# Parlay (gambling)

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 it 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.[1][citation needed]

## 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 generally has a payout of 2.6:1 if both picks are correct.[citation needed] 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.

## Examples

### Example 1: NFL

Mulroe places a three-team NFL parlay on the Packers, Bears, and Bengals. If any one of those teams fail to cover the spread, Mulroe loses his parlay bet. But if all three teams beat the spread, Mulroe gets paid \$600 for every \$100 bet.

If Mulroe pushes on one of those picks, he then has a two-team parlay. If he pushes on two picks, he would then have a straight bet.

### Example 2: English Premier League

Premier League Fixtures
Home teamAway teamHome winDrawAway winResult
Arsenal F.C.Manchester United F.C.1.703.204.500–0 (draw)
Chelsea F.C.Fulham F.C.1.703.304.402–1 (home win)
Liverpool F.C.Tottenham Hotspur F.C.1.304.008.503–1 (home win)

#### Winning example

Sam wagers £1,000 on Arsenal/Manchester United to draw, Chelsea to win, and Liverpool to win. Sam wins £6,072 as he correctly predicted all three results.

The calculation is: £1,000 × 3.2 × 1.7 × 1.3 = £7,072, less the stake of £1,000.

#### Losing example

Sam wagers £1,000 on Manchester United to win, Chelsea to win, and Liverpool to win. He loses the wager if either Manchester United, Chelsea, or Liverpool loses.

### Typical payouts for up to 11 team parlay bet

The following is an example of a traditional Las Vegas Parlay Card, which shows the typical payouts for an up to 11 team parlay bet (amount won is assuming \$100 is bet):

NumberOddsAmount wonPayout (if push)
2 Team Parlay13 to 5\$260\$360
3 Team Parlay6 to 1\$600\$700
4 Team Parlay10 to 1\$1,000\$1,100
5 Team Parlay20 to 1\$2,000\$2,100
6 Team Parlay40 to 1\$4,000\$4,100
7 Team Parlay75 to 1\$7,500\$7,600
8 Team Parlay150 to 1\$15,000\$15,100
9 Team Parlay300 to 1\$30,000\$30,100
10 Team Parlay700 to 1\$70,000\$70,100
11 Team Parlay1100 to 1\$110,000\$110,100

## 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[2] 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 BetsCorrect Odds at 50%Odds Payout at sportsbookCorrect odds of winning parlay at 55%
23 to 12.6 to 12.3 to 1
37 to 16 to 15.0 to 1
415 to 112 to 19.9 to 1
531 to 124 to 118.9 to 1
663 to 148 to 135.1 to 1
7127 to 192 to 164.7 to 1
8255 to 1176 to 1118.4 to 1
9511 to 1337 to 1216.1 to 1
101,023 to 1645 to 1393.8 to 1
112,047 to 11,233 to 1716.8 to 1

The table illustrates that with even a 55% chance of winning each individual bet parlays are still not profitable in the long term. [? no, this table does not illustrate that] Compare this with the expected value you receive on an individual bet with a 55% chance of winning. (.55)(10/11) - (.45)(11/10) = .005 This may not seem like much but it indicates that at even a 55% win ratio every single bet you place will increase your bankroll by .5%. When wagering the ideal amount of money, according to the Kelly criterion, the real amount of money will compound exponentially as your bankroll increases. There are many Kelly calculators available on the internet which illustrate the correct amount of money to wager on any event given the payout and win percentages.