The Math Behind Parlays: Why the House Always Wins (More)
Parlays are the most profitable product sportsbooks sell. Here's exactly how vig compounds across legs and why the true hold is worse than you think.
How parlays work
A parlay combines multiple bets into one. All legs must win for the parlay to pay out. The payout is calculated by multiplying the decimal odds of each leg together.
Three legs at -110 (1.909 decimal):
Parlay odds = 1.909 x 1.909 x 1.909 = 6.966
Bet $100, win $596.60 in profit. Sounds great. Here's why it isn't.
How vig compounds
Each -110 leg on a fair 50/50 has a book sum of about 104.8% — roughly 4.5% vig. You might think a 3-leg parlay carries 3 x 4.5% = 13.5% vig. That's wrong. It's worse.
Here's the real math. The fair odds of winning three 50/50 coin flips are:
0.50 x 0.50 x 0.50 = 0.125 (12.5%)
Fair decimal odds: 1/0.125 = 8.00
The sportsbook is paying 6.966 instead of 8.00. The implied probability of the parlay payout is 1/6.966 = 14.36%.
True hold = (14.36% - 12.5%) / 12.5% = 14.9%
A 3-leg parlay at standard juice carries roughly 15% vig. Not 4.5%.
The compounding problem
The vig doesn't add — it multiplies. Each leg slightly inflates the implied probability, and those inflations compound:
| Legs | Fair Odds | Parlay Pays | True Hold |
|---|---|---|---|
| 1 | 2.00 | 1.909 | ~4.5% |
| 2 | 4.00 | 3.645 | ~9.7% |
| 3 | 8.00 | 6.966 | ~14.9% |
| 4 | 16.00 | 13.30 | ~20.3% |
| 5 | 32.00 | 25.41 | ~25.9% |
By five legs, the house is keeping more than a quarter of the expected value. That's not a bet — it's a donation.
Same-game parlays are even worse
Sportsbooks price same-game parlays (SGPs) using correlated odds models where they control the correlation assumptions. There's no transparent market to compare against. The vig embedded in SGPs is often 20-40%, sometimes higher — and you have no way to verify it without independent probability estimates.
When parlays make sense
There's exactly one scenario: correlated parlays where the book hasn't fully priced the correlation. If event A makes event B more likely, and the book treats them as independent, the parlay can be +EV even after the compounded vig.
This is rare. And finding it requires you to know the true probabilities, which means de-vigging the individual legs first.
Do the math first
Run your parlay through the parlay calculator to see the true odds and the hidden hold. Use the de-vig calculator to find the fair probability of each leg. Check the total margin with the hold calculator.
If the combined vig makes the parlay -EV, you already know the answer. Don't bet it.
For a primer on how vig works at the single-bet level, read what is vig. To understand why even +EV parlays need proper sizing, see the Kelly Criterion guide.