Counting 3-3-3-3-9

Ray emailed our emergency scoring help department with this question:

we had a discussion on counting one hand with one 9 and four 3. one said total is 24 and another said 20 which is it please.

Regular readers will know the standard Cribbage Corner method for counting this and other tricky hands:

  1. First count 15s. The only way to make 15 with this hand is with the 9 and a pair of 3s. As we've outlined in other forum posts, there are 6 ways to pick a pair from 4 cards. So there are 6 ways to make 15, scoring 12 points in all.
  2. Then count pairs - again, there are 6 different pairs of 3s, scoring another 12 points.
  3. Then count runs, flushes and nobs - there are none, so the total is 24.

I hope this helps settle an argument!

4 3's and 9

My total is 20 not 24. There is no fifteen 12 there. Please reply.

Score 24

ptmelnyk, this hand is hard to see without having the cards layed out on a table. Get the deck out and place all of the 3s in a large square and place the 9 in the center of the square. Now we know that each pair of the 3s is going to equal 15 and we already know that the quads of 3s equals 12. Start from the top left corner and work clockwise one card at a time:

3C 3H

9

3S 3D

So here is the scoring:
3C + 3H
3C + 3D
3C + 3S
3H + 3D
3H + 3S
3D + 3S

That is 6 different and distinct combinations of 15 which equals 12 points + 12 points for the quads=24 points.