How the prices are made

A market at -110 on both sides implies 52.38% twice, which sums to 1.0476. That 4.76% is the overround — how far the book is from fair. It is not what the book keeps.

What it keeps is the hold, and the hold is measured against the money taken rather than against a fair book:

hold = overround ÷ (1 + overround)

which comes to 4.55%. The gap is small and it is also about five percent of the number itself, so quoting one where the other is meant overstates a book’s take on every market it writes. A bettor needs 52.38% to break even at that price — the source of every “you have to hit 52.4% to beat the juice” you have read.

It is the same margin taken repeatedly. Writing a leg’s expected return as r = p × d — true probability times quoted decimal — a parlay returns the product of its legs, so the book’s edge is

edge = 1 − (1 − h)ⁿ

Nothing about a parlay is worse leg-for-leg. Five legs at the standard price is the same 4.55% compounded five times, and it comes to nearly 21%. That is the entire reason a book advertises them.

The product is only correct if the legs are independent, and two legs from the same game rarely are. If a team covers by four touchdowns the game almost certainly went over the total, so

κ = P(all legs) ÷ Π P(leg)

runs above one, and a parlay priced by multiplying wins more often than its price assumes. It becomes beatable exactly when κ × Π r > 1 — for two legs at standard juice, a premium above 1.098. A favourite-and-over pairing clears that comfortably, which is why correlated parlays were refused outright for decades.

This book prices them instead. Every leg is a predicate on a simulated final score, so evaluating all of them against the same hundred thousand draws gives the joint probability directly — with whatever correlation the scoring model implies, and correct for three-way and non-monotone combinations where a single correlation coefficient would not even be meaningful. The slip shows you both numbers: what multiplying would have paid, and what the joint distribution says it is worth.

Football margins are lumpy. Mass piles up on 3 and 7, and the gaps at 1, 2 and 5 are real. So moving a spread off a whole number is worth exactly the mass sitting on that number — the push that disappears — and that quantity is different in every sport.

In college football a margin of 3 turns up about 6% of the time; in the NFL it is closer to 14%. The same half point is worth more than twice as much in one than the other, and no model that treats margin as a smooth curve can tell you either figure. It is the best argument there is for pricing football from a distribution rather than a formula.

A teaser moves every leg toward you and pays less. The book’s arithmetic is simple and it holds almost everywhere, because points bought at a flat rate are worth wildly different amounts depending on which points they are.

Teasing a favourite from -7.5 to -1.5 sweeps up both 3 and 7 together; teasing from -20 to -14 crosses almost nothing. Same six points, same price.

A two-team six-pointer at -110 needs 72.4% a leg, and a leg winning 72.4% of the time is a heavy favourite in its own right. The famous version of this trade was an NFL phenomenon, where margins are tight and 3 and 7 carry about 14% and 9% of the mass. College football is flatter and wider — this model puts a teased -7.5 at roughly 67% — so the same six points fall short of the same price. The slip tells you which, per leg, rather than leaving you the folklore.

A balanced book earns the hold whatever happens: equal money on both sides of a -110 market returns 4.55% of the handle and no result matters. A book is almost never balanced, so the rest of the work is measuring the distance from that state — the worst case by outcome, the stake that would flatten it, and the limit that stops the question arising.

Limits are the real control, not the line. Moving a number discourages the next bet; a limit stops it. Both are here, and derivatives carry smaller ones than the core market, because a same-game parlay priced off a correlation estimate deserves less money behind it than a spread.