Parlay calculator
Updated
A parlay pays only if every leg lands, so its chance is the legs multiplied together. Enter them below and this gives you the combined price, the payout, and the two numbers most parlay calculators skip: how much the bookmaker’s margin grows with each leg you add, and how far the answer can move if your legs are related rather than independent.
Parlay calculator
- 52.4%
- 52.4%
- 40.0%
- Parlay price
- +811
- 9.11 decimal · 11¢
- Chance it lands
- 11.0%
- if the legs are independent
- Pays
- $91.12
- $81.12 profit
- The book’s total cut
- 12.9%
- 3 legs compounded
Multiplying the legs assumes they are independent. If they are related — same game, same team, same weather — the real chance lies somewhere between 0.0% and 40.0%, and no amount of arithmetic narrows that without knowing how they move together.
Why the margin grows with every leg
Each leg is priced a little worse than its true chance, and a parlay multiplies those prices together — so it multiplies the shortfalls too. At a standard 4.5% per leg:
- 2 legs
- 8.8%
- 3 legs
- 12.9%
- 4 legs
- 16.9%
- 6 legs
- 24.0%
The payout gets bigger and the share of your stake that never had a chance gets bigger with it. That is the trade, and it is worth seeing as a number rather than as a feeling.
When multiplying is wrong
Multiplying is only correct if the legs are independent. Two legs from the same game usually are not: a quarterback throwing for 300 yards and his team winning tend to happen together, so the parlay is more likely than the multiplication says. Legs that pull against each other are less likely.
Without knowing how they move together, the honest answer is a range. The Fréchet–Hoeffding bounds give the widest that range can be: no dependence structure can put the true probability above the least likely leg, or below the sum of the legs minus one less than their count. The calculator shows both ends. Papermarkets prices its own combos inside the same bounds rather than multiplying and hoping.
Questions
- How are parlay odds calculated?
- Convert each leg to its implied probability and multiply them together — a parlay pays only if every leg lands. Three legs at 50%, 50% and 40% give 0.5 × 0.5 × 0.4 = 10%, which is +900 in American odds. Converting that combined probability back to odds gives the price the book quotes.
- Why do parlays have worse value than single bets?
- Because the margin compounds. A bookmaker taking 4.5% on each leg is not taking 4.5% on the parlay: it takes 1 - 0.955 to the power of the leg count, which is about 8.8% on two legs, 12.9% on three and 16.9% on four. The payout looks larger, and the share of your stake the book keeps grows with every leg you add.
- Does multiplying work when the legs are related?
- No. Multiplying assumes the legs are independent, and legs from the same game rarely are — a quarterback throwing for 300 yards and his team winning move together. The true probability then sits somewhere in the Fréchet range this calculator shows, which can be far from the multiplied figure in either direction.
- What is a correlated parlay?
- One whose legs influence each other. Books usually refuse the obviously correlated combinations, or price them as a single 'same game' product with its own margin, precisely because multiplying would misprice them.
- Can I build parlays on Papermarkets?
- Yes — they are called combos, and they trade with simulated money like everything else here. Legs are priced against live Polymarket and Kalshi markets, and the price is clamped to the same Fréchet bounds this page shows rather than being a straight multiplication.
Build one without staking anything
Papermarkets lets you build the same thing as a combo across live Polymarket and Kalshi markets, with simulated money. Pick legs from the live markets, size the position with the Kelly criterion calculator, or convert a single leg first with the implied probability calculator. If the whole idea is new, the paper trading guide starts from the beginning.