How parlays and system bets work: odds, payouts, examples
How parlay odds multiply, what a push does, how a 2/3 system works and how often tipster parlays really win.
BetBuddyRank grades tipster parlays from X against final scores too: 911 two-leg parlays and 963 of six legs or more so far, each marked won or lost. Below are the parlay and system formulas on one worked example, the push rules and data on how often these bets actually win.
A parlay (an accumulator in the UK) combines several picks into one bet. The decimal odds multiply, and the bet wins only if every leg wins: one miss and the whole stake is lost.
| Leg | Decimal | American | Implied probability |
|---|---|---|---|
| Leg 1 | 1.85 | −118 | 54.1% |
| Leg 2 | 2.10 | +110 | 47.6% |
| Leg 3 | 1.72 | −139 | 58.1% |
| Parlay | 6.68 | +568 | 15.0% |
A $100 stake returns 100 × 6.68 = $668, a profit of $568. When the legs are unrelated, the parlay probability is the product of the leg probabilities: about 15% here, so a parlay like this wins roughly one time in seven. With American odds, convert each leg to decimal first: −118 becomes 1 + 100 / 118 = 1.85 and +110 becomes 1 + 110 / 100 = 2.10.
If a leg pushes or is voided (a draw on a draw no bet pick, a postponed game, a total landing exactly on the line), it counts at odds of 1.00 and the parlay rides on the other legs. In the example, a push on leg 2 leaves 1.85 × 1.72 = 3.18.
Asian quarter lines can win or lose by half. Most sportsbooks turn a half-won leg into odds of (k + 1) / 2 and a half-lost leg into 0.5. A half win at 1.90 counts as 1.45 in the parlay, and a half loss halves the payout. House rules differ, so check them in advance.
A system bet, called a round robin in the US, is a set of parlays built from every combination of the chosen picks. A 2/3 system is three two-leg parlays: the total stake is split evenly and the return adds up every winning parlay.
| Parlay in the system | Odds | Return on $100 per parlay |
|---|---|---|
| Legs 1 and 2 | 1.85 × 2.10 = 3.885 | $388.50 |
| Legs 1 and 3 | 1.85 × 1.72 = 3.182 | $318.20 |
| Legs 2 and 3 | 2.10 × 1.72 = 3.612 | $361.20 |
The total stake is $300. If all three legs win, the system returns 388.50 + 318.20 + 361.20 = $1,067.90. If leg 3 loses, only the parlay of legs 1 and 2 pays: $388.50, a profit of $88.50. With only one winning leg no parlay pays and the $300 is lost.
How many parlays a system has
| System | Parlays | Wins needed for a return |
|---|---|---|
| 2/3 | 3 | 2 |
| 2/4 | 6 | 2 |
| 3/4 | 4 | 3 |
| 2/5 | 10 | 2 |
| 3/5 | 10 | 3 |
| 4/5 | 5 | 4 |
The number of parlays in a k/n system is the number of combinations, n! / (k! × (n − k)!). In the UK full-cover bets have names: a Trixie is 3 picks in 4 bets (three doubles and a treble) and a Yankee is 4 picks in 11 bets. A return at the minimum number of wins does not always cover the total stake: the odds decide.
Every sportsbook price sits a little below the fair one, and the gap is the margin, or vig. In a parlay the margin multiplies along with the odds, so the book’s share grows with every leg. At about 5% per leg:
| Legs in the parlay | Parlay margin |
|---|---|
| 1 | 4.8% |
| 2 | 9.3% |
| 3 | 13.6% |
| 4 | 17.7% |
| 5 | 21.6% |
| 6 | 25.4% |
| 8 | 32.3% |
| 10 | 38.6% |
The expected return of a parlay is the product of the expected returns of its legs. If each leg returns 95 cents on the dollar on average, a six-leg parlay of such legs returns less than 75 cents. The margin of a given market is worked out by the no-vig calculator.
We graded every tipster parlay from X in our database against final scores. A parlay’s expectation comes from its price with every leg’s margin taken out or, without a price, from the product of the leg probabilities.
| Legs | Parlays | Hit rate | Expected | ROI |
|---|---|---|---|---|
| 2 | 911 | 44.2% | 40.2% | −5.1% |
| 3 | 438 | 23.1% | 23.8% | −32.5% |
| 4 | 574 | 11.8% | 12.3% | −40.5% |
| 5 | 352 | 7.1% | 8.9% | −34.9% |
| 6 or more | 963 | 1.8% | 2.5% | −57.6% |
Two-leg parlays win 44.2% of the time and parlays of six legs or more 1.8%. ROI counts parlays with a stated price up to 30 at 1 unit per bet: −5.1% for doubles and −57.6% for the longest, against −5.5% for all priced tipster picks. How ROI works is covered in the guide to ROI in sports betting.
- A parlay does not create an edge. If no leg beats its price, the parlay only multiplies the margin.
- A system lowers the swings but not the margin: each of its combinations is still a parlay with its own vig.
- Correlated legs from one game, such as a side and the over, are either refused in one parlay or priced together by the book.
- When judging a tipster, look at their singles: over a short run long parlays say almost nothing about skill. How to tell a strong tipster from a lucky one is in the guide on how to check a tipster.
How many parlays are in a 3/5 round robin?
Ten. A k/n system has as many parlays as there are combinations of k picks out of n: three in a 2/3, six in a 2/4, four in a 3/4 and five in a 4/5.
How many picks must win in a 2/3 system to make a profit?
It depends on the odds. With two winners one parlay of the three pays: at odds near 2.00 it returns 4 units on 3 staked, at odds near 1.50 only 2.25, a loss.
How is a half win settled in a parlay?
At most sportsbooks a half-won leg counts at (k + 1) / 2 and a half-lost leg at 0.5. A half win at 1.90 counts as 1.45 in the parlay.
How often do tipster parlays win?
In our data two-leg parlays win 44.2% of the time against 40.2% expected, and parlays of six legs or more 1.8% against 2.5%.
Are parlays or singles better?
Over time singles lose less: the margin is paid once, while in a parlay it multiplies. A parlay buys a bigger payout with a lower probability but does not change the expectation.
- 1Work out the odds and payout of your parlay with the parlay calculator.
- 2Turn each leg into a probability with the implied probability chart.
- 3See how often a given tipster’s parlays win in their profile: find it with the tipster lookup by handle.
- 4When you compare parlays with singles, look at ROI, not the hit rate.