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Cribbage hands and cribs total amount sorted by score
David Vongrad has calculated the total amount of all possible cribbage hands and cribs, sorted by the score points.
From his letter: The below table is explained as follows:
A 52 card deck is sorted with the ace to king of hearts first, followed by the ace to king of spades and then the ace to king of diamonds and finally the ace to king of clubs
such that the "lowest" card is the ace of hearts and the "highest" is the king of clubs (I chose this order arbitrarily for the purposes of calculating all possible scores in a computer program).
Then 5 cards are taken at a time, sorted as described above and scored according to cribbage rules.
If the "lowest" card (Card 1) in any given 5 card hand is the cut card, the score is 0 for 196,812 of those hands if that hand is the dealer or pone hand (H) and 0 for 199,452 if the cards represent the crib (C).
Similar numbers are counted if the second "lowest" card (Card 2) is the cut card and so forth.
Thus, the number of points in each of the hand and crib for every 5 card combination is shown below. The total amount of each score for the hand and crib when each of the 5 cards is the cut card is 12994800.
Card 1 Card 2 Card 3 Card 4 Card 5 Total
====== ====== ====== ====== ====== =======
0H: 196812 196812 196812 215460 203112 1009008
0C: 199452 199452 199452 218100 205752 1022208
1H: 24948 24948 24948 6300 18648 99792
1C: 24948 24948 24948 6300 18648 99792
2H: 547338 546066 561678 581532 577182 2813796
2C: 551520 551520 567360 587628 581772 2839800
3H: 114720 114720 104928 84408 86232 505008
3C: 115500 115500 105708 85188 87012 508908
4H: 561438 562026 560796 580536 590880 2855676
4C: 563856 565080 563784 583356 592884 2868960
5H: 150166 148942 145948 127704 124748 697508
5C: 151432 150208 147076 128868 125912 703496
6H: 353866 355062 355168 368368 367804 1800268
6C: 351736 352824 352420 364972 365224 1787176
7H: 155888 154800 153632 142424 144580 751324
7C: 156692 155604 154388 143240 145396 755320
8H: 222284 225506 231776 231380 226290 1137236
8C: 218186 221258 228020 227972 222900 1118336
9H: 78024 74952 70648 69570 68030 361224
9C: 77358 74286 70072 69096 67556 358368
10H: 77438 78548 76288 77986 78480 388740
10C: 75716 76100 74044 75700 76680 378240
11H: 11972 11588 11060 8208 8852 51680
11C: 10400 10016 9524 6648 7292 43880
12H: 61935 62425 63559 64153 65268 317340
12C: 61143 61321 62053 62353 64086 310956
13H: 5017 4839 4071 3653 2076 19656
13C: 4429 4251 3519 2963 1386 16548
14H: 17604 18092 18076 18140 18188 90100
14C: 17340 17468 17524 17804 17996 88132
15H: 2116 2020 1984 1696 1352 9168
15C: 2104 2008 1984 1660 1316 9072
16H: 11268 11788 12032 11802 11358 58248
16C: 11112 11500 11744 11616 11316 57288
17H: 2572 2152 1976 2128 2368 11196
17C: 2572 2152 1976 2128 2368 11196
18H: 558 636 530 474 510 2708
18C: 492 492 392 396 492 2264
19H: 0 0 0 0 0 0
19C: 0 0 0 0 0 0
20H: 1554 1600 1642 1662 1610 8068
20C: 1542 1546 1564 1596 1580 7828
21H: 530 526 496 464 480 2496
21C: 518 514 496 464 480 2472
22H: 84 84 84 96 96 444
22C: 84 84 84 96 96 444
23H: 76 76 76 64 64 356
23C: 76 76 76 64 64 356
24H: 736 736 736 736 736 3680
24C: 736 736 736 736 736 3680
25H: 0 0 0 0 0 0
25C: 0 0 0 0 0 0
26H: 0 0 0 0 0 0
26C: 0 0 0 0 0 0
27H: 0 0 0 0 0 0
27C: 0 0 0 0 0 0
28H: 15 15 15 15 16 76
28C: 15 15 15 15 16 76
29H: 1 1 1 1 0 4
29C: 1 1 1 1 0 4
Hand: 2598960 2598960 2598960 2598960 2598960 12994800
Crib: 2598960 2598960 2598960 2598960 2598960 12994800
The above cribbage statistic table by courtesy of David C. Vongrad
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