Sub-Parlays

Keywords :

Sub-parlays are the possible smaller parlays (or subsets) of a bigger parlay. In order to have sub-parlays a parlay must consisting of 3 or more selections. A 2-play parlay has only singles as a subset, thus it has no sub-parlays. A 3-play parlay has three possible 2-play parlays; for a 4-play parlay there are 4 possible 3-play parlays and 6 possible 2-play parlays. As an example the sub-parlays of a 5-play are shown in the following tables.

Don't be surprised if you are familiar with sports-betting and never heard of the word sub-parlay. We had to coin this word because the practice of betting on subsets of a parlay is not common in sportsbooks.

Normally, if you have formed a 5-play parlay as shown above, and if any one of the selection is incorrect then you lose all your wager. However, if your sportsbook allows betting on sub-parlays, then you can bet on any four, any three, or any two of the five selections to be correct. This will indeed allow you to recover some of your money, or even win a small amount even if some of your selections turn out to be incorrect. 

Suppose you have placed a bet on all 5 to be correct, and also more bets on any 4 and on any 3 but not any 2. Then, if selection-3 is incorrect while the others are all correct, you will win with the '1-2-4-5' of the 4-play sub-parlays and also with ' 1-2-4', '1-2-5', '1-4-5', and '2-4-5' of the 3-play parlays. That is, you'll win with all sub-parlays that do not contain selection-3.  Cute!! Eh?

Interesting as it may look, it comes with a little more expenditure. A stake of $1 on a 4-play sub-parlay means that you have to wager $1 for each of the five 4-play sub-parlays, thus costing you $5. If you wager $1 on a 3-play sub-parlay, you'll pay $10 more.

The payouts of the sub-parlays that you have won will be calculated by multiplying your stake ($1) by the product of the odds of the winning selections.

The following is an example of a winning bet slip on college football. 

As you can see this is a 6-play parlay and bets have been placed on 4- and 5-play sub-parlays: $2 on the fifteen 4-play combinations (total $30); $2 on the six 5-parlay combinations (total $12); and $8 on all 6. Since all the six selections were correct, the $8 bet brought a payout of $862.62. In addition, all the fifteen 4-play sub-parlays paid a total of $680.47, and all the six 5-play sub-parlays paid a total of $593.55. Plus there was about $436 bonus too, making the total payout about $2572.

The breakdown of the sub-parlay bets are shown below:

Now, let's see the what-if scenarios. What if events 1 & 2 had been incorrect? Then only one combination, namely, 3/4/5/6 of the 4-play sub-parlay would have won resulting in a payout of $43.57. Thus the bettor would have ended up losing only $6.43 of his total wager of $50.  What if only event 1 had been incorrect? In this case there would have been 5 winners from the 4-play sub-parlays with a total payout of $221.20, and one winner, namely, 2/3/4/5/6 of the 5-play sub-parlay which paid $95.85. All in all this 5-correct results would have paid out $317.05. Not bad for a 5 out of 6 selections.

Calculation of the number of sub-parlays

In case you are wondering how the number of sub-parlays are determined, here is the formula.

c = n!/[(n-s)! * s!]

where, c = number of sub-parlay combinations, n = total plays in the parlay, s = plays in the sub-parlay. The ! represents a factorial.

Example: How many a) 6-play and b) 8-play sub-parlays are there in a 13-play parlay?

Answer: For this case, n = 13, then,

             a) s = 6,  thus  c = 13!/[13-6)! * 6!]  = 13!/[7! * 6!]  = 1716 Ans.

             b) s = 8,  thus  c = 13!/[13-8)! * 8!]  = 13!/[5! * 8!]  = 1287 Ans.

Furthermore, if you do not want to spend your precious time meddling with the formula, here is a table that calculates and displays the combinations. Just select the value of n from the drop-down list (2 to 15), then the box lists the c values for various s values.

Besides displaying the number of sub-parlay combinations, the above table can also be used to determine how many of your sub-parlays are winners in case you do not get all correct. To illustrate, let us suppose that you had formed a 12-play parlay and placed bets on the 4,7,10,11,and the 12 sub-parlays. If 11 of your selections turn out to be winners, how many of your sub-parlays are winners?

To determine this just select '11-play' from the top drop-down menu, and the resulting list will tell you the winning number of each sub-parlay. Note that selecting 12-play will show you on how many combinations you have betted on. Thus,