Why parlays are -EV at standard prices

At true 50/50 win probabilities and -110 prices, expected loss is 4.55% for one leg, 8.88% for two legs, and 13.0% for three legs. Three -110 legs pay 6.96 decimal (+596 American) against the fair 8.00 decimal price for a 12.5% outcome.

Parlays are profitable in three narrow scenarios: (1) every leg is independently +EV beyond the per-leg vig, (2) the legs are positively correlated and the book hasn't priced the correlation in, or (3) you're betting a same-game parlay where the book's correlation pricing has slipped. Most rec-book parlays satisfy none of these.

Recommended workflow

Use the No Vig Calculator to get a fair probability for each leg from the book's odds.
Adjust each leg's "Your true prob" if your own model disagrees with the market — even 1 point of disagreement compounds across legs.
Read the per-leg edge readout. If any leg is meaningfully -EV (worse than -1%), drop it or reprice it before parlay-ing.
If the parlay EV is +EV, size the bet with the Kelly Calculator using the parlay probability and combined decimal odds.

FAQ

Are parlays profitable? +

In expectation, almost never. Each leg of a parlay carries its own vig, and books multiply those prices together for the combined payout. A 3-leg parlay of true 50/50 sides priced at -110 has a 13.0% expected loss per dollar staked. The math gets worse with more legs. Parlays are profitable in two narrow cases: when individual legs are independently +EV (rare), or when the legs are positively correlated and the book has not priced the correlation in.

What does "correlated parlay" mean? +

Two legs are correlated when the outcome of one shifts the probability of the other. Classic example: betting the over on team total points and the over on game total — if team A scores more, the game total is more likely to also go over. Books reject many same-game parlays for this reason, or price the multiplier lower than the product of leg odds. Legs that share a game or player ID switch the EV to a conservative haircut scenario (dependence can push the real probability either way, and this page has no fitted model); with no shared IDs, legs are treated as independent and the page says "no correlation applied."

How is parlay EV calculated? +

For independent legs: parlay_prob = Π(leg_prob_i); payout_multiplier = Π(decimal_odds_i); win_payout = stake × payout_multiplier; EV = parlay_prob × win_payout − (1 − parlay_prob) × stake. The leg edges shown in the table tell you whether each individual leg is +EV at the offered odds; even one −EV leg can drag a parlay's combined EV negative.

Why does the parlay show -EV even when every leg is +EV? +

For independent legs at the displayed product payout, it should not: each leg has an expected-return factor of true probability × decimal odds, and multiplying factors above 1 stays above 1. A negative scenario EV means shared game or player IDs triggered the illustrative correlation haircut, or at least one displayed leg is not actually +EV at its entered probability and price.

Should I round-robin instead of parlay? +

Round-robins (a set of smaller parlays from a pool of legs) reduce variance but not vig — the round-robin's EV is the average of the constituent parlay EVs, weighted by stake. If each constituent is -EV, the round-robin is -EV. Use round-robins only when individual parlays are +EV and you want to smooth variance.

Parlay EV Calculator