Parlay Math: Why Multi-Pick Payouts Shrink Your Edge
A parlay combines several picks into one entry that pays only if every leg wins. The payout looks attractive because it grows quickly with each added leg. The arithmetic behind it is less flattering, and it is worth seeing in numbers before you decide how much weight to give a big multiplier. This article covers how parlay odds are built, what happens to the margin, and why correlation complicates things.
How parlay odds are built
A parlay multiplies the decimal odds of each leg. Decimal odds are the total return per 1 staked, including the stake. A -110 price is 1.909 in decimal (100 / 110 + 1). The odds converter can translate any American price.
Two legs at -110 each:
- 1.909 x 1.909 = 3.645
- A 100 stake returns about 364.46 if both win, a profit of 264.46. In American terms, about +264.
Three legs at -110:
- 1.909 x 1.909 x 1.909 = 6.958
- A 100 stake returns about 695.79, a profit of about 595.79, or about +596.
You can check this with the parlay payout calculator. Small differences from the numbers here can come from rounding or from how a particular operator rounds payouts.
The chance of winning every leg
For separate, independent events you multiply the probabilities. If each leg were a fair 50% proposition:
- 2 legs: 0.5 x 0.5 = 25.0%
- 3 legs: 12.5%
- 4 legs: 6.25%
- 5 legs: 3.125%
If your legs each had a 60% chance, three legs would be 0.6 x 0.6 x 0.6 = 21.6%, and five legs 0.6^5 = 7.8%. Each extra leg multiplies the chance by something below 1, so the probability of cashing falls fast. A hit rate that looks strong on one prop becomes a much smaller number across several. For example, three props each with a 70% hit rate give 0.7^3 = 34.3% if the games are independent. See how to read a hit rate for why those individual rates are already uncertain.
What happens to the margin
Here is the part that surprises people. A fair parlay of two 50% legs would pay 4.00 in decimal terms (a 1 in 4 chance paid at 4 to 1 including the stake, or +300). The book pays 3.645.
Expected value per 1 staked, assuming each leg truly has a 50% chance:
- Single bet at -110: 0.50 x 1.909 - 1 = -0.0455, or -4.5%
- 2-leg parlay at -110: 0.25 x 3.645 - 1 = -0.0889, or -8.9%
- 3-leg parlay: 0.125 x 6.958 - 1 = -0.130, or -13.0%
- 4-leg parlay: 0.0625 x 13.284 - 1 = -0.170, or -17.0%
- 5-leg parlay: 0.03125 x 25.359 - 1 = -0.208, or -20.8%
Each leg's margin compounds. The vig on a single -110 bet is a few percent. Stack legs and the margin on the combined entry is the product of all the small ones. This is arithmetic, not opinion, and it holds whenever every leg is priced with margin and the chances are what the market says they are.
Break-even per leg
Another way to see it: what does each leg need to clear for the parlay to break even?
At 3 legs paying 6.958, the combined chance needed is 1 / 6.958 = 14.37%. The cube root of that is 0.5238, so each leg must win 52.38% of the time, the same as the break-even for a single -110 bet. The parlay does not lower the hurdle. It makes you clear it on every leg at once, with far less room for ordinary misses.
If you had a genuine edge on every leg, say each really won 55% of the time, the combined chance would be 0.55^3 = 16.6%, and the 3-leg expected value would be 0.1664 x 6.958 - 1 = +0.158, about +15.8%. So the compounding works in both directions, and some people use parlays for that reason. But a 55% true chance on a player prop is an assumption almost nobody can verify, and the downside is that you lose far more often. At 16.6% to win, a typical run of ten entries has no winners about 16% of the time (0.834^10 = 0.16).
Correlation: when legs are not independent
All the multiplication above assumes legs are independent. In player props they often are not.
Suppose a parlay includes a quarterback's passing yards over and his top receiver's receiving yards over from the same game. If the quarterback has a big day, the receiver likely did too. The two legs rise and fall together. They are positively correlated, and the true chance of both winning is higher than 0.5 x 0.5.
Books know this. Many either refuse to combine same-game legs they consider correlated or price them with their own adjustment, so you cannot assume the multiplied payout applies. Correlation also cuts the other way: a parlay with a player's points over and a teammate's points over is partly a bet against a blowout. Whether a combination helps or hurts depends on details no calculator knows, which is why same-game parlay math is murkier than the clean multiplication in the tables above.
Pick'em style entries
Some fantasy-style products ask you to choose over or under on several players and pay a fixed multiplier for the number of correct picks, rather than a price per leg. The same logic applies: a 3-pick entry paying 6x needs the three picks to win together about 16.7% of the time to break even (1 / 6), which is 55.0% per pick if independent (the cube root of 0.1667). Payout tables differ by operator and change over time, so read the current terms. The next article, Pick'em vs sportsbook player props, compares the formats in more detail.
Practical takeaways
- A bigger payout is paid for with a smaller chance, and with a larger total margin.
- Break-even per leg does not shrink as you add legs; it applies to every leg at once.
- Use hit rates and no-vig prices to judge each leg alone first. A weak leg does not become strong by being combined. See what a no-vig price is.
- Be wary of any claim that a parlay "boosts" your odds. It boosts the payout and lowers the probability together.
- Same-game legs are rarely independent; check the operator's rules.
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