# Parlay

A parlay, accumulator (or acca), combo bet, or multi is a single bet that links together two or more individual wagers, usually seen in sports betting. Winning the parlay is dependent on all of those wagers winning together. If any of the bets in the parlay lose, the entire parlay loses. If any of the plays in the parlay ties, or "pushes", the parlay reverts to a lower number of wagers with the payout odds reducing accordingly. Parlay bets are high-risk, high-reward; linking the possibilities drastically reduces the chance of the bet paying off overall. The benefit of the parlay is that there are much higher pay-offs, although as usual, casinos and bookkeepers offering parlays often exploit the poor calculation of gamblers by not increasing the pay-out as much as the odds truly demand, with the effect of the house edge increasing in parlays.
Although a variety of bets can be used to build a parlay bet, correlated parlays are usually not allowed by traditional bookmakers. Correlated parlays are two or more bets from the same game that rely on a closely related outcome: for example, betting that a football (soccer) team might both score more than three goals in a match, and also win the match. These are not independent events, as a team that scores more than three goals is also very likely to win the match. A naive application of odds that treated these events as uncorrelated would not accurately reflect the probability of the linked bet. However, with the rise of sports betting through mobile gambling apps in the late 2010s–2020s, this traditional hesitance has weakened. These newer apps often allow "microbets" on propositions such as if the current possession will end in a score, and further allow these props to be bundled into parlays. The system then attempts to compensate on how correlated these props are. While these systems usually prefer to lean heavily in the house's favor, the increased volatility from these bundles has resulted in some notable cases where bettors have found favorable odds. This isn't always a windfall for the bettors, though, as these newer-style sportsbooks have sometimes simply refused to pay out in those cases if the parlay comes through.

## History

Parlays were introduced into New York-area racetrack gambling in 1988, but a 1989 newspaper article indicated that they still weren't very popular, perhaps due to the large surcharges and fees charged by off-track betting (OTB) parlors.

## Odds and payout

Parlay bets are paid out at odds higher than the typical single game bet, but still below the "true" odds. For instance, a common two-team NFL parlay based entirely on the spread generally has a payout of 2.64:1. In reality, however, if one assumes that each single game bet is 50/50, the true payout should instead be 3:1.

## Examples
### Typical payouts for up to 10 team parlay bet

The following is an example of a traditional Las Vegas Parlay Card, which shows the typical payouts for an up to 10 team parlay bet based on −110 prices (amount won is assuming $100 is bet) and if every match is 50/50:
| Number | Odds | Amount won | Payout |
| 2 Team Parlay | 2.6 to 1 | $260 | $360 |
| 3 Team Parlay | 6 to 1 | $600 | $700 |
| 4 Team Parlay | 11 to 1 | $1,100 | $1,200 |
| 5 Team Parlay | 22 to 1 | $2,200 | $2,300 |
| 6 Team Parlay | 45 to 1 | $4,500 | $4,600 |
| 7 Team Parlay | 90 to 1 | $9,000 | $9,100 |
| 8 Team Parlay | 180 to 1 | $18,000 | $18,100 |
| 9 Team Parlay | 360 to 1 | $36,000 | $36,100 |
| 10 Team Parlay | 720 to 1 | $72,000 | $72,100 |

## Profitability of parlays in sports betting

The best way to analyze if a parlay is profitable in the long term is by calculating the expected value. The formula for expected value is: $E[X]=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}\dots x_{k}p_{k}$. Since the probability of all possible events will add up to 1 this can also be looked at as the weighted average of the event. The table below represents odds.
Column 1 = number of individual bets in the parlay
Column 2 = correct odds of winning with 50% chance of winning each individual bet
Column 3 = odds payout of parlay at the sportsbook
Column 4 = correct odds of winning parlay with 55% chance of winning each individual bet
| Number of individual bets | Correct odds at 50% | Odds payout at sportsbook | Correct odds of winning parlay at 55% |
| 2 | 3 to 1 | 2.6 to 1 | 2.3 to 1 |
| 3 | 7 to 1 | 6 to 1 | 5.0 to 1 |
| 4 | 15 to 1 | 12 to 1 | 9.9 to 1 |
| 5 | 31 to 1 | 24 to 1 | 18.9 to 1 |
| 6 | 63 to 1 | 48 to 1 | 35.1 to 1 |
| 7 | 127 to 1 | 92 to 1 | 64.7 to 1 |
| 8 | 255 to 1 | 176 to 1 | 118.4 to 1 |
| 9 | 511 to 1 | 337 to 1 | 216.1 to 1 |
| 10 | 1,023 to 1 | 645 to 1 | 393.8 to 1 |
| 11 | 2,047 to 1 | 1,233 to 1 | 716.8 to 1 |
The table illustrates that if a 55% chance of winning each individual bet were achievable, parlays would be profitable in the long term against the usual house edge. Compare the expected value received on an individual bet at a typical price of −110 with a 55% chance of winning: ((100/110+1)*.55)−1 = .05 (exactly 5 cents won for every dollar bet on average), multiplied by 11 = .55, to the expected return on the 11 game parlay ((1234/717.8)−1) = .719 (72 cents won for every dollar bet on average).