KEY TAKEAWAYS
To calculate parlay odds, convert each leg’s odds to decimal odds and multiply them together. The product is the parlay’s decimal odds, and the payout is the stake times that product. Three hypothetical legs at −110, +150 and −200 convert to 1.9091, 2.50 and 1.50, which multiply to about 7.1591, so a $20 stake returns about $143.18, a profit of $123.18.
The same arithmetic shows what a large payout hides. Each extra leg multiplies the price, and it also multiplies the vig built into the odds. Two −110 legs need a 27.44% chance of both winning just to break even, and if each leg is truly a 50% chance, the two-leg parlay has an expected value of about −8.88% per dollar, against −4.55% for a single bet at −110.
This guide gives the formula with every symbol defined, three fully worked examples with different inputs, a reference table by number of legs, the most common mistakes, and a routine for checking an answer. All lines are hypothetical, no picks are offered, and every step is done by hand.
What a Parlay Is and Why Odds Multiply
A parlay is a single bet that combines two or more selections, called legs. Every leg must win for the parlay to pay, and the payout is far larger than the payouts of the same legs bet separately. One losing leg loses the whole stake.
The payout is built by multiplication. Suppose a leg is priced fairly at decimal odds D. Then D is 1 divided by the probability of the leg winning, and for independent events the chance of all legs winning is the product of the individual chances. Multiplying the legs’ decimal odds therefore gives the price of the combined event.
American odds such as −110 or +150 cannot be multiplied directly, because they use two different scales for favorites and underdogs. Convert every leg to decimal odds first, multiply, and convert back only if an American price is wanted. The conversion rules are covered in how to convert American odds to decimal odds.
Two assumptions apply throughout. The legs are independent, meaning one result does not change the chance of another, and every leg is settled as a win or a loss. Related legs and tied results are handled by the rules of each market, so those rules vary and are not part of the basic formula.
The Parlay Odds Formula, Step by Step
Step 1 converts each leg’s American odds to decimal odds.
American −A → decimal = 1 + 100 ÷ A
where:
A is the number in the American odds without its sign, for example 150 in +150 or 110 in −110.
Decimal odds include the returned stake, so they are always greater than 1.
Step 2 multiplies the decimal odds of all legs.
where:
D₁, D₂ and so on are the decimal odds of each leg.
n is the number of legs.
Step 3 turns the parlay odds into a payout and a profit.
profit = total payout − stake
where:
The stake is the amount wagered in dollars.
The total payout includes the returned stake.
Step 4 gives the probability needed to break even.
If an American price is wanted at the end, convert the parlay decimal odds back: for D of 2 or more, American = +(D − 1) × 100, and for D below 2, American = −100 ÷ (D − 1).
The formula works because the break-even probability of the parlay equals the product of the legs’ break-even probabilities. Each leg’s price already contains the vig, so that margin is multiplied along with the odds. Keep at least four decimal places until the final step, because rounding early shifts the payout.
Worked Examples, Step by Step
Example 1: three legs, $20 stake. The legs are −110, +150 and −200.
Step 1: −110 → 1 + 100 ÷ 110 ≈ 1.9091.
Step 2: +150 → 1 + 150 ÷ 100 = 2.50.
Step 3: −200 → 1 + 100 ÷ 200 = 1.50.
Step 4: parlay decimal odds = 1.9091 × 2.50 × 1.50 ≈ 7.1591.
Step 5: total payout = 20 × 7.1591 ≈ $143.18, so the profit is about $123.18.
Step 6: break-even probability = 1 ÷ 7.1591 ≈ 13.97%, which matches 52.38% × 40.00% × 66.67% ≈ 13.97% from the three legs’ implied probabilities.
Example 2: two −110 legs, $50 stake.
Step 1: both legs convert to 1.9091, so the parlay decimal odds are 1.9091 × 1.9091 ≈ 3.6446.
Step 2: total payout = 50 × 3.6446 ≈ $182.23, a profit of about $132.23. In American terms, (3.6446 − 1) × 100 ≈ +264.
Step 3: break-even probability = 1 ÷ 3.6446 ≈ 27.44%.
Step 4: if each leg is truly a 50% chance, both win with probability 0.50 × 0.50 = 25%, so EV per $1 = 0.25 × 3.6446 − 1 ≈ −0.0888, or −8.88%. On $50, the average loss is about $4.44.
Example 3: four legs quoted in decimal odds, $10 stake. The legs are 1.80, 2.10, 1.65 and 3.00, so no conversion is needed.
Step 1: parlay decimal odds = 1.80 × 2.10 × 1.65 × 3.00 = 18.711.
Step 2: total payout = 10 × 18.711 = $187.11, a profit of $177.11, or about +1,771 in American odds.
Step 3: break-even probability = 1 ÷ 18.711 ≈ 5.34%, the same as 55.56% × 47.62% × 60.61% × 33.33% ≈ 5.34%. In words, the parlay must win about 1 time in 19 just to break even.
Common Mistakes and Misconceptions
The first mistake is adding or multiplying American odds directly. Combining +150 and −110 as numbers gives a meaningless result. Convert to decimal first.
The second is reporting the total payout as the profit. The payout includes the returned stake, so the profit is the payout minus the stake.
Third, many readers think a parlay increases the odds of winning. The payout rises, but the chance of winning falls, because the probabilities of the legs are multiplied. Two 50% legs win together only 25% of the time.
Fourth, rounding each decimal to two places early can move a long parlay’s payout by several dollars. Finally, treating related legs as independent overstates or understates the true chance.
Quick Reference and How to Check Your Answer
The table shows parlays built from identical −110 legs. Each added leg multiplies the payout and also the vig, as the last column shows for legs that are each a true 50% chance. The break-even win rate falls quickly, which is why long parlays pay so much, but the expected value falls with it: from −4.55% for one leg to −20.75% for five.
| Legs | Parlay decimal odds | Payout on $10 | American equivalent | Break-even win rate | EV per $1 if each leg is 50% |
|---|---|---|---|---|---|
| 1 | 1.9091 | $19.09 | −110 | 52.38% | −4.55% |
| 2 | 3.6446 | $36.45 | +264 | 27.44% | −8.88% |
| 3 | 6.9579 | $69.58 | +596 | 14.37% | −13.03% |
| 4 | 13.2833 | $132.83 | +1,228 | 7.53% | −16.98% |
| 5 | 25.3591 | $253.59 | +2,436 | 3.94% | −20.75% |
Check an answer in four steps. Confirm that the parlay decimal odds exceed every single leg’s odds. Confirm that 1 ÷ parlay decimal odds equals the product of the legs’ implied probabilities. Confirm that the payout is larger than the stake and the profit is the payout minus the stake. Finally, convert the parlay odds back to American and check that the price is consistent with the decimal figure.
Related Concepts and Next Steps
Parlay payouts depend on the conversions in converting American odds to decimal odds, and the average result of any bet comes from the expected value formula. The idea that independent chances multiply is explained in probability in gambling.
Frequently Asked Questions
