Definition
Parlay combines multiple bets; all legs must win for payout. Winnings from each leg roll into the next. Quoted odds like −110 imply a probability (110 ÷ 210 = 52.38%), not the bettor's true win probability — the gap between them is the vig. If two legs are each truly 50/50, independent of each other, the true combined win probability is 0.5 × 0.5 = 25%, so a fair no-vig payout would be +300 (1 ÷ 0.25 − 1). Multiplying the quoted −110/−110 implied probabilities instead (0.5238 × 0.5238 = 27.44%) prices the parlay near +260 — each leg's vig carries through and compounds rather than cancelling, so +260 is worse for the bettor than the true fair +300, not "roughly fair." Three or more legs increasingly favor the house. This all assumes the legs are independent; correlated legs (same-game parlays, related props) break the simple multiplication and need a joint probability instead.
Worked Example
Three legs each at −110 (implied 52.38% each — not true probability, see Definition). Multiplying those implied probabilities, assuming independence: 0.5238 × 0.5238 × 0.5238 = 14.4% combined implied probability. The payout that implies is 1 ÷ 0.144 − 1 = +595. Books typically pay +595–600 for 3-team parlays, close to that implied-probability multiplication — which still carries each leg's vig forward, not a de-vigged fair price. Adding +EV legs compounds edge; adding −EV legs compounds negative expectation.
Why It Matters
Parlaying +EV bets amplifies edge. Parlaying −EV bets at better-than-fair parlay boosts are common sharp plays — but only if individual legs are already positive EV.
