# Parlay (gambling)

(Redirected from Accumulator (bet))

A parlay, accumulator, combo bet or multi 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.[citation needed] In reality however, if one assumes that each single game bet is 50/50, the true payout should instead be 3:1 (10% expected value for the house). A house may average 20-30% profit on spread parlays compared to perhaps 4.5% profit on individual sports bets.

Aside from "spread" parlays, another way to parlay is to bet on two or more teams simply winning straight up. In order to calculate the payout of this parlay, one must multiply out the payout for all games. For example, if 3 teams are -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%.

## Examples

### Typical payouts for up to 10 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 10 team parlay bet based on -1.10 prices (amount won is assuming \$100 is bet)[citation needed]:

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

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.[citation needed]

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 (an arguably impossible task), parlays would be profitable in the long term. Compare the expected value you receive 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). In this case a parlay has a much higher expected value than individual bets with greatly increased variance in outcomes.