To calculate parlay odds, convert every leg to decimal odds, multiply those decimals together, then multiply by your stake for the total payout. Subtract the stake to get profit. Three legs at −110 multiply to 6.9579, so a $20 ticket returns $139.16 in total and $119.16 in profit.
Run your own ticket through the parlay calculator, or compare every leg count at once in the parlay odds chart.
The parlay odds formula
Combined decimal odds = leg 1 × leg 2 × ... × leg n, with every leg expressed in decimal odds.
Total payout = stake × combined decimal odds.
Profit = total payout − stake.
Decimal odds already contain the returned stake, which is why the payout formula has no addition in it. Three legs at −110 convert to 1.909091 each and multiply to 6.9579, so a $20 ticket returns $139.16 in total and $119.16 in profit.
One convention holds for every example below: decimal odds are displayed rounded, and every product is computed from the unrounded value. Multiplying the displayed column instead is the single most common reason a hand calculation misses a sportsbook slip, and the size of that miss is worked out at the end of this page.
How to calculate a parlay step by step
A two-leg parlay, both legs at −110, staked $25.
- Convert each leg to decimal odds. −110 becomes
1 + (100 / 110) = 1.909091. - Multiply the legs together, at the precision step 1 produced:
1.909091 × 1.909091 = 3.6446. - Multiply by the stake. $25 returns
$91.12in total. - Subtract the stake for profit:
$66.12.
The combined American price is +264, and the implied probability is 27.44%.
How to calculate parlay payout and profit
Payout and profit are two different numbers and the difference is exactly the stake. The same three-leg −110 ticket, at five stakes:
| Stake | Total payout | Profit |
|---|---|---|
| $5 | $34.79 | $29.79 |
| $10 | $69.58 | $59.58 |
| $20 | $139.16 | $119.16 |
| $50 | $347.90 | $297.90 |
| $100 | $695.79 | $595.79 |
Combined decimal odds 6.9579 (+596), computed from the unrounded per-leg decimal.
Payout scales linearly with stake because the combined decimal price does not depend on how much is staked. The price is set by the legs alone.
How to convert American odds to decimal
For a positive price: decimal = 1 + (price / 100). +150 becomes
1 + 1.50 = 2.50.
For a negative price: decimal = 1 + (100 / |price|). −200 becomes
1 + 0.50 = 1.50.
Implied probability is 1 ÷ decimal, and profit on a $100 stake is
100 × (decimal − 1). The full reference:
| American | Decimal | Implied probability | Profit on $100 |
|---|---|---|---|
| −1,000 | 1.100 | 90.91% | $10.00 |
| −500 | 1.200 | 83.33% | $20.00 |
| −300 | 1.333 | 75.00% | $33.33 |
| −250 | 1.400 | 71.43% | $40.00 |
| −200 | 1.500 | 66.67% | $50.00 |
| −175 | 1.571 | 63.64% | $57.14 |
| −150 | 1.667 | 60.00% | $66.67 |
| −140 | 1.714 | 58.33% | $71.43 |
| −130 | 1.769 | 56.52% | $76.92 |
| −120 | 1.833 | 54.55% | $83.33 |
| −110 | 1.909 | 52.38% | $90.91 |
| −105 | 1.952 | 51.22% | $95.24 |
| +100 | 2.000 | 50.00% | $100.00 |
| +105 | 2.050 | 48.78% | $105.00 |
| +110 | 2.100 | 47.62% | $110.00 |
| +120 | 2.200 | 45.45% | $120.00 |
| +130 | 2.300 | 43.48% | $130.00 |
| +140 | 2.400 | 41.67% | $140.00 |
| +150 | 2.500 | 40.00% | $150.00 |
| +175 | 2.750 | 36.36% | $175.00 |
| +200 | 3.000 | 33.33% | $200.00 |
| +250 | 3.500 | 28.57% | $250.00 |
| +300 | 4.000 | 25.00% | $300.00 |
| +500 | 6.000 | 16.67% | $500.00 |
| +1,000 | 11.000 | 9.09% | $1,000.00 |
25 prices, from −1,000 to +1,000. The odds converter handles any price not listed, in either direction.
A worked three-leg parlay with mixed odds
Nothing requires the legs to share a price.
| Leg | American odds | Decimal odds |
|---|---|---|
| Team A | −120 | 1.8333 |
| Team B | +135 | 2.3500 |
| Team C | −105 | 1.9524 |
Multiply the decimal column: 1.8333 × 2.3500 × 1.9524 =
8.412. A $10 stake returns
$84.12 in total, $74.12 of it profit. The combined
American price is +741 and the implied probability is
11.89%.
A worked four-leg parlay across four market types
The arithmetic does not care what the legs are, only what they cost.
| Leg | Market | American odds | Decimal odds |
|---|---|---|---|
| 1 | Spread | −110 | 1.9091 |
| 2 | Total | −105 | 1.9524 |
| 3 | Moneyline | +145 | 2.4500 |
| 4 | Prop | −125 | 1.8000 |
1.9091 × 1.9524 × 2.4500 × 1.8000 = 16.4373, which is
+1,544. A $20 stake returns $328.75 in
total and $308.75 in profit, against an implied
6.08%.
How parlay win probability is calculated
When the outcomes are independent, multiply the probability of every leg. Three
outcomes that are each truly 50% combine to
0.50 × 0.50 × 0.50 =
0.125, or 12.5%. That is once in
8 attempts on average.
The probability implied by a posted price is a different quantity. Three −110 legs price to an implied 14.372%, which is 1.872 points above the 12.5% that genuine coin flips deliver. The gap is the sportsbook's margin, compounded three times. Our parlay probability page tabulates that gap for every leg count.
Why the margin compounds
A parlay does not strip the margin out of its legs. It multiplies prices that each already carry one, so the margin is applied once per leg rather than once per ticket. Adding legs raises the headline price and raises the number of ways the ticket can lose at the same time.
Correlation runs the other way. Two legs from the same game are frequently not independent, and sportsbooks price same-game parlays with their own models instead of multiplying the displayed odds. The formula on this page describes independent legs.
What happens when a leg pushes
Under the common house rule a pushed or voided leg is removed and the ticket reprices as though it had been bought one leg shorter. A 4-leg −110 parlay staked $20 is +1,228 and would return $265.67. With one leg pushed it becomes a 3-leg parlay at +596 returning $139.16, so $126.51 of the potential return goes with the voided leg. House rules on voids vary by book and by market, so confirm the rules that apply to your account.
Why a hand calculation and a sportsbook slip diverge
The largest single cause is rounding the inputs. −110 is 1.909091 in decimal, not 1.91. Multiplying the display-rounded 1.91 three times gives 6.9679 and a $20 payout of $139.36. Multiplying the unrounded value gives 6.9579 and $139.16. The $0.20 difference is entirely an artefact of when the rounding happened, and it grows with every leg added.
Every figure on this page rounds once, at the end. Other reasons a slip can differ: a boosted or capped price, an alternate line priced separately, a same-game correlation model, the book's own display rounding, and its rules for voided legs.
Payout versus profit
- Payout is the total returned, including the original stake.
- Profit is the payout minus the stake.
- Decimal odds quote payout. American odds quote profit against a $100 reference.
A $20 ticket at +596 has a $139.16 payout and a $119.16 profit. Both describe the same ticket.
How this was measured
- Source. Closed-form arithmetic, not a sample. There is no data set behind this page, no window and no n: an American price converts to decimal, the decimals multiply, and the product is the parlay's price.
- Conversion. A positive price becomes
1 + price/100; a negative price becomes1 + 100/|price|. So −110 is 1.9091 and +100 is 2.0000. - Precision. Every figure is computed at 40 significant digits and rounded once, at the end. No rounded value is fed back into a calculation, which is why multiplying the displayed decimal column by your stake can land a few cents away from the payout column.
- Assumptions. Legs are independent and are multiplied as posted. No boost, no promotional cap, no alternate-line price and no same-game correlation adjustment is applied. Sportsbooks price correlated legs with their own models rather than by multiplying, so this arithmetic does not describe a same-game ticket.
- Reproducing it. Every table is stamped onto the page from the output of one committed, re-runnable script, which shares its price conversions with our parlay probability page so the two cannot round a price differently. A separate auditor reads the published page back and re-derives every cell in it a second time; the page does not ship if a single figure has moved.
Next steps
Frequently asked questions
How do you calculate parlay odds?
Convert every leg to decimal odds, multiply the decimals together, then multiply by the stake. Three −110 legs give 6.9579, so $20 returns $139.16.
Do you add or multiply parlay odds?
Multiply, and multiply decimal odds rather than American ones. Adding American prices together produces a number with no meaning.
How do you calculate parlay payout?
Multiply the stake by the combined decimal odds. The payout includes the stake, so profit is that figure minus the stake: a $20 three-leg −110 ticket pays $139.16 and profits $119.16.
How do you calculate a parlay with different odds formats?
Convert every leg to decimal first, then multiply. The conversion table on this page covers American prices in both directions.
Why does my sportsbook show a different payout?
Most often rounding: −110 is 1.909091 in decimal and multiplying the rounded 1.91 instead shifts a $20 three-leg payout by $0.20. Boosts, caps, alternate lines, same-game correlation models and void rules also change the figure.
What happens if one leg pushes?
Under the common rule the leg is removed and the ticket reprices one leg shorter. A 4-leg −110 parlay staked $20 drops from $265.67 to $139.16. House rules vary by book and by market.
What does a 3-leg parlay at −110 return?
6.9579 in decimal odds, +596 in American terms, and $69.58 back on a $10 stake. The parlay odds chart lists every leg count from 2 to 12.
Related: parlay calculator · parlay odds chart · what percentage of parlays win · odds converter · how sportsbooks price parlays · betting glossary
This guide explains how a betting market works and how the arithmetic is done. It is information, not betting advice: Nebula Insights publishes no picks, no selections and no recommended wagers. Sportsbook rules vary by book and jurisdiction, so always confirm the house rules that apply to your account. You must be of legal gambling age in your jurisdiction.