Parlays, same-game parlays and correlation
A parlay ties several bets into one ticket that pays only if every leg wins. The payouts are big because the chances are small. For a sharp the question is the same as for any bet: does the price beat the chance? Usually it doesn't, for two reasons.
The hold compounds
A parlay pays the legs' decimal odds multiplied together. At −110 each leg returns 1.909 per $1, where a fair coin flip would return 2.00. Four legs widen the gap: the book returns 13.28 (+1228) where a fair price returns 16.00 (+1500). On average that costs about 17 cents per dollar bet, against 4.5 cents on a single −110 bet. Every leg pays the book's cut, and the cuts multiply.
So a parlay of no-edge legs isn't a cheap lottery ticket; it is an expensive one. The only good case is legs that each carry a real edge, because then the edges compound too. That is rarer than parlay marketing suggests, and the extra variance is large: a four-leg ticket of true coin flips hits once in 16 tries.
Correlation
Multiplying assumes the legs are independent, that one leg winning says nothing about the next. Legs from different games mostly are. Legs from the same game often aren't: a favorite winning big and the over hitting tend to happen together, and so do a quarterback's passing yards and his team's points. That is correlation.
With positive correlation, the true chance that both legs win is higher than the product of their chances. If a book simply multiplied the prices, it would be paying as if a likely combination were rare. Books know this, which is why most won't accept two correlated legs from one game in a regular parlay and send you to the same-game parlay (SGP) menu instead. There, the book's own model cuts the payout for correlation, and books hold far more on SGPs than on straight bets.
Where an SGP edge can exist
When there is an edge in an SGP, it lives in the gap between how much correlation the book charges for and how much is really there. Sharp SGP bettors look for combinations whose legs all depend on the same game script and that the book's model underrates. Those are rare, books cut them quickly, and finding them takes a real estimate of the joint chance, not a hunch.
How Consensus Edge prices them
Our parlay tools treat legs from different games as independent and handle same-game legs cautiously: where the correlation is uncertain, our number leans against the ticket, not toward it. We show the chance the whole ticket hits next to the odds you are paid. If that chance doesn't beat the payout's break-even, the ticket loses money on average, however good each leg looks.
We don't suggest a stake for a parlay. If you bet one, stake less than you would on a single bet: every leg's error multiplies into the ticket, so a parlay deserves a smaller share of your bankroll than any one of its legs.
Example. Two NFL legs, each a true 50% and each priced −110 (illustrative numbers, not live data). Two legs at −110 return 1.909 × 1.909 = 3.645 per $1, which is +264. Legs from different games both win 50% × 50% = 25.0% of the time. Suppose two legs from the same game tend to win together, and both win 28.0% of the time; a fair price for 28.0% is 1 ÷ 0.28 = 3.571, or +257.
| Ticket | Chance both win | Payout | Average result per $100 |
|---|---|---|---|
| Two games, regular parlay | 25.0% | +264 | 0.25 × $364.46 − $100 = −$8.88 |
| Same game, if priced as independent | 28.0% | +264 | 0.28 × $364.46 − $100 = +$2.05 |
| Same game, SGP at +230 | 28.0% | +230 | 0.28 × $330.00 − $100 = −$7.60 |
Correlation alone would flip the ticket to a winner at the independent price, which is exactly why books don't offer it. At the SGP price the book has charged for the correlation and then some, and you are back to losing about the same as the ordinary parlay.
Terms in this lesson
ParlaySame-Game ParlayCorrelationHoldVigDecimal OddsBreak-evenExpected Value