A parlay combines several bets (legs) into one. Every leg has to win. The payout is large because the chance is small, and the vig on each leg compounds.
Parlay odds
Multiply the legs' decimal odds. Three legs at 1.91, 2.10 and 1.80:
- 1.91 × 2.10 × 1.80 = 7.22, or +622
- implied probability: 1 ÷ 7.22 = 13.85%
Unitley takes parlays of 2 to 25 legs.
The vig compounds
Two legs at −110, each a true coin flip:
- payout: 1.909 × 1.909 = 3.645, or about +264
- a fair price for a 25% chance would be +300
- EV: 0.25 × 3.645 − 1 = −8.9%, against −4.55% on a single −110 bet
Each leg adds its margin to the parlay's, so a parlay of fairly priced legs is a worse bet than any one of them. A parlay is only worth making when the legs themselves have an edge.
Correlation
Multiplying the legs' chances gives the parlay's chance only when the legs are independent: when one winning tells you nothing about the others. Legs on the same game rarely are.
- A favorite to cover and the game to go over the total often go together: a blowout win usually means plenty of points.
- A quarterback's passing yards and the team's points rise and fall together.
- A running back's rushing yards often go with the team leading late.
Correlated legs win together more often than the multiplied chance says, or less often if they pull against each other. Bookmakers know this. Same-game parlays are priced with the correlation and usually with a bigger margin than the legs carry on their own. Many books will not take some correlated legs together at all.
In Unitley
calc_parlay multiplies the legs' prices and returns the parlay's decimal and American odds and implied probability. Give every leg your win chance and it also returns the combined chance and EV, which are honest only for independent legs. Legs that share a game id get a correlation warning: their combined chance is then unreliable, so treat it as a rough guide, not a number to bet on.
Names set like this are Unitley’s tools: what your AI agent, or the analyst in the web app, calls to get these numbers. See the docs