Last Updated: Sept. 19, 2014

Parlay Bets in the NFL

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Introduction

In gambling terms, "parlay" means to bet on at least two events, letting the winnings ride after each win. Usually you lose, but when you win, and depending in part on how many events were parlayed, you can win big.

In sports betting, the bettor can parlay wins even if the games occur simultaneously. This can be done either "off the board" or with parlay cards. This page address both methods and included three common types of parlay cards. What I hope to convey via this page is that randomly making selections on parlay cards is a bad way to bet sports and results in a high house edge. However, the sharp bettor can take advantage of line moves off common margins of victory in the NFL and gain a strong advantage, of 30% or more, on half point parlay cards.

Let me make a disclaimer to take any win probabilities and expected returns on this page with a grain of salt. I had to make assumptions about how point spreads on parlay cards were deliberately moved to either an integer or not an integer, depending on the card. My data also does not reflect the fact that lines often move from the time a parlay card is printed to the time of the game. On the one hand, the card maker may carefully set the point spreads to minimize player advantage. On the other, it is a known fact that closing lines are sharper than opening lines, and the player can take advantage of these line movements by putting in parlay cards at the last minute. All things considered, I believe there are large advantages to be gained with half point parlay cards, but the advantages can not be calculated exactly. They could be greater or smaller.

After reading this page, skeptics may wonder if it is so easy to beat half point parlay cards, why isn't everybody doing so? A lot of bettors are. Sports books are nervous about taking them, because they do tend to get hammered on the same side of certain hot games. However, I imagine to many professional gamblers, they are not a viable advantage play because:

  1. It is hard to get a lot of money down. The most you can usually bet on a single parlay card is $200, and even a bet of $100 may set off red flags if all the choices are correlated on the hot sides.
  2. They are time consuming to bubble in.
  3. It is feast or famine. Generally speaking, the more legs the player makes, the greater the advantage. For example, an 8-leg half point parlay pays at most 200 to 1. Of course, such long-shot bets usually lose.

You'll have to decide for yourself if parlay cards are for you. However, if you do bet them, hopefully you'll learn a thing or two from my analysis.

Methodology

All win percentages in this page are based on the 4,950 games played in the 1994 to 2012 seasons. Except as noted, all picks refer to betting against the spread. I don't recommend betting totals on parlay cards unless there is a significant line movement.

Off the Board Parlays

"Off the Board" parlays are based on the current point spreads on the betting board at the time of the bet. No card is filled out. Instead, the bettor tells the writer the bet numbers he wishes to parlay and the amount of the bet. The following table shows what parlay bets pay according to the number of picks and the sports book group, assuming that odds on each leg individually are -110 (bettor must risk $11 to win $10). Wins in this table are on a "to one" basis. In other words, the original wager is returned if the bet wins.

Parlays off the Board — Pay Table

Sportsbook Legs
2 3 4 5 6 7 8 9 10
Boyd 2.6 6 10 20 40 80 160
Cantor 2.6 6 10 20 40
Golden Nugget 2.6 6 11 22 40 75 140
Caesars 2.6 6 10 20 40 75 140
LVH 2.6 6 11 22 40 75 140
Jerry's Nugget 2.7 6.5 13 26 47 92 180
MGM 2.6 6 10 20 40 80 150
Stations 2.6 6 11 22 40 80 150
Stratosphere 2.6 6 11 22 40 80 160
Treasure Island 2.6 6 10 20 40 80 160
William Hill 2.6 6 11 22 45 90 180 360 720
Wynn 2.6 6 10 20 40
South Point 2.6 6 10 20 40 75 150

What this table shows is that Jerry's Nugget has the most liberal off the board parlay odds across the board. Other than convenience, there should be no reason to make off the board parlay bets anywhere else in Vegas.

When players include a leg in a parlay that doesn't pay -110 odds, then the above pay tables are not used. Instead, when the writer enters the legs of the parlay, the computer will perform a calculation for what the bet should pay. It does this as if each bet were independently made, letting all wins ride. For example, if you parlay one game against the spread at -110 and another against the money line at +250, and both win, then you will be paid (210/110)×(350/100) - 1 = 5.68 to 1.

With the exception of the three-leg parlay, and the generous Jerry's Nugget odds, you will get a better value mixing in at least one leg not at -110 in a parlay. Here are three ways to do it:

  • Mix in a money line bet, preferably on an underdog.
  • Mix in a lopsided line, which are usually off of three points. For example, laying 105 or 115 on one leg.
  • Buy a half point off of one leg. They probably won't let you do it off of three points, so preferably lay 120 to get +7.5 on a 7-point underdog, or -6.5 on a 7-point favorite. When in doubt, go with the underdog at +7.5.

Let's see how this works with an example.

  • Jesse does a six-leg parlay, all against a -110 spread, at one of the many sports books that pay 40 to 1. His probability of winning is (1/2)6 = 1.5625%. His expected return is (1/2)6×(40+1) = 64.06%.
  • Walter also does a six-leg parlay on the same teams. Five he leaves alone at -110 odds. On the sixth, he buys the half point off a 7-point underdog, to get +7.5. He must pay -120 for the half point. The parlay will pay (210/110)5×(220/120) - 1 = 45.49 to 1. Besides getting a much larger win, his probability of winning goes up too, because of the extra half point. To be specific, the probability of winning the leg with the extra half point off seven is 51.95%. So, his overall probability of winning is (1/2)5 × 0.5195 = 1.6234%. His expected return is 0.016234 × (45.49+1) = 77.10%.

So, by buying that half point off of seven, Walter increases his expected return by 13% compared to Jesse.

As mentioned, an exception to the above advice is the standard pay of 6 for a three-leg parlay is more generous than what the 5.96 that the calculation method would give you. To summarize here is my advice for off the board parlays.

At Jerry's Nugget: Stick with -110 events, except for a six-team parlay, where it is marginally better to mix in at least one pick that isn't -110.
Not at Jerry's Nugget: With a three-team parlay, stick with -110 events. Otherwise, mix in any event that isn't -110.

Yet another piece of advice, and this is the single most important piece of advice when it comes to betting sports, is to bet on underdogs! Since 1994, 51.6% of underdogs beat the spread in games resolved. If you think that trend is over, the following table shows the underdog win rate against the spread year by year.

Underdog Win Rate against the Spread

Season Wins Losses Win Rate
1994 236 206 53.39%
1995 254 226 52.92%
1996 244 240 50.41%
1997 248 210 54.15%
1998 222 254 46.64%
1999 274 228 54.58%
2000 266 234 53.20%
2001 248 230 51.88%
2002 284 236 54.62%
2003 254 254 50.00%
2004 272 240 53.13%
2005 214 298 41.80%
2006 298 218 57.75%
2007 244 260 48.41%
2008 264 250 51.36%
2009 264 254 50.97%
2010 268 250 51.74%
2011 264 238 52.59%
2012 262 252 50.97%
Average 4880 4578 51.60%

It is important to emphasize this point, so let me give you a chart as well.


In conclusion, my advice for betting parlays "off the board" is:

  1. Bet on underdogs.
  2. Bet at Jerry's Nugget or make at least one pick that isn't -110 odds.
  3. If you must stick to the -110 events, and aren't at Jerry's Nugget, bet only the three-leg parlay.

Half Point Parlay Cards

What distinguishes half point parlay cards from other parlay cards is every point spread or total always ends in one half. Thus, there can never be a tie. Most places call these a "1/2 Point Parlay Card," but some just title them a "Parlay Card." The random picker can expect to get 50% of picks correct.

However, the smart picker can gain an extra half point compared to integer "off the board" numbers. For example, suppose the Saints are a five-point favorite over the Falcons, off the board. The half point card is very likely to move that point spread to either 4.5 or 5.5. If they move it to 4.5, then bet Saints -4.5. If they move it to 5.5, then bet Falcons +5.5. Better yet, get those extra half points of the key numbers of 3 and 7, because 25.35% of NFL games end in a margin of victory of one of those two key numbers.


The following table shows what half point parlay cards pay at various sports books around Las Vegas. Wins in this table are on a "for one" basis. In other words, the original wager is not returned, even if the bet wins. If forced to choose the best, I would say it is William Hill, who have the best, or tied for the best, payoffs for all number of picks except 10 and 12. In those cases, MGM Premium Payout card is the best.

Half Point Parlay Card — Pay Table

Sportsbook Legs
3 4 5 6 7 8 9 10 11 12
Aliante 6.5 12 25 50 100 180 375 800 1300 2500
Boyd 6.5 12 25 46 90 170 375 800
Caesars 6 12 22 40 85 170 340 700 1400/60/61
Golden Nugget 6.5 12 25 50 100 180 400 800
Jerry's Nugget 6.5 12 25 40 80 160 375 750
LVH 6.5 12 22 42 80 156 400 800 1500
MGM 6 11 22 42 85 170 340 700 1400
MGM-PP 45 88 190 375 850 1600 3000/50
South Point 6.5 12 25 50 100 175 375 800
Stations 6.5 12 22.5 40 80 160 350 800
Stratosphere 6.5 12 25 45 85 170 375 800
William Hill 6.5 13 25 50 100 190 400 825 1500 3000

Note:

  1. The Caesars Super Parlay Special pays 1,400 for catching 12, 60 for 11, and 6 for 10 .
  2. The MGM pick-12 Premium Payout parlay card pays 3,000 for catching 12, and a "bad beat" pay of 50 for catching 11. More on those below.

Random Picker

The following table shows the probability of winning and expected return of a random picker, based on the William Hill odds. The probability of each pick winning is exactly 50.0%. The table shows a very high house edge. If you must pick randomly, the lowest house edge is 16.92% on both the pick-10.

Half Point Parlay Card — Random Picker

Legs Pays Prob. Win Exp. Value
3 6.5 0.125000 -0.187500
4 13 0.062500 -0.187500
5 25 0.031250 -0.218750
6 50 0.015625 -0.218750
7 100 0.007813 -0.218750
8 200 0.003906 -0.218750
9 400 0.001953 -0.218750
10 850 0.000977 -0.169922
11 1,600 0.000488 -0.218750
12 3,000 0.000244 -0.267578

Gaining a Half Point


This parlay, which I bet twice, lost
on the Packers only, who won by 2.

The following table shows the probability of winning and expected return of someone who randomly picks off all games with an integer point spread on the board, to gain the extra half point. The probability of each pick winning is exactly 52.76%. The table shows a player advantage starting with the pick-4, with a maximum advantage of 38.35% on the pick-12. The best Kelly bet is on the pick-6, where the ratio of advantage to variance is 0.001403.

Half Point Parlay Card — Half Point Picker

Legs Pays Prob. Win Exp. Value
3 6.5 0.146839 -0.045548
4 13 0.077468 0.007081
5 25 0.040870 0.021743
6 50 0.021562 0.078082
7 100 0.011375 0.137528
8 190 0.006001 0.140239
9 400 0.003166 0.266435
10 825 0.001670 0.378025
11 1,500 0.000881 0.321827
12 3,000 0.000465 0.394713

Gaining a Half Point off of 3 and 7.

The following table shows the probability of winning and expected return of someone who randomly picks off all games with integer point spreads of 3 and 7 only, to gain the extra half point. The probability of each pick winning is exactly 54.42%. The table shows a player advantage on every number of picks, with a maximum advantage of 103% on the pick-12. However, 25.03% of NFL games have a point spread of 3 or 7. Based on a 16-game week, you can expect four games only to meet that criteria. The best Kelly bet is conveniently on the pick-4, where the ratio of advantage to variance is 0.010380.

Half Point Parlay Card — Half Point off 3 and 7 Picker

Legs Pays Prob. Win Exp. Value
3 6.5 0.161187 0.047718
4 13 0.087722 0.140384
5 25 0.047740 0.193507
6 50 0.025981 0.299068
7 100 0.014140 0.413966
8 190 0.007695 0.462074
9 400 0.004188 0.675146
10 825 0.002279 0.880285
11 1,500 0.001240 0.860536
12 3,000 0.000675 1.025093



MGM Premium Payout Card

The next table analyzes the MGM pick-12 Premium Payout parlay card. This bet is characterized as paying a "bad beat" win of 50 if the player picks 11 out of 12 correctly. The following table analyzes the bet for a random picker. The lower right cell shows a return of 87.89%.

12-Leg Premium Payout — Random Picker

Correct Picks Pays Probability Return
12 3,000 0.000244 0.732422
11 50 0.002930 0.146484
10 or less 0 0.996826 0.000000
Total 1.000000 0.878906

The next table shows the return for the pick-12 Premium Payout for a "half point" picker, who always chooses lines a half point above the market line. The lower right cell shows a return of 164%!

Premium Payout Pick 12 — Half Point Picker Picker

Correct Picks Pays Probability Return
12 3,000 0.000465 1.394713
11 50 0.004996 0.249788
10 or less 0 0.994539 0.000000
Total 1.000000 1.644501

Caesars Super Parlay Special

The next table analyzes the Caesars pick-12 Super Parlay Special. This bet is characterized as paying 1,400 for catching all 12 picks, 60 for 11, and 6 for 10. The following table analyzes the bet for a random picker. The lower right cell shows a return of 61.43%. Compared to the 95% return for the MGM's Premium Payout card, under the same assumptions, the odds are not as good.

Super Parlay Special — Random Picker

Correct Picks Pays Probability Return
12 1,400 0.000244 0.341797
11 60 0.002930 0.175781
10 6 0.016113 0.096680
9 or less 0 0.980713 0.000000
Total 1.000000 0.614258

The next table shows the return for the Super Parlay Special where the bettor always gets a half point in his favor. The lower right cell shows a return of 109.02%. Compared to the 176% return for the MGM's Premium Payout card, under the same assumptions, the odds are not as good.

Super Parlay Special — Half Point Picker

Correct Picks Pays Probability Return
12 1,400 0.000461 0.645619
11 60 0.004963 0.297754
10 6 0.024476 0.146858
9 or less 0 0.970100 0.000000
Total 1.000000 1.090231

Ties Win Parlay Cards

Normally on a parlay card, if there is a tie, then it "reduces," as if the bettor never picked that game to begin with. For example, if a pick-5 card resulted in four wins and one tie, then the bettor would be paid based on a pick-4 card. However, as the name states, a tie counts as a win on a "ties win" card. To make things even better, most spreads are integers, making ties more likely.

The only point spread you generally don't see is 3 and -3, because 15.7% of games in the NFL end in a margin of victory of 3. It would be too advantageous to give those ties to the player, so they move those spreads to 2.5 or 3.5.


My advice on ties win parlay cards is as follows:

  1. Pick spreads on a "key number." In other words, a frequent margin of victory. The table below shows the top ten.
  2. Pick games where there is at least a half point difference between the market "off the board" line and the line on the card.

Margin of Victory

Rank Margin of Victory Frequency
1 3 15.7%
2 7 9.3%
3 10 6.2%
4 6 5.4%
5 4 5.0%
6 14 4.8%
7 1 4.0%
8 17 3.6%
9 2 3.5%
10 5 3.2%

For example, suppose the Chargers are a 9.5-point underdog off the board but 10 points on the card. This is like getting 10.5 points on the Chargers, or a full extra point, because of the ties win rule.

The following table shows what ties win parlay cards pay at various sports book groups around Las Vegas. Wins in this table are on a "for one" basis. In other words, the original wager is not returned, even if the bet wins. It is hard to choose the best group, because it depends on the number of picks made, as follows:

  • Pick 3: Lots pay 6.
  • Pick 4: Treasure Island at 11.
  • Pick 5: Lots at 20.
  • Pick 6: Golden Nugget and South Point at 40.
  • Pick 7: Lots at 75.
  • Pick 8: Lots at 150.
  • Pick 9: LVH at 305.
  • Pick 10: Jerry's Nugget at 625.

Ties Win Parlay Card — Pay Table

Sportsbook Legs
Pick 3 4 5 6 7 8 9 10 11 12
Aliante 6 10 20 40 75 150 305 600 1200 2000
Boyd 6 10 20 36 75 150 275 600
Golden Nugget 6 10 20 40 75 150 275 600
Jerry's Nugget 6 10 20 39 70 150 302 625
LVH 6 10 18 33 62 120 305 600 1150
South Point 6 10 20 40 75 150 275 600
Stations 6 10 20 35 65 130 250 600
Stratosphere 6 10 20 36 75 140 275 600
Treasure Island 6 11 20 38 75 140 300 600

To estimate the value of Ties Win cards, I had to make assumptions about how the sports books created the lines on the card. As mentioned, they like to give the player the chance at a tie, by making integer spreads, except +/- 3. Where the point spread is +/- 3 off the board, I moved it to +/- 2.5. Otherwise, if the point spread is already an integer off the board, I assume it will stay the same on the card. If it ends in 1/2, I move it a half point to an integer spread. Based on these line-making assumptions, I show the overall probability of a tie is 2.89%. Otherwise, the probability of win or loss is equal at 48.56% each. So, the random picker can expect to get 51.44% of picks correct.

The following table shows the expected return for a random picker based on the best available win for each number of picks. As you can see, the house edge ranges from 20% to 31%, depending on the number of picks.

Ties Win Parlay Card — Random Picker

Pick Pays Prob. Win Exp. Value
3 6 0.136149 -0.183104
4 11 0.070041 -0.229546
5 20 0.036032 -0.279353
6 40 0.018537 -0.258535
7 75 0.009536 -0.284795
8 150 0.004906 -0.264133
9 305 0.002524 -0.230256
10 625 0.001298 -0.188544
11 1,150 0.000668 -0.231894
12 2,000 0.000344 -0.312786

It should be noted that sometimes the card makers don't like point spreads of +/- 7 either, which would lower the probability of winning to under 51.44%.

The next table shows the expected return for the bettor who makes picks only where the point spread on the card is a half point better than the "off the board" spread. Such a bettor can expect to win 53.18% of picks. Again, this table assumes the maximum available win. The return column shows a range of a house edge of 14.9% to a player edge of 13.1%.

Ties Win Parlay Card — Extra Half Point Picker

Pick Pays Prob. Win Exp. Value
3 6 0.150409 -0.097545
4 11 0.079989 -0.120117
5 20 0.042539 -0.149214
6 40 0.022623 -0.095084
7 75 0.012031 -0.097665
8 150 0.006398 -0.040255
9 305 0.003403 0.037821
10 625 0.001810 0.130994
11 1,150 0.000962 0.106716
12 2,000 0.000512 0.023591

Ties Lose Parlay Cards


Ties lose parlay cards are a horse of a different color. Unlike other parlay and teaser cards, ties lose parlay cards are usually based on just one or two games. During the regular NFL season, they are often based on the Sunday and Monday night games. As well as picking against the side and total, there are a host of props the player may choose from. An example of a selection likely to fall on a tie is over or under two interceptions. The following is my advice for playing ties lose parlay cards, if you must:

  • Don't pick any event that is likely to end in a tie. For example, over/under three field goals.
  • Don't pick any event that has more than two possible outcomes. For example, first score to be a touchdown pass, touchdown run, field goal, or any other score.
  • Look for correlations. For example, the final score of one team to be odd and the other team to be even. 55.9% of games end in an odd total, which must be the sum of one odd and one even number.

Here are some miscellaneous statistics, which may or may not come in handy, based on the 2000 to 2012 seasons. An exception is the average number of field goals, which is based on the 2000 to 2010 seasons, for lack of data on the other years. Of course, you should also consider the dynamics of the actual game you are betting on. A couple things this table should show is the danger of betting over/under two interceptions or three field goals, since those are very close to the averages, and thus have a high probability of falling on a tie.

NFL Averages

Event Average
First quarter points 8.54
Second quarter points 13.16
Third quarter points 8.94
Fourth quarter points 12.05
Interceptions 2.03
Penalties 12.46
Fumbles 2.97
Fumbles lost 1.43
Punts 9.65
Field goals 2.98
First downs 37.46
Rushing touchdowns 1.42
Passing touchdowns 2.82

As with any kind of parlay or teaser card, always shop around for the best pays. The following table shows what various sports book groups pay on ties lose cards. Wins in this table are on a "for one" basis. In other words, the original wager is not returned, even if the bet wins.

Ties Lose Parlay Card — Pay Table

Sportsbook Legs
3 4 5 6 7 8 9 10
Boyd 11 20 40 80 160 350 800
Golden Nugget 6 11 20 40 80 150 300 800
MGM 6 11 20 40 80 150 300 600/20
South Point 6 11 20 40 80 160 350 700
Stations 6 12 23 45 80 160 320 800

The next table shows the expected return for each number of picks, assuming the best available pay table and a 50% chance of winning each pick. The right column shows the house advantage ranges from 21.9 to 37.5% (ouch!).

Ties Lose Parlay Card — Random Picker

Pick Pays Prob. Win Exp. Value
3 6 0.125000 -0.250000
4 12 0.062500 -0.250000
5 23 0.031250 -0.281250
6 45 0.015625 -0.296875
7 80 0.007813 -0.375000
8 160 0.003906 -0.375000
9 350 0.001953 -0.316406
10 800 0.000977 -0.218750

The following table shows the possible outcomes for the MGM pick-10 ties lose card, assuming a 50% chance of each event winning. The lower right cell show an expected return of 78%.

MGM Pick 10 Ties Lose — 50% Picker

Correct Picks Pays Probability Return
10 600 0.000977 0.585938
9 20 0.009766 0.195313
8 or less 0 0.989258 0.000000
Total 1.000000 0.781250

Hopefully, I have convinced you that ties lose parlay cards are a terrible value. There is an exception, though. Sometimes parlay cards for the Super Bowl have soft lines. However, it is beyond the scope of this page to explain how to spot them.

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