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A parlay, accumulator, or combo bet is a single bet that links together two or more individual wagers and is dependent on all of those wagers winning together. The benefit of the parlay is that there are much higher payoffs than placing each individual bet separately, since the difficulty of hitting all of them is much higher. 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 teams with the odds reducing accordingly.
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 2-team NFL parlay based entirely on the spread generally has a payout of 2.6:1 if both picks are correct. In reality, however, if one assumes that each single game bet is a coin flip and would be expected to pay out at 1:1, the true payout should instead be 3:1, a substantial difference.
The house makes a 20-31% profit on spread parlays, compared to a 7% profit on individualized sports bets. 
An alternate way to do a parlay is to bet on two or more favorites simply winning straight up. In order to calculate the payout of this parlay, one must multiply out the payout for all 3 games. For example, if 3 teams are all +385 favorites, a successful parlay on all 3 teams winning would pay out at a ratio of approximately 1/1. This is because (385/485)^3 is approximately 50%
Typical payouts for up to 11 team parlay bet
The following is an example of a traditional Las Vegas Parlay Card at William Hill Sports Book, which shows the typical payouts for an up to 11 team parlay bet (amount won is assuming $100 is bet):
|2 Team Parlay||2.6 to 1||$260||$360|
|3 Team Parlay||6.5 to 1||$650||$750|
|4 Team Parlay||13 to 1||$1,300||$1,400|
|5 Team Parlay||25 to 1||$2,500||$2,600|
|6 Team Parlay||50 to 1||$5,000||$5,100|
|7 Team Parlay||100 to 1||$10,000||$10,100|
|8 Team Parlay||180 to 1||$18,000||$18,100|
|9 Team Parlay||400 to 1||$40,000||$40,100|
|10 Team Parlay||825 to 1||$82,500||$82,600|
|11 Team Parlay||1500 to 1||$150,000||$150,100|
Profitability of parlays in sports betting
Many gamblers have mixed feelings as to whether or not parlays are a wise play. The best way to analyze if they are profitable in the long term is by calculating the expected value. The formula for expected value is: E[X] = x1p1 + x2p2 + x3p3…xkpk . 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 with even a 55% chance of winning each individual bet parlays are profitable in the long term. Compare the expected value you receive on an individual bet with a 55% chance of winning. (.55)-(.45) = .1 (ten cents won for every dollar bet on average) to the expected return on the 11 game parlay ((1233/716.8)-1)=.72 (72 cents won for every dollar bet on average). In this case a parlay has much higher expected returns than individual bets but unfortunately greatly increased variance in outcomes.
- "Betting Guides and Terminology – Help - TheGamblingTimes". TheGamblingTimes. Archived from the original on 2014-03-29. Retrieved 2014-01-09.
- Lappan, Glenda (January 2006), "What Do you Expect: Probability and Expected Value", Prentice Hall