methodology
Why a Parlay Compounds the Margin, Not Just the Odds
A parlay is a bet on a bet
A parlay, or accumulator, ties several selections together. The stake and the winnings of the first leg roll onto the second, and so on. Every leg has to win. The payout is the product of all the odds, which is why a handful of ordinary prices turn into a number that looks large.
The product is also where the cost hides. The margin is built into each leg’s price, and multiplying the prices multiplies the margin with them.
The margin multiplies
Assume every leg is an even match, so each side has a true 50% chance, and every market carries a margin of 3.4%, the median we measured in tennis moneylines. The price per leg is then 1.934 instead of 2.000. Nothing here depends on picking well: the bettor has no edge, so this is the cost of simply playing.
| Legs | Parlay odds | Fair odds | Expected value |
|---|---|---|---|
| 1 | 1.93 | 2.00 | -3.3% |
| 2 | 3.74 | 4.00 | -6.5% |
| 3 | 7.24 | 8.00 | -9.5% |
| 4 | 14.00 | 16.00 | -12.5% |
| 5 | 27.07 | 32.00 | -15.4% |
A single bet loses 3.3% of the stake on average. Two legs lose 6.5%, three lose 9.5%, and five lose 15.4%. The same money, staked as five separate single bets, costs 3.3% each. See what the margin costs for where the single-bet figure comes from.
With a real edge, it multiplies too
The compounding is neutral. It applies to whatever each leg is worth. If every leg had a genuine +4% expected value, two legs would be worth 8.2% and three legs 12.5%. A parlay is leverage on the per-leg expectation, in both directions.
The condition is the hard part. Each leg must have an edge that beats its own margin, and you must be sure about it for all legs at once. One leg whose true probability is only the market’s, or lower, drags the whole product down. Anyone who has an edge gets the same expected profit per unit staked from singles, with much less to go wrong.
The variance gets worse faster than the payout
A two-leg parlay on even legs wins 25% of the time. A single bet wins 50% of the time. The longest losing run you should expect gets longer accordingly: ten losses in a row has a probability of 0.1% at a 50% hit rate and 5.6% at a 25% hit rate.
That is why a parlay bankroll behaves differently from a singles bankroll even when the expected value is the same. See flat staking versus Kelly for how stake size interacts with swings like these.
Same-match legs are not independent
Everything above assumes the legs have nothing to do with each other. Combining outcomes from the same match breaks that assumption. A tennis match that goes to three sets tends to have more games than one that ends in straight sets, so a bet on a long match and a bet on the underdog winning a set point in the same direction. Bookmakers know this and adjust the combined price, which can make it better or worse than multiplying the single prices. We have not measured how they do it, so we do not put a number on it. If you want to know, ask for the single prices and compare the product with the combined offer.
Betting involves risk and is for adults only (18+). Never stake money you cannot afford to lose. Help and limits are explained on our responsible gambling page.
Frequently asked questions
- Is a parlay a worse bet than two single bets?
- Without an edge, yes, because the margin of each leg is multiplied. Two legs at a 3.4% margin lose 6.5% on average against 3.3% for a single bet. With a real edge on every leg, a parlay multiplies that edge as well, but with much higher variance.
- Do bookmakers charge more margin on parlays?
- The margin of every leg stays in the price, and multiplying the legs compounds it. Some bookmakers add a further adjustment for combined bets, which we have not measured. Compare the combined odds with the product of the single prices.
- Why does a parlay lose more often even when each leg is likely to win?
- Every leg has to win. If each of two legs wins 70% of the time, both win together only 49% of the time (0.7 × 0.7), and with five such legs the figure falls to about 17%.