Parlay true-odds
calculator.
Add up to twelve legs. Get the combined parlay payout, the bookmaker's implied probability, and the fair no-vig price. Provide your model's fair probability per leg to compute the parlay's hold and your edge.
Provide your fair probability per leg to compute parlay hold and edge. Leave blank to see the book payout only.
Parlay odds
multiply.
parlay_decimal = leg_1 × leg_2 × … × leg_n
parlay_fair_prob = p_1 × p_2 × … × p_n
The book parlay decimal is the product of every leg's book decimal. The fair parlay probability is the product of every leg's no-vig probability. The bookmaker's hold on the parlay is the gap between the book payout and the fair payout, expressed as a percent of the fair price.
Per-leg hold compounds. A single -110 leg keeps roughly 4.55% for the book. Four -110 legs keep about 17%. Eight legs keep over 30%. That is why parlays are the highest-margin product in any sportsbook.
Questions,
answered.
Why do parlays usually carry such high hold?
Bookmaker hold compounds across legs. A single -110 leg has roughly 4.55% hold; a four-leg parlay of -110 legs has hold around 17%, and an eight-leg parlay pushes past 30%. Even a small per-leg margin becomes punishing once you multiply it across many independent picks.
How is a parlay's true (fair) price calculated?
Multiply the fair (no-vig) probability of each leg, then take the reciprocal. If your model gives every leg a 55% fair probability, a four-leg parlay has a true probability of 0.55 to the fourth power, or about 9.15%. That implies fair decimal odds of 10.93. Compare to the book's payout to see whether the parlay is +EV.
Can a parlay be +EV?
Yes, but only when each leg carries a fair probability above what the book is implying, and the cumulative edge survives compounding the bookmaker's per-leg hold. Same-game and correlated parlays are even harder because the legs are no longer independent and most pricing engines assume they are.
Why don't round-robin parlays fix the vig problem?
A round-robin breaks one big parlay into many smaller ones, which reduces variance but does not change the expected value. Each smaller parlay still carries compounded per-leg hold. If the legs are -EV individually, the round-robin is -EV in aggregate. The math does not care how you slice it.
Are same-game parlays priced differently?
Yes. Same-game parlay legs are correlated, so books use joint pricing models rather than naive multiplication. That correlation cuts both ways: it can hide additional vig, but it also occasionally creates gaps when the book's correlation assumption is wrong. This calculator assumes leg independence, which is correct for cross-game parlays and approximate at best for same-game.
Need fair probabilities
to plug in?
Parlays are only solvable with calibrated leg-by-leg probabilities. VAR's simulators produce them across NFL, NBA, College Basketball, and UFC.
See our methodology