Monday, October 17, 2005

Sports Betting: How to beat Parlay Cards in Vegas

Sports: How to beat Parlay Cards in Vegas

Many sportsbooks in Las Vegas have parlay cards. It is usually the highest profit area in the sportsbook due to the bad odds and the stupid bettors. However, there are ways to beat the parlay cards.

There are many different variations, but I’ll stick with one example to illustrate. With just a few adjustments, you should be able to calculate the numbers for any other variation using this example as a guide.

The example I’ll choose is one that has the least variance, and the highest chance of the player winning – the 3 team parlay. Some casinos will have different parlay cards, so you have to be careful in checking the odds that are offered (see the back of the card). The odds that is usually the best are the ones that offer 6.5 for 1. This means the casino will pay you $6.50 for every $1 that you bet. In other words, it really is 5.5 to 1, since you are only winning $5.50 for every $1 you bet. They are just refunding you the $1 that you wagered to begin with. This is a tricky way to state odds, and is different than the way sportsbooks state their odds for futures bets. It’s similar to how some craps table shows the odds (10 for 1 or 8 for 1 on some hardways bets).

So, 6.5 for 1 = 5.5 to 1 = 1/6.5 = 15.38%

Since there are three teams, we take the cube root of 15.38%. This is not as scary as it sounds. Simply type in =15.38%^(1/3) in excel. This means taking 15.38% to the 1/3rd power. The answer is 53.58%.

So we need to be able to win each game at the rate of 53.58% in order to break even to the parlay card. In order to check the work, multiply 53.58% by itself 3 times:

53.58% x 53.58% x 53.58% = 15.38%

For four or more teams, do a similar analysis. Say a 4 team parlay pays 11 for 1. In percentages, 11 for 1 = 1/11 = 9.09% Take 9.09% to the (1/4) power, and you get: 9.09% ^ (1/4) = 54.9%. These odds are worse than the 3 team 6.5 for 1 payout.

Typically, these odds wouldn’t be exciting. Since betting a team at -110 is a breakeven rate of 52.4%, having to win at 53.58% is a bad bet. However, the difference is that the lines on the parlay cards may not be accurate at the moment. These parlay cards are printed earlier in the week (Tuesday, Wednesday, Thursday), so when the lines move as the week progresses, the lines in the parlay card will be off a touch. The casinos realize this too, and will often post something like “Game #15 is off the parlay card”. So when a game line moves a few points, you won’t get to take advantage of them. However, a line doesn’t have to move all that much for the player to gain some edge. The key is to know what a half point or a point is worth depending on the game (College or NFL) and the value of the point.

So aside from looking for 1 or 2 point differences on the card versus the board, you want to look for parlay cards that show half points only or ties win. And then compare those lines to the current lines. The NFL is typically better for half point differences because the frequency of pushes on certain key points is greater than it’s College counterpart (see Stanford Wong’s Sharp Sports Betting for more info). The most common is when the favorite is a 3 point favorite – in that case the probability of the favorite winning the game is about 10%. So let’s imagine there are 3 games lined at 3 in the NFL. If you can find a parlay card with half points or ties win, then you have a decent wager and can beat the parlay card. Here’s an example.

Current lines show

But the parlay cards show:
ATL -2.5 DAL
PIT -3.5 NYJ
SD -2.5 OAK

In this case, you would consider taking ATL, NYJ and SD in the parlay card, because you are getting the free half point. So how often do you expect to win given the free half point? Here’s some quick math:


ATL is expected to win by exactly 3 points roughly 10% of the time. If the line is efficient, then that means they should win by more than 3 about 45% of the time, and lose the game (or win by 1 or 2) about 45% of the time.

ATL wins by 4 or more: 45%
ATL wins by 3 : 10%
ATL wins by 1 or 2 or loses the game: 45%
Total: 100%

If you can twist the 3 into a win, then that would make your winning chances go up to 55% (45% + 10%).

So ATL -2.5 is a 55% play.

The same can be show for NYJ +3.5 and SD -2.5….and so you have 3 55% plays.

55% x 55% x 55% = 16.64%

That is greater than the breakeven rate of 15.38% that is on the 6.5 for 1 parlay cards. So we have a winning bet.

Now in practice, it isn’t as easy as this. Often you may find two games that are off, but not a third. Since the minimum number of games needed on the parlay cards is typically three games, you’ll have to find another game. This is when you’ll need to know the push percentages of every key point in the NFL. So say you find:

ATL -2.5 (current line -3)
PIT -2.5 (current line -3)

But no other game that is off by a half point from the 3. But you do find:

IND -6.5 (current line -7)

Then you’ll need to know exactly what the 7 is worth. It is about 6%. So that means IND -6.5 is a 53% winner if the IND -7 is a fair market line. 53% is less than the 53.58% we require to breakeven, but may still be useful to use this game, even though it is less than 53.58% because otherwise we wouldn’t be able to take advantage of the two 55% games.

55% x 55% x 53% = 16.03%

In fact, if we have two 55% games, we need a third game of greater than 50.85% in order to give us an edge in the parlay cards. Knowing this is helpful, you can use a “losing bet” in order to get that 3rd team in.

It gets a bit dicier if there is only one game off by a half point from the 3, but two games off a half point from the 7. Then you get:

55% x 53% x 53% = 15.45%

15.45% is only a smidge greater than 15.38%. If you have an opinion on any of those games and would have bet them anyway, then this may be worthwhile because you are getting into a zero expectancy bet, and don’t have to lay the vig in order to get your action.

Once you start playing these parlay cards, you’ll see some other issues which will become important. For example, how do you adjust a game when the current line is:

ATL -3 -120 NYJ
NYJ +3 +100 ATL

So the line is a bit shaded towards ATL -3, and the fair market line is ATL -3 -110.

In that case, if you see ATL -2.5 on the parlay card, then it is greater than a 55% play. But if you see NYJ +3.5, then it is a worse than a 55% play.

So you will have to keep abreast of the current lines, know how to adjust based on the vig on the line.

Let’s use the example where we had 3 teams lined at 3, and we are getting a free half point on each of them on the parlay card. In that case, the expected winning percentage of the 3 team parlay is 16.64%. If the wager was for $100, then the expectancy is:

= ($550 x 16.64%) + (-$100 x (100% - 16.64%))
= ($550 x 16.64%) + (-$100 x 83.36%)
= $91.52 - $83.36
= $8.16

The Return on Investment is very high. 8.16%.

Actually betting:
Casinos and their employees are not the brightest people in the world, but they are not dumb either. Especially after some losses, they will re-think their position and make a few adjustments. As for these parlay cards, they do keep an eye when there are many games lined at 3. And when game lines move away from the posted lines on the parlay cards, they will take them off the card and not allow bettors to take advantage of them. If you try to put too many high dollar wagers, they may stop you and take a small portion or none of them. By a high dollar wager, I mean a $300 bet or higher. Usually this is nothing for an individual game, even in the smaller casinos, but because the payoff is higher (the casino could lose $1650 on a $300 wager), they often have to get approval from the supervisor.

It takes a lot of work to bet these parlay cards profitably. Because of the low dollar amount that most books will take, the way to do it correctly is to stay under the radar and to bet them at many books for low dollar amounts. You can imagine how much work this takes. A ton of driving, a ton of walking. It's a real tough job to do it right for a significant amount of money. But one doesn't have to do it for a living to have fun with it while getting positive expectancy.

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