Why a parlay's margin compounds

Each leg carries its own overround, and combining legs multiplies the prices — which multiplies the margins along with them. Four legs at −110 produce a fair price near 13.3 to 1 and an offered price near 12 to 1.

Multiplication is the mechanism. A single −110 bet gives away about 4.8 points of overround; four of them give away roughly four times that, because each leg's fee is applied to a payout that already had the previous fees taken out of it.

None of this makes a parlay irrational. A correlated combination the book has mispriced can be excellent value, and a small stake on a long shot is a legitimate purchase of entertainment. The compounding is a cost, not a verdict.

What follows from that is less comfortable. The payout is advertised and the compounding is not. A menu showing '12/1!' is showing the half of the arithmetic that sells.

What to do with it. Price each leg separately, multiply them yourself, and compare the result to what is being offered. The gap is what you are paying.

The parlay calculator multiplies the legs out, which is the easiest way to see the compounding rather than take it on trust.