# How many 24 hands are there?

Submitted by admin on Fri, 06/19/2009 - 14:56

Edie Cappy writes:

How many combinations to make a 24 hand?

Can any mathematically inclined readers answer this?

## As far as I know, the 24

As far as I know, the 24 hands are 33339, 44447, 66663, 7777A, 45566, 44566, 44556, 67788, 77889. If you take into account the different suits, there are 4 ways to get each of the first 4 listed, and 144 ways to get each of the other 5. For example: in the 33339 hand, there is only one way to choose the 3s, and 4 ways to choose the 9. This gives 4 ways to get the 33339 hand. In the 45566 hand, there are 4 ways to choose the 4, 6 ways to choose 5s and 6 ways to choose 6s. This gives 4x6x6=144 ways to get that particular 24 hand. The others use the same argument. This makes 4x4+5x144=736 different 24 hands. If you care about what card is cut then the figure changes by a factor of 5. For example: if you consider 3h 3d 3c 3s with 9h cut to be a different hand than 3h 3d 3c 9h with 3s cut, the number of 24 hands will be 5x736=3680. I will run a program to check it for sure because I am not sure if I got all of the base hands right, though I am confident.

## Cribbage

Please show me how 66663 equals 24. Been playing Cribbage for more than 50 years and never experienced anyone counting this as 24 until recently. Would appreciate clarification.

Thank you.

## 66663 = 24

663 = 15 of course and that can be done 6 ways with 4 6's = 12 pts, then you have 6*4 = 12 points giving you 24 pts.

To demonstrate this we have 6-1, 6-2, 6-3, 6-4 and 3

6-1 + 6-2 + 3 = 15-2

6-1 + 6-3 + 3 = 15-4

6-1 + 6-4 + 3 = 15-6

6-2 + 6-3 + 3 = 15-8

6-2 + 6-4 + 3 = 15-10

6-3 + 6-4 + 3 = 15-12

## Ther is 12 @15s. Six pairs of

Ther is 12 @15s. Six pairs of 6s and a 3.

4 of a kind is 12

## Any three cards

Any three cards that equal 15, like 771 or 663 and if you have quads you will have 24. If it takes 4 cards then you will have 20 if you have quads. 99996 etc.

## four 24 hands

Have you ever heard of four people getting a 24 hand because of the cut? A six was cut. Do you know what he odds of that happening are? -James from Canada

## Never

Never heard of it, but it would be possible. Here are the hands that the four would have to hold. One players could hold 8,8,7,7 and two or three players must hold a combination of 4, 4, 5, 5 or 4, 5, 5, 6 or 4, 4, 5, 6, lastly one player could hold 9, 6, 6, 6 but that would mean that no other 6 was in another hand. So you would have to have 8877 or 4455 in two of the hands. In case you were wondering 3, 3, 3, 3 and a 6 cut is only 20.

## four 24 point hands

Yes it is possible, and it was done. However, what I was interested in, was the odds of that happening, four 24 point hands because of the cut. We have for years known the odds of getting a 29 hand are. I always wondered if the odds were greater than or less than getting a 29 hand, which by the way I've never had. I've had two 28 hands in my life, one I was able to use the other 28 hand I wasn't. -Thanks for the reply, James

## Not possable, there is simply

Not possable, there is simply not enough 4s or 5s or 6s to make 4 hands of 24 by cutting a 6 possable. The best you could do is 3. Try the odds of this one tho. I kept in my hand last night, 2,7s, an 8 and a 9. I cut an 8. After the hand was played out, we descovered that my opponent also had 2,7s an 8 and a 9. Now what are the odds of getting 2 identical 24 hands? Have witness and pics to prove. I have asked guiness the same question

## Hey Phil

I just got done proving it above...and so did you. If there are 4 of us are playing, the simplest way are these hands dealt to the four players:

4, 4, 5, 5

4, 4, 5, 5

7, 7, 8, 8

7, 7, 8, 8

So now what happens when a 6 is cut Phil? Are those not ALL 24 hands everyone is holding? Oh and Phil...there are even more. Some might be holding 4, 4, 5, 6 and a six cut would ALSO give ALL 24 hands to everybody. Two identical 24 hands happen all the time. Have no idea what the odds are, but as you can see above, it is pretty rare but can and does happen.

## four 24 hands

Yes it is possible. It happened to me and my brother. In addition, I've set up the cards like that to show that because the 6 was cut all four players got a 24 point hand. What I was initially trying to find out what are the odds of that happening. We know the odds of getting a 29 hand, so why can't we figure out what the odds of 4 people getting a 24 hand is. -James