How parlay payouts are actually calculated, why the book's margin compounds with every leg, what correlation does to same-game parlays, and the narrow cases where a parlay is the right bet.
Parlays are the most profitable product most books sell, and that fact is the most useful thing to know about them. The payout looks large because the probability is small, and the margin compounds on the way.
That does not make every parlay wrong. It makes most of them wrong, for a reason worth understanding.
A single bet at -110 carries roughly 4.5% hold. Parlay two of them and the book is not charging 4.5% — it is charging closer to 9%, because the margin on each leg multiplies through. At five legs you are giving up over 20% before any handicapping.
This is why a parlay needs a much larger edge per leg to break even than a straight bet does. Small edges that are genuinely profitable individually become losses once combined.
Multiplying probabilities assumes independence. Legs from the same game are rarely independent: if a quarterback throws for 350 yards, his top receiver clearing a yardage line is far more likely than his standalone price suggests.
Books know this, which is why same-game parlays are priced by a correlation model rather than by multiplication. The consequence is that the obvious correlated stack — quarterback over, receiver over, team to win — is usually priced with the correlation already removed, and sometimes over-removed.
When a book prices correlated legs as if they were independent, the parlay is underpriced and the correct bet is the parlay. This happens most often in less-attended markets and in cross-market combinations the pricing model does not cover.
Negative correlation is the mirror image and is more common than people expect: two 'under' legs in the same game are often anti-correlated with each other in ways that make the combined price worse than it looks.
Keep the leg count low — two or three, where the compounding margin is survivable. Only combine legs you would bet individually. Size them smaller than straight bets, because the variance is much higher and the win frequency much lower.
And do not treat a parlay as a way to turn a small edge into a big payout. It turns a small edge into a smaller one, and multiplies the swing.