Parlays and accumulators explained
How a parlay's odds multiply leg by leg, why linked outcomes break the maths, and how the sportsbook's margin compounds with every leg.
A parlay joins several selections, called legs, into one bet. In the UK and Ireland the same bet is an accumulator, or acca (two and three legs are often called a double and a treble), and in Australia and New Zealand a multi. Every leg has to win for the parlay to pay, and in return the odds are far longer than any single leg's.
How combined odds multiply
A parlay's price is the product of its legs' decimal odds. Take three legs:
| Leg | Decimal | Implied probability |
|---|---|---|
| Leg 1 | 2.00 | 50.00% |
| Leg 2 | 1.50 | 66.67% |
| Leg 3 | 1.80 | 55.56% |
| Parlay | 5.40 | 18.52% |
The parlay pays 2.00 × 1.50 × 1.80 = 5.40. A stake of 10 returns 54.00 if all three win, a profit of 44.00. In American odds that is +440, and in fractional odds 22/5. The implied probability multiplies the same way: 50% × 66.67% × 55.56% = 18.52%, which is also 1 ÷ 5.40.
Multiplication only works in decimal, so convert American or fractional prices first (the odds converter does it, and the decimal odds guide explains it). A price of -110 is 1.9091 in decimal, so two legs at -110 give 1.9091 × 1.9091 = 3.645, or about +264.
If a leg is void, for example a game postponed beyond the sportsbook's time limit (which varies by sportsbook and sport), most sportsbooks drop it and pay on the rest, as if that leg's odds were 1.00. If leg 2 above were void, the parlay would pay 2.00 × 1.80 = 3.60. Each sportsbook's terms set the exact rule.
Read as decimal odds: 1.91
Read as decimal odds: 2.50
2 of 10 legs
A stake of 10.00 returns 47.75 if every leg wins.
Each leg's price carries its own margin, so a parlay's margin grows with every leg added.
Correlation: when multiplying is wrong
Multiplying probabilities assumes the legs are independent: the result of one tells you nothing about the others. Legs from different games usually are. Legs from the same game often are not.
Say a team's chance of winning is 50% and the game's chance of going over the total is also 50%. Multiplied, the chance of both is 25%, a fair price of 4.00. But if this team usually wins when the game is high scoring, the real chance of both might be 30%, a fair price of 1 ÷ 0.30 = 3.33. Multiplying the two prices would pay more than the combination is worth. The link can run the other way too: a team winning and its opponent's star scoring heavily may happen together less often than the product suggests.
Many sportsbooks refuse linked legs in a standard parlay and offer them instead as a same-game parlay, priced by their own model of how the outcomes move together. That price is not the plain product of the legs, and it usually carries extra margin, so the multiplication in the table above does not apply to it.
How the margin compounds
Every leg comes with the sportsbook's margin built in, and the margins multiply along with the odds. Take a market priced -110 on both sides. As the vig guide shows, the fair price of each side is 2.00, and -110 (1.909) pays about 95.45% of that. On average a single at -110 gives up 4.55% of the stake.
Chain several such legs and the shortfall grows:
| Legs | Parlay price | Fair price | Share of fair | Average cost |
|---|---|---|---|---|
| 1 | 1.909 | 2.00 | 95.45% | 4.55% |
| 2 | 3.645 | 4.00 | 91.12% | 8.88% |
| 3 | 6.958 | 8.00 | 86.97% | 13.03% |
| 5 | 25.359 | 32.00 | 79.25% | 20.75% |
The share of fair is 21/22 (1.909 ÷ 2.00, about 0.9545) raised to the number of legs. Three legs at -110 pay +596 where the fair price is +700; five legs pay about +2436 where fair is +3100. A small cost per leg becomes a large one on a long parlay, which is why its expected value falls with every leg added.
Why small price differences grow in a parlay
Because prices multiply, small differences between sportsbooks multiply too. Three legs at 1.91 make a parlay of 6.968. The same three legs at 1.95 make 7.415, about 6.4% more, from a gap of about 2% per leg.
A parlay is placed with one sportsbook, so you cannot take the best price for each leg from a different one. What counts is each sportsbook's product across all your legs. Where OddsKeepr lists sportsbooks, it works out that product for each one licensed where you are that prices all of your legs, one leg per game, so you can compare whole parlays rather than single legs. Where it shows fair prices only, the parlay shows the fair combined price. The guide to comparing odds explains how to read the prices.
A parlay loses the whole stake if any one leg loses, so keep it to money you can afford to lose. Before using any sportsbook, check that it is licensed where you are, and if gambling stops feeling like entertainment, free and confidential help is listed for every country under where to get help.