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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