Guide
Are Parlays Worth It? The Math of Stacking Legs
By Agatha Research Desk. Updated
Record numbers refresh hourly; last refreshed .
The math
Every price a book offers has its margin built in. In a -110 / -110 market each side pays 1.909 in decimal odds, while the fair price of an even chance is 2.000. That gap is the book's 4.55% hold, and on a single bet you pay it once.
A parlay multiplies the decimal odds of its legs. The fair payout multiplies too, and the ratio between them compounds: each leg keeps only (1 - hold) of its fair value, so n legs keep (1 - hold) to the power n.
payout = d1 x d2 x ... x dn fair = (1 / p1) x (1 / p2) x ... x (1 / pn) keeps = 1 - payout / fair = 1 - (1 - hold) ^ n
| Legs | Pays (decimal) | Fair payout | Book keeps | American |
|---|---|---|---|---|
| 1 | 1.91 | 2.00 | 4.5% | -110 |
| 2 | 3.64 | 4.00 | 8.9% | +264 |
| 3 | 6.96 | 8.00 | 13.0% | +596 |
| 4 | 13.28 | 16.00 | 17.0% | +1228 |
| 5 | 25.36 | 32.00 | 20.8% | +2436 |
| 6 | 48.41 | 64.00 | 24.4% | +4741 |
| 7 | 92.42 | 128.00 | 27.8% | +9142 |
| 8 | 176.45 | 256.00 | 31.1% | +17545 |
Payouts include the stake. Fair odds remove the margin from each -110 / -110 market.
Two legs give up 8.9% of the fair payout, three give up 13.0% and eight give up 31.1%, against 4.5% on a single bet. The bigger payout is real; so is the bigger share the book keeps. Check any ticket in the parlay calculator.
From the odds Agatha tracks
With the holds we measured
Real markets rarely sit at exactly -110 on both sides. Across 70,020 two-way moneylines at the books Agatha tracks over the last 30 days, the median closing hold was 4.88%. At that margin a 3-leg parlay gives up 13.9% of its fair value and a 5-leg parlay 22.1%, for a bettor whose picks are no better than the market's own fair price.
The gap between leagues matters. NFL moneylines held 4.50% (a 3-leg parlay gives up 12.9%), while esports held 6.94% (19.4% on three legs). Shopping each leg for the best price across books cuts the margin you pay on every leg.
| League | Median hold | 2 legs | 3 legs | 5 legs |
|---|---|---|---|---|
| NFL | 4.50% | 8.8% | 12.9% | 20.5% |
| MLB | 4.51% | 8.8% | 12.9% | 20.6% |
| NHL | 4.58% | 9.0% | 13.1% | 20.9% |
| CFL | 4.61% | 9.0% | 13.2% | 21.0% |
| WNBA | 4.74% | 9.3% | 13.6% | 21.6% |
| NCAAF | 4.83% | 9.4% | 13.8% | 21.9% |
| UFC | 4.91% | 9.6% | 14.0% | 22.3% |
| ATP | 5.11% | 10.0% | 14.6% | 23.1% |
| WTA | 5.30% | 10.3% | 15.1% | 23.8% |
| Esports | 6.94% | 13.4% | 19.4% | 30.2% |
| Every league | 4.88% | 9.5% | 13.9% | 22.1% |
From Agatha's record
Agatha's picks as parlays
Take every day of Agatha's record and build every parlay that day's graded picks allow, one pick per game, at the prices listed: 3,810,995 three-leg parlays in all, and 2,466,493,983 with 5 legs. The table compares them with the same picks bet as singles.
As singles the picks returned -2.16%. Every leg added made it worse: 2 legs -5.59%, 3 legs -9.33%, 4 legs -12.44%, 5 legs -14.33%. A parlay magnifies whatever its legs do, and these legs did not clear the margin.
Busy days weigh more. A board day with 149 graded picks can build up to 540,274 three-leg parlays; a day with 7, up to 35. One good or bad Saturday counts many times over, which is why the parlay figures are not simply the singles figure compounded.
| Legs | Parlays | Cashed | ROI | Singles compounded |
|---|---|---|---|---|
| Single | 2,591 | 58.5% | -2.16% | -2.16% |
| 2 | 114,050 | 33.3% | -5.59% | -4.27% |
| 3 | 3,810,995 | 18.6% | -9.33% | -6.33% |
| 4 | 105,033,186 | 10.2% | -12.44% | -8.35% |
| 5 | 2,466,493,983 | 5.7% | -14.33% | -10.33% |
Cashed counts every ticket that returned money, including tickets a pushed leg repriced. Singles compounded is the singles' return taken to the power of the legs: what the parlays would return if every day counted the same.
As of . See the full track record
Same-game legs
A same-game parlay joins legs from one game, and those legs are not independent: a quarterback's passing yards and his team's points tend to rise together. Multiplying their prices would misstate the real chance, so books price same-game parlays with a model of their own and a margin you cannot read off the individual legs. That makes the cost harder to see, not smaller.
It is also why the combinations above use at most one pick per game: two legs from one game would be priced as if they were independent, and they are not.
Pushes and voids in a parlay
A pushed leg (a tie against the line) or a void leg (a game postponed or canceled, a player who never took part) drops out, and the ticket reprices from the legs that remain. Any lost leg loses the ticket. One leg left grades as a single bet; no legs left returns the stake.
On a $10.00 ticket of three -110 legs that returns $69.58 when all three win: one push makes it a 2-leg parlay returning $36.45; two drops leave a single returning $19.09; three drops return the $10.00 stake.
Agatha settles her own parlays exactly this way; the full rulebook is in how Agatha grades. Books differ on details, such as how long a postponed game has to be played before its leg is void, so check your own book's house rules. The parlay calculator settles pushes and voids leg by leg.
When a parlay can make sense
Only when every leg is a price better than fair. Then the compounding works for you: two legs each worth +3% against a fair price make a parlay worth +6.09%. Finding one such leg is hard; finding several on the same day is harder, and one leg below fair can erase the rest.
Otherwise treat a parlay as entertainment: a small stake you would spend anyway, sized so that losing it changes nothing. Never use one to win back losses; the margin compounds against that plan on every ticket. Responsible play has tools for setting limits.
Questions
Are parlays a bad bet?
For most bettors, yes: the margin compounds with every leg. Three -110 legs give up 13.0% of their fair payout, against 4.5% on a single bet. Built from Agatha's own graded picks, three-leg parlays returned -9.33%.
How much does a 3-leg parlay pay at -110?
6.958 times the stake. A $10.00 ticket returns $69.58: $59.58 in winnings plus the stake. At fair odds on each leg the same ticket would return $80.00. Price any ticket in the parlay calculator.
What happens if one leg of a parlay pushes?
It drops out and the parlay reprices from the other legs; a 3-leg ticket becomes a 2-leg ticket. A void leg drops the same way. See how Agatha grades.
Do parlay boosts fix the math?
Sometimes. A boost raises the payout, so compare the boosted payout with the fair payout of the same legs. If the boost lifts it above fair, the ticket is worth more than it costs; if not, it only takes a smaller bite. At the 4.88% median hold measured at the books Agatha tracks, a 3-leg parlay of -110 legs needs a boost of about 18.9% on its winnings, the way most books quote a boost, just to reach fair (16.2% on the whole payout, stake included).
Is a same-game parlay better or worse?
Harder to judge. Its legs move together, so the book prices the ticket with its own model and a margin you cannot see in the individual prices. Treat it as the most expensive kind of parlay until you can price it yourself.