091 = 0.9545 per dollar. You lose 4.5% on one leg. But that 0.9545 multiplies: at three legs you are down −13.0%, at six −24.4%, and at ten −37.2%.
This is the honest answer to why parlays are profitable for books. Not because the payouts are wrong — the arithmetic on the payout is exactly right — but because every leg you add applies the margin one more time. More on hold and the vig.
The part that surprises people: break-even per leg doesn't move
You would expect a ten-leg parlay to demand a higher win rate per leg than a two-legger. It does not. Break-even needs (p × d)ⁿ = 1, and that reduces to p × d = 1 — the number of legs cancels out entirely. At −110 the answer is 52.38% per leg whether you play two or ten.
What legs actually change is two other things: the total margin you hand over, and variance. A four-leg parlay cashes 7.5% of the time. You can be a genuinely winning bettor and lose that ticket nine times running.
When a parlay is genuinely +EV
When the legs are. Edges compound in precisely the same multiplicative way the margin does — so a real per-leg edge gets amplified, not diluted. Each leg priced 5% in your favour:
| Legs | Combined EV |
|---|---|
| 2 | +10.3% |
| 3 | +15.8% |
| 4 | +21.6% |
| 5 | +27.6% |
The practical test is simple: if you would not bet each leg on its own at that price, the parlay does not fix it. Finding those legs is what the board is for, and the devig calculator works out what a single leg is really worth.
Same-game parlays and correlation
Multiplying probabilities is only valid when the legs are independent. Legs in the same game usually are not. If a quarterback throws for 350 yards, his top receiver going over 80 is far more likely than his standalone price suggests — the two outcomes move together.
Books know this. A same-game parlay is priced with the correlation built in, which is why the combined number is shorter than multiplying the individual legs would give you. That cuts both ways: any calculator that multiplies independent legs — including this one — will overstate the payout and the true EV of a correlated ticket. Use the output as the independence case and treat a same-game number as a ceiling, not an estimate.
How many legs is too many
There is no magic number, but the table gives you the trade honestly. Every leg multiplies the margin by another 4.5% at standard pricing, and it divides the cashing chance by about two. At six legs you are paying −24.4% for a 2.1% shot. At ten, −37.2% for 0.2%.
If you are parlaying for the lottery-ticket distribution, that is a preference and the price of it is now visible. If you are parlaying because you think it improves your returns, the arithmetic disagrees unless every leg is independently +EV.
Round robins versus parlays
A round robin takes the same legs and bets every smaller combination of them — four legs as six separate two-leg parlays, for example. You stop needing every leg to land, so one miss no longer zeroes the ticket. What you give up is the top end, because your stake is spread across many shorter prices. Expected value per dollar is unchanged from the legs themselves; you are choosing a distribution, not buying an edge.
Teasers versus parlays
A teaser is a parlay where you move each line in your favour and accept a shorter price for it. Whether that trade is good depends entirely on how much win probability those points actually buy at that specific number — moving through key totals is worth far more than moving between them. It is the same multiplication as a parlay with different per-leg probabilities, so the same rule applies: the ticket is only +EV if the teased legs are.
Hedging a parlay before the last leg
If the first legs land, you are holding a position whose value has moved. Betting the other side of the final leg locks in a guaranteed amount instead of a coin flip. Whether to do it is a question about your own risk tolerance, not about EV — hedging usually costs a little expected value in exchange for certainty. The hedge calculator works out the stake and the guaranteed profit.
Book rules that change what you actually get paid
- Pushes. Most books drop a pushed leg and re-price the parlay as if you had bet the rest — a three-leg with one push pays as a two-leg. Some void the whole ticket. The difference is large.
- Voided legs. A cancelled game or a scratched player is usually treated the same way as a push, but the definition of "did not play" varies by book and by market.
- Maximum payout caps. Long parlays can exceed a book's per-ticket cap, in which case you are paid the cap rather than the calculated return. On a ten-leg at +64208 this is a real constraint, not a theoretical one.
- Correlation blocks. Books refuse combinations that are too strongly linked. If a parlay is rejected, that is usually why.
Are parlay boosts worth it?
A boost adds a percentage to your profit, so it raises expected value by roughly that percentage of the pre-boost return. That makes it arithmetic, not a judgement call. A 30% profit boost applied to a four-leg ticket sitting at −17.0% does not reach break-even. The same boost on a ticket already close to fair can push it positive. Work out the unboosted EV first — the boost is only as good as the ticket underneath it.
Common mistakes
- Adding a heavy favourite to "make the parlay safer." It barely lifts the price and it can still bust the ticket.
- Treating same-game legs as independent, which overstates both the payout and the EV.
- Reading a big payout number as a good bet. The payout is correct; the margin behind it is the question.
- Comparing parlay prices at one book only — the same ticket pays differently across books, and the gap compounds with every leg.
- Chasing a boost into a ticket you would not otherwise place.
Terms used on this page
- Fair odds — the price a bet would carry with no margin attached.
- Hold, or the vig — the book's built-in margin on a market.
- Expected value — what a bet returns on average per dollar staked.
- Decimal odds — the total multiplier on your stake, including the stake.
Questions
How are parlay odds calculated?
Convert every leg to decimal odds and multiply them. Two legs at −110 are 1.9091 × 1.9091 = 3.6446, which converts back to +264. Your stake rides from leg to leg, so the payout multiplies the same way the price does.
What win rate do I need per leg to break even on a parlay?
At −110 legs, 52.38% — and that number does not change with the number of legs. Break-even needs (p × d) to the power of n to equal 1, which reduces to p × d = 1, so n cancels out. Adding legs does not raise the bar per leg; it multiplies whatever edge or deficit each leg already carries, and it sharply increases variance.
Why is the true EV of a parlay usually negative?
Because the margin compounds. An edgeless −110 leg returns 0.9545 per dollar staked, so two legs return 0.9545² and give up 8.9%, four legs give up 17.0%, and ten legs give up 37.2%. Unless your own fair probabilities beat the implied ones, more legs means more margin paid.
When is a parlay actually +EV?
When enough individual legs are +EV, because edges compound exactly the way margin does. Three legs each priced 5% in your favour combine to +15.8%. If you would not bet every leg on its own, the parlay maths does not rescue it.
Does this calculator assume the legs are independent?
Yes. It multiplies your fair probabilities, which is only valid when the legs are unrelated. Same-game parlays are correlated — a quarterback throwing for 300 yards makes his receiver going over 80 more likely — and books price that correlation in. Treat the true-EV output as the independence case, and read the same-game section below before trusting it on a correlated ticket.
What does leaving a leg’s fair probability blank do?
It uses that leg’s implied probability instead, which is the same as saying "I think this price is fair and I have no opinion." That prices the leg at zero edge, so the combined EV shows you exactly what the vig costs across the whole ticket and nothing else.
What happens to a parlay if one leg pushes?
At most books the pushed leg drops out and the parlay re-prices as if you had bet the remaining legs — a three-leg parlay with one push pays as a two-leg. A few books void the whole ticket instead. It changes the payout materially, so check the rules at the book you are using.
Are parlay boosts worth taking?
Sometimes, and it is arithmetic rather than opinion. A boost adds a percentage to the profit, so it lifts EV by roughly that percentage of the pre-boost return. A 30% boost on a ticket sitting at −17% EV still leaves you short of break-even; the same boost on a ticket near fair can push it positive. Price it before you take it.
Is a round robin better than a parlay?
It is not better or worse, it is less variance for less upside. A round robin splits your stake across every smaller combination of the same legs, so you can cash something when one leg misses. The expected value per dollar is the same as the underlying legs — you are choosing a distribution, not buying an edge.
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