A 52 Card Hand
Kevin Kurowski, a paraplegic (car accident) in a New Hampshire rehabilitation center, sent me an email on January 8, 2006, asking how many points would you have if the entire deck was dealt to you. So we started working it out. Here's what we came up with.
combinations | total points | |||
---|---|---|---|---|
Flushes | 0 (cards must all be same suit) | 0 | x1 | 0 |
Pairs | 13x6 | 78 | x2 | 156 |
Straights | 13x4^13 | 872,415,232 | x1 | 872,415,232 |
Fifteens | see table below | 34,528 | ||
Total | 872,449,916 |
Now I want to know if it's possible to hold all 52 cards with one hand? <grin>
Fifteens | ||||
---|---|---|---|---|
cards | combinations | total | points | |
10,5, | 16x4 | 64 | ||
10,4,1 | 16x4x4 | 256 | ||
10,3,2 | 16x4x4 | 256 | ||
10,3,1,1 | 16x4x6 | 384 | ||
10,2,2,1 | 16x6x4 | 384 | ||
10,2,1,1,1 | 16x4x4 | 256 | ||
total | 1,600 | x2 | 3,200 | |
9,6, | 4x4 | 16 | ||
9,5,1 | 4x4x4 | 64 | ||
9,4,2 | 4x4x4 | 64 | ||
9,4,1,1 | 4x4x6 | 96 | ||
9,3,3 | 4x6 | 24 | ||
9,3,2,1 | 4x4x4x4 | 256 | ||
9,3,1,1,1 | 4x4x4 | 64 | ||
9,2,2,2 | 4x4 | 16 | ||
9,2,2,1,1 | 4x6x6 | 144 | ||
9,2,1,1,1,1 | 4x4x1 | 16 | ||
total | 760 | x2 | 1,520 | |
8,7 | 4x4 | 16 | ||
8,6,1 | 4x4x4 | 64 | ||
8,5,2 | 4x4x4 | 64 | ||
8,5,1,1 | 4x4x6 | 96 | ||
8,4,3 | 4x4x4 | 64 | ||
8,4,2,1 | 4x4x4x4 | 256 | ||
8,4,1,1,1 | 4x4x4 | 64 | ||
8,3,3,1 | 4x6x4 | 96 | ||
8,3,2,2 | 4x4x6 | 96 | ||
8,3,2,1,1 | 4x4x4x6 | 384 | ||
8,3,1,1,1,1 | 4x4x1 | 16 | ||
8,2,2,2,1 | 4x4x4 | 64 | ||
8,2,2,1,1,1 | 4x6x4 | 96 | ||
total | 1,376 | x2 | 2,752 | |
7,7,1 | 6x4 | 24 | ||
7,6,2 | 4x4x4 | 64 | ||
7,6,1,1 | 4x4x6 | 96 | ||
7,5,3 | 4x4x4 | 64 | ||
7,5,2,1 | 4x4x4x4 | 256 | ||
7,5,1,1,1 | 4x4x4 | 64 | ||
7,4,4 | 4x6 | 24 | ||
7,4,3,1 | 4x4x4x4 | 256 | ||
7,4,2,2 | 4x4x6 | 96 | ||
7,4,2,1,1 | 4x4x4x6 | 384 | ||
7,4,1,1,1,1 | 4x4x1 | 16 | ||
7,3,3,2 | 4x6x4 | 96 | ||
7,3,3,1,1 | 4x6x6 | 144 | ||
7,3,2,2,1 | 4x4x6x4 | 384 | ||
7,3,2,1,1,1 | 4x4x4x4 | 256 | ||
7,2,2,2,2 | 4x1 | 4 | ||
7,2,2,2,1,1 | 4x4x6 | 96 | ||
7,2,2,1,1,1,1 | 4x6x1 | 24 | ||
total | 2,348 | x2 | 4,696 | |
6,6,3 | 6x4 | 24 | ||
6,6,2,1 | 6x4x4 | 96 | ||
6,6,1,1,1 | 6x4 | 24 | ||
6,5,4 | 4x4x4 | 64 | ||
6,5,3,1 | 4x4x4x4 | 256 | ||
6,5,2,2 | 4x4x6 | 96 | ||
6,5,2,1,1 | 4x4x4x6 | 384 | ||
6,5,1,1,1,1 | 4x4x1 | 16 | ||
6,4,4,1 | 4x6x4 | 96 | ||
6,4,3,2 | 4x4x4x4 | 256 | ||
6,4,3,1,1 | 4x4x4x6 | 384 | ||
6,4,2,2,1 | 4x4x6x4 | 384 | ||
6,4,2,1,1,1 | 4x4x4x4 | 256 | ||
6,3,3,3 | 4x4 | 16 | ||
6,3,3,2,1 | 4x6x4x4 | 384 | ||
6,3,3,1,1,1 | 4x6x4 | 96 | ||
6,3,2,2,2 | 4x4x4 | 64 | ||
6,3,2,2,1,1 | 4x4x6x6 | 576 | ||
6,3,2,1,1,1,1 | 4x4x4x1 | 64 | ||
6,2,2,2,2,1 | 4x1x4 | 16 | ||
6,2,2,2,1,1,1 | 4x4x4 | 64 | ||
total | 3,616 | x2 | 7,232 | |
5,5,5 | 4 | 4 | ||
5,5,4,1 | 6x4x4 | 96 | ||
5,5,3,2 | 6x4x4 | 96 | ||
5,5,3,1,1 | 6x4x6 | 144 | ||
5,5,2,2,1 | 6x6x4 | 144 | ||
5,5,2,1,1,1 | 6x4x4 | 96 | ||
5,4,4,2 | 4x6x4 | 96 | ||
5,4,4,1,1 | 4x6x6 | 144 | ||
5,4,3,3 | 4x4x6 | 96 | ||
5,4,3,2,1 | 4x4x4x4x4 | 1024 | ||
5,4,3,1,1,1 | 4x4x4x4 | 256 | ||
5,4,2,2,2 | 4x4x4 | 64 | ||
5,4,2,2,1,1 | 4x4x6x6 | 576 | ||
5,4,2,1,1,1,1 | 4x4x4x1 | 64 | ||
5,3,3,3.1 | 4x4x4 | 64 | ||
5,3,3,2,2 | 4x6x6 | 144 | ||
5,3,3,2,1,1 | 4x6x4x6 | 576 | ||
5,3,3,1,1,1,1 | 4x6x1 | 24 | ||
5,3,2,2,2,1 | 4x4x4x4 | 256 | ||
5,3,2,2,1,1,1 | 4x4x6x4 | 384 | ||
5,2,2,2,2,1,1 | 4x1x6 | 24 | ||
5,2,2,2,1,1,1,1 | 4x4x1 | 16 | ||
total | 4,388 | x2 | 8,776 | |
4,4,4,3 | 4x4 | 16 | ||
4,4,4,2,1 | 4x4x4 | 64 | ||
4,4,4,1,1,1 | 4x4 | 16 | ||
4.4.3.3.1 | 6x6x4 | 144 | ||
4,4,3,2,2 | 6x4x6 | 144 | ||
4,4,3,2,1,1 | 6x4x4x6 | 576 | ||
4,4,3,1,1,1,1 | 6x4x1 | 24 | ||
4,4,2,2,2,1 | 6x4x4 | 96 | ||
4,4,2,2,1,1,1 | 6x6x4 | 144 | ||
4,3,3,3,2 | 4x4x4 | 64 | ||
4,3,3,3,1,1 | 4x4x6 | 96 | ||
4,3,3,2,2,1 | 4x6x6x4 | 576 | ||
4,3,3,2,1,1,1 | 4x6x4x4 | 384 | ||
4,3,2,2,2,2 | 4x4x1 | 16 | ||
4,3,2,2,2,1,1 | 4x4x4x6 | 384 | ||
4,3,2,2,1,1,1,1 | 4x4x6x1 | 96 | ||
4,2,2,2,2,1,1,1 | 4x1x4 | 16 | ||
total | 2,856 | x2 | 5,712 | |
3,3,3,3,2,1 | 1x4x4 | 16 | ||
3,3,3,3,1,1,1 | 1x4 | 4 | ||
3,3,3,2,2,2 | 4x4 | 16 | ||
3,3,3,2,2,1,1, | 4x6x6 | 144 | ||
3,3,3,2,1,1,1,1 | 4x4x1 | 16 | ||
3,3,2,2,2,2,1 | 6x1x4 | 24 | ||
3,3,2,2,2,1,1,1 | 6x4x4 | 96 | ||
3,2,2,2,2,1,1,1,1 | 4x1x1 | 4 | ||
total | 320 | x2 | 640 | |
grand total | 34,528 |
January 2006