Inspecting the real odds of parlays

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This past week, I received a most intriguing request from a reader. He asked me to review “again” the true odds associated with parlay cards.

I found the “again” quite amusing as to the best of my knowledge this is not a topic I have ever evenly remotely covered. At first, I couldn’t even figure what I would write about. Then, after giving it more thought, I realized there might be some math information that parlay players would like. I apologize that I’m waiting until after the football season to present this information.

The first thing you need to understand about any sports wager is that the goal of the sports book is to get half of the money on each side. Since a straight wager generally pays 10 to 11 (meaning you wager $11 to win $10), if the money is evenly split between the two sides they’re going to make money.

They control this is by adjusting the line. In football this is the point spread or the OVER/UNDER line. If a sports book moves the pointspread from +5 to +6, it doesn’t really mean they think one team is another point better, but that they need more money on the underdog.

They still have some risk the final score could be very close to that 5- or 6-point spread and things can get ugly in that case. But, they use very sophisticated computer programs to help them manage the risks, so don’t cry for the sports books.

In the end, we pretty much have to assume the probability of picking the winner of a game, including the pointspread or the OVER/UNDER is essentially 50%. If you have some inside knowledge of injuries or the like, obviously, you can affect that. But, for most of us mortals, it’s going to be a 50/50 shot.

Given this, calculating the ‘true odds’ of a parlay is as simple as multiplying 0.50 by itself for each additional line on your parlay. So, the odds of picking 1 out of 1 is 50%, 2 out of 2 is 25%, 3 out of 3 12.5%, etc… Flip these around to get the payout you’d like to see for a 100% payout. The table below shows, these numbers

So, all things being equal, if you go for a 4-line parlay, you’d love to get paid 16 for 1 (or 15 to 1, which is the same). You’re probably not going to get anywhere near that. If you’re lucky, probably 11 or 12 to 1.

As I said earlier, I wasn’t sure how much there was to write about this topic. But, then I remember those ‘Teaser’ parlays and the ‘Ties Win’ parlays. Most parlays use half points to avoid any ties. Some will simply remove a tie from the equation.

 So if you pick 4 lines and one ends a tie, it is as if you picked a 3 line parlay with the other lines. With a Ties Win parlay, your odds of winning any line (and thus the parlay) goes up. There is no way to determine by how much.

If I had a database of all games available to me, I might be able to figure out how often a tie (with the point spread) actually occurs. Since I don’t have this, I’ll have to give you some estimates. So, I’ll assume two possibilities for the Ties win parlay – that your probability to win is 52% or 55%.

With the Teaser parlay, the point spread is increased in both directions so that the probability that you can pick any particular line increases significantly. Again, I don’t have hard numbers to know by how much, so I’ll use 60 and 65%. The tables below show the probability and true payout for a 100% payback for each of these probabilities

As the probability of picking any one game correctly goes up, the probability of picking multiple games rises even more. So, as the probability goes from 55% to 65%, the probability of 8 out of 8 increase nearly four-fold. Accordingly, the expected payout gets cut by a factor of 4.

If you want to know the real payout you are getting, multiply the probability by the actual payout. Of course, you have to decide what the probability of you picking a game correctly is. There’s a good reason why my father used to always joke to not bet on any event where the participants have two legs! Good luck!

Table 1
Parlay Lines Probability True Odds Line
2 of out 2 25.00% 4 for 1
3 out of 3 12.50% 8 for 1
4 out of 4 6.25% 16 for 1
5 out of 5 3.13% 32 for 1
6 out of 6 1.56% 64 for 1
7 out of 7 .78% 128 for 1
8 out of 8 .39% 256 for 1

 

Table 2
Teaser 52% 55%
Parlay Lines Probability True Odds Line Probability True Odds Line
2 out of 2 27.04% 3.70 for 1 30.25% 3.31 for 1
3 out of 3 14.06% 7.11 for 1 16.64% 6.01 for 1
4 out of 4 7.31% 13.68 for 1 9.15% 10.93 for 1
5 out of 5 3.80% 26.30 for 1 5.03% 19.87 for 1
8 out of 8 0.53% 187.06 for 1 0.83% 119.43 for 1

 

 

Table 3
Teaser 60% 65%
Parlay Lines Probability True Odds Line Probability True Odds Line
2 out of 2 36.00% 2.78 for 1 42.25% 2.37 for 1
3 out of 3 21.60% 4.63 for 1 27.46% 3.64 for 1
4 out of 4 12.96% 7.72 for 1 17.85% 5.60 for 1
5 out of 5 7.78% 12.86 for 1 11.60% 8.62 for 1
6 out of 6 4.67% 21.43 for 1 7.54% 13.26 for 1
7 out of 7 2.80% 35.72 for 1 4.90% 20.40 for 1
8 out of 8 1.68% 59.54 for 1 3.19% 31.38 for 1

 

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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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