Advantage with Parlay Cards

King Yao is the author of Weighing the Odds in Hold‘em Poker, and Weighing the Odds in Sports Betting. He uses his experience from making millions in financial derivative markets and translates it into gambling. Since he left his trading position in 2000, he has been playing poker and betting on sports. He travels to Las Vegas frequently, especially during football season.

Prospective sports bettors should know the basic principles of sports betting. You should not be betting online or anywhere else without this fundamental knowledge.

The NFL parlay card advantage

You do have one advantage in NFL parlay cards: The lines may not be sharp. Parlay cards are printed on Wednesday or Thursday, using then-current lines. When lines move after that, the lines on the parlay card no longer reflect current market conditions. The casinos realize this, and will sometimes eliminate certain games from the parlay card with signs like this: “Game #15 is off the parlay card.” After a game line has moved several points, you will not get to take advantage of the old line on the parlay cards. However, a line does not have to move much for you to gain some edge. For lines that moved only slightly on the board, sportsbooks will usually keep them as printed on the parlay card. The key is to know how much of a difference a half point or a full point makes in the winning percentage. Differences in the lines between parlay cards and the current market are more valuable in NFL games, where a half-point difference can mean as much as a 5% difference in the winning percentage. Sometimes a half point can be useful in college football games.

Look for “half-point” and “ties-win” parlay cards. A game landing right on the number is a win on ties-win cards and can be a winner if you have the proper half point on a half-point card, but is a loser on “ties-lose” parlay cards. Ties-lose cards generally offer better odds but worse value.

There are certain numbers with high push rates in the NFL. The most frequent push number is a line of 3, where the probability of the favorite winning the game by exactly 3 is about 10%. If there are three or more NFL games with lines of 3 on a parlay card,then there might be positive-EV opportunity with half-point or ties-win cards. Here is an example.

Current lines on the board are:

ATL -3 DAL

PIT -3 NYJ

SD -3 OAK

Lines on the “half-point” parlay card show:

ATL -2.5 DAL

PIT -3.5 NYJ

SD -2.5 OAK

Consider taking ATL -2.5, NYJ +3.5 and SD -2.5 in the parlay card, because you are getting an extra half point on each game compared to the current line.

You can figure out how often you expect to win given extra half points in these games. Let’s take a look at one team first.

ATL is expected to win by exactly 3 points about 10% of the time. If the line is efficient, then ATL will cover the 3 points 45% of the time, as well as not cover the 3 points 45% of the time.

45%: ATL wins by 4 or more

10%: ATL wins by 3

45%: ATL wins by 1 or 2 or loses the game

100%: Total

Thus ATL -2.5 is a winner 55% of the time (45% + 10%). The same can be shown for NYJ +3.5 and SD -2.5. All three plays are 55% plays. Three 55% plays should all cover at the same time 16.64% of the time (55% x 55% x 55% = 16.64%). This 3-team parlay is a positive-EV bet because its winning percentage is greater than the break-even winning percentage of 15.38% for a 3-team parlay that pays 6.5 for 1.

In practice it is not usually this straightforward. The minimum number of games that must be played on most parlay cards is three, but you may not find three different lines with this much edge. In order to bet a 3-team parlay, you may have to include other plays that are not as strong. If you know the push percentages of every key point in the NFL, you can calculate whether a parlay is worthwhile. Let’s say you find two games that are off by a half point versus a market line of -3.

ATL -2.5 (current line -3)

SD -2.5 (current line -3)

But the best you can find for a third game to include in your 3-team parlay is this one:

IND -6.5 (current line -7)

For the IND game you need to know the approximate push percentage of NFL games lined at 7. If it is worth 5%, then that means IND -6.5 is a 52.5% winner (assuming IND -7 is a fair line). 52.5% is less than the 53.58% break-even winning percentage, but this game may still be useful as a filler to complete the 3-team parlay. The combination of two 55% games and one 52.5% game has value. The expected winning percentage of this combination is 15.88% (55% x 55% x 52.5% = 15.88%).

If there are two 55% games, then a third game of 50.85% makes the 3-team parlay paying 6.5 for 1 into a zero EV bet (55% x 55% x 50.85% = 15.38%). If one game is 55% and two games are 52.5%, then there is negative value in the parlay (55% x 52.5% x 52.5% = 15.16%). 15.16% is below 15.38%, thus there is slight negative EV in this 3-team parlay. However, if you happen to have an opinion on some games and want to bet them individually anyway, then the parlay card may be a good alternative to making straight plays at -110 juice.

Another issue to consider is when the accompanying money line on the point spread is not -110. Here is an example.

BAL -3 -120 CHI

CHI +3 +100 BAL

The line is shaded towards BAL -3, and the fair market line is BAL -3 -110. In that case, if you see BAL -2.5 on the parlay card, then it is greater than a 55% play. An estimate is 57.4% (52.4% reflects -110 and add 5% for the extra half point). On the other hand, if the parlay card has CHI +3.5, then it is a worse than a 55% play, at about 52.6% (47.6% + 5% = 52.6%). You will have to keep abreast of the current lines and know how to adjust the expected winning percentages based on the accompanying vig.

This is part of an occasional series of articles.

Excerpted with permission from the e-book version of Weighing the Odds in Sports Betting by King Yao, edited for this format.