The math
Nothing here needs more than multiplication. But these few pages of arithmetic are the entire reason sportsbooks are buildings and bettors are customers. Work the examples and you know the business.
The only equation that matters
Everything the house does reduces to one line:
Margin is how far above fair value you price. Volume is how many tickets you fill. Luck is real but averages toward zero as volume grows — margin does not. The whole craft is keeping margin positive while keeping volume alive, and surviving the luck term in between.
What a parlay is actually worth
A parlay pays only if every leg hits. If the legs are independent, its true probability is the legs multiplied together — and that number falls off a cliff as legs stack:
That gap between how likely a parlay feels and how likely it is — that is the raw material of the entire parlay business.
Why small edges get big
The house does not need a big margin on any leg — because margin multiplies exactly the way probability does. Shade each leg slightly and the total margin compounds with every leg added:
This is why parlays — not straight bets — are the most profitable product in sports betting, and why the house side of them is worth automating well.
Expected value, per ticket
Expected value (EV) is what a ticket is worth to you on average, before the games are played. It is just the gap between your price and fair value, applied to the payout:
Any night can lose
EV is the average; a night is one draw. Parlays lose often for the bettor, which means the house wins small amounts often and pays out rarely-but-big. That shape means streaks — in both directions.
Two things tame variance: volume (more tickets, more averaging) and caps (bounding what any night can take from you). You control both.
Sizing: how big should a ticket be?
The classic mistake is betting the bankroll on the edge. The house survives by making sure no single outcome matters. Pregame’s recommendations follow that shape:
- Per ticket: ~5% of bankroll. One worst-case ticket dents you 5% — the edge rebuilds that faster than it stings.
- Open book: ~30% of bankroll. If every open ticket paid out at once (it will not), you lose a third, not the roll.
- Per team: ~12% of bankroll. Tickets sharing a team win together — cluster risk deserves its own cap.
Correlation: the trap that eats naive books
Multiplying leg probabilities assumes the legs are independent. Legs from the same game are not: if the Yankees win, Judge probably had a good night. Price them as independent and you sell the parlay far too cheap.
Longshots: where small errors are huge
Pricing error is relative to the price. A 1¢ mistake on a 60¢ leg is noise; a 1¢ mistake on a 2¢ parlay is half the price.
Long parlays are also where the payout multiples get scary: a $10 stake at 2¢ is $500 of payout. Longshot appetite is a setting, not a default.
Pricing against other makers
You are not quoting into a void — other makers answer the same requests, and the bettor takes the best price. Price too wide and you never fill; price at fair and you fill everything, profitlessly. The craft is the middle:
Pregame’s follow-the-market mode automates this: it tracks what winning quotes clear at, per leg count, and prices at your chosen percentage of that — undercut to fill more, price over to earn more per fill.
A real ticket, worked end to end
The desk’s first live fill, every number real:
Rules of thumb
- Multiply to price: independent legs multiply; so does margin. Long tickets carry big total edge.
- Think EV, not outcomes: you are paid for the price you set, not for how one night lands.
- Volume is the variance cure: more small tickets beats few big ones at the same total risk.
- Cap by cluster: ticket ~5%, open book ~30%, any one team ~12% of bankroll.
- Never price correlation as independence: decline instead.
- Fear cheap tickets: relative error explodes below a few cents. Use the price floor.
- Margin is a market: track what fills, undercut deliberately, and let the fill rate tell you when you're too greedy.