Cribbage Statistics - Odds

Odds

  • The odds of getting a 28 hand in a two-player game are 1 in 15,028.
  • The odds of getting a perfect 29 hand in a two-player game are 1 in 216,580.
  • The odds of getting a perfect 29 hand in a three- or four-player game are 1 in 649,740.


Scoring Breakdown

Score Number of hands
(out of 12,994,800)		 Percentage of hands Percentage of hands at least as high
0 1009008 7.7647 100
1 99792 0.7679 92.2353
2 2813796 21.6532 91.4674
3 505008 3.8862 69.8142
4 2855676 21.9755 65.928
5 697508 5.3676 43.9525
6 1800268 13.8538 38.5849
7 751324 5.7817 24.7311
8 1137236 8.7515 18.9494
9 361224 2.7798 10.1979
10 388740 2.9915 7.4181
11 51680 0.3977 4.4266
12 317340 2.4421 4.0289
13 19656 0.1513 1.5868
14 90100 0.6934 1.4355
15 9168 0.0706 0.7421
16 58248 0.4482 0.6715
17 11196 0.0862 0.2233
18 2708 0.0208 0.1371
19 0 0 0.1163
20 8068 0.0621 0.1163
21 2496 0.0192 0.0542
22 444 0.0034 0.0350
23 356 0.0027 0.0316
24 3680 0.0283 0.0289
25 0 0 0.0006
26 0 0 0.0006
27 0 0 0.0006
28 76 0.0006 0.0006
29 4 0.00003 0.00003
  • Mean = 4.7692
  • Standard deviation = 3.1254
  • Skewness = 0.9039
  • Excess kurtosis = 1.4599

Note that these statistics do not reflect frequency of occurrence in 5 or 6-card play. For 6-card play the mean for non-dealer is 7.8580 with standard deviation 3.7996, and for dealer is 7.7981 and 3.9082 respectively. The means are higher because the player can choose those four cards that maximize their point holdings. For 5-card play the mean is about 5.4.

Slightly different scoring rules apply in the crib - only 5-point flushes are counted, in other words you need to flush all cards including the turn-up and not just the cards in the crib. Because of this, a slightly different distribution is observed:

Scoring Breakdown (crib/box hands only)

Score Number of hands (+/- change from non-crib distribution)
(out of 12,994,800)		 Percentage of hands Percentage of hands at least as high
0 1022208 (+13200) 7.8663 100
1 99792 (0) 0.7679 92.1337
2 2839800 (+26004) 21.8534 91.3658
3 508908 (+3900) 3.9162 69.5124
4 2868960 (+13284) 22.0778 65.5962
5 703496 (+5988) 5.4137 43.5184
6 1787176 (-13092) 13.7530 38.1047
7 755320 (+3996) 5.8125 24.3517
8 1118336 (-18900) 8.6060 18.5393
9 358368 (-2856) 2.7578 9.9332
10 378240 (-10500) 2.9107 7.1755
11 43880 (-7800) 0.3377 4.2648
12 310956 (-6384) 2.3929 3.9271
13 16548 (-3108) 0.1273 1.5342
14 88132 (-1968) 0.6782 1.4068
15 9072 (-96) 0.0698 0.7286
16 57288 (-960) 0.4409 0.6588
17 11196 (0) 0.0862 0.2179
18 2264 (-444) 0.0174 0.1318
19 0 (0) 0 0.1144
20 7828 (-240) 0.0602 0.1144
21 2472 (-24) 0.0190 0.0541
22 444 (0) 0.0034 0.0351
23 356 (0) 0.0027 0.0317
24 3680 (0) 0.0283 0.0289
25 0 (0) 0 0.0006
26 0 (0) 0 0.0006
27 0 (0) 0 0.0006
28 76 (0) 0.0006 0.0006
29 4 (0) 0.00003 0.00003
  • Mean = 4.7348

As above, these statistics do not reflect the true distributions in 5 or 6 card play, since both the dealer and non-dealer will discard tactically in order to maximise or minimise the possible score in the crib/box.

Read more about this topic:  Cribbage Statistics

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