Parlays: the math, and correlation

A parlay is not a bigger bet, it is several bets whose fees multiply. Sometimes that is worth it; the calculation tells you when.

A parlay is not a bigger bet. It is several bets whose fees multiply together. Sometimes that is worth it; the calculation tells you when, and it is not often.

The math

Convert every leg to decimal odds and multiply. Two -110 legs give 1.909 × 1.909 = 3.645, or about +264. All legs must win; one loss kills the whole ticket.

Where the money goes on a two-leg parlay

Both legs are true coin flips, priced at -110.
Fair price for both landing: 0.5 × 0.5 = 25%, which is +300.
The book offers +264.
+264 implies 27.5%.

You are being paid 264 for something worth 300. The fee on the parlay is about 8.7% — nearly double the 4.55% on either leg alone.

The fee compounds. Two legs is roughly double the single-bet fee; five legs is roughly five times it. A five-leg -110 parlay holds over 20%, which puts it in futures territory.

What each extra leg costs, at standard juice
Legs	Payout	Fair payout	Approximate hold
2	+264	+300	~8.7%
3	+596	+700	~13%
4	+1228	+1500	~17%
5	+2436	+3100	~21%

Correlation

The multiplication above assumes the legs are independent. Often they are not. If a quarterback throws for 350 yards, his team's total is more likely to go over — the legs move together.

Positive correlation makes a parlay more likely to win than the multiplication suggests, which is why books have always refused the obvious combinations. Negative correlation — a team's over and the opponent's under, say — makes it less likely, and books are perfectly happy to take those.

Same-game parlays

A same-game parlay is the book's answer: rather than forbid correlated legs, it reprices them with a model that accounts for how they move together. That repricing is where almost all of its fee lives.

SGPs are the most expensive product on the board

Typical hold on a same-game parlay is 15-25%, and it is not visible anywhere on the ticket. You cannot check it by multiplying the legs, because the legs are no longer priced independently — which is precisely what makes it hard to tell how much you are paying.

When a parlay is defensible

Each leg is independently +EV. If every leg beats its fair price by enough to cover the compounding fee, the parlay can still be positive. This is rare and it is arithmetic, not a feeling.
A correlated combination the book has underpriced. Real, occasionally, and mostly closed by the SGP models.
You want the variance. A small stake at a long price for entertainment is a legitimate purchase. Just call it what it is.

What does not make a parlay defensible is confidence. Three bets you like are three bets; combining them multiplies the fee and adds nothing to the analysis. A round robin does not fix this either — it spreads the same compounded fee across more tickets.

Build a slip and see its true price against what the book is offering. Open the parlay builder.