Cribbage (statistics)

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Main article: Cribbage

Some cribbage statistics are

Contents 1 Distinct hands 2 Maximum scores 3 Minimum scores 4 Odds 5 Point scoring 6 Card combinations 7 References

[edit] Distinct hands

• There are 12,994,800 possible hands in Cribbage: 52 choose 4 for the hand, and any one of the 48 left as the starter card.

• 1,009,008 (approximately 7.8%) of these score zero points.^[1]

[edit] Maximum scores

• The highest score for one hand is 29: 555J in hand with the starter 5 of the same suit as the Jack (8 points for four J-5 combinations, 8 points for four 5-5-5 combinations, 12 points for pairs of 5s and one for his nob).
• The second highest score is 28 (hand and starter together comprise any ten-point card plus all four 5s, apart for the 29-point hand above).
• The third highest score is 24 (A7777, 33339, 36666, 44447, 44556, 44566, 45566, 67788 or 77889).
• The highest score as a dealer from the hand and crib is 53. The starter must be a 5, the hand must be J555, with the Jack suit matching the starter (score 29), and the crib must be 4466 (score 24), or vice versa.
• The highest number of points possible (excluding pegging points) in one round is 77. The dealer must score 53, the opponent must then have the other 4466 making another 24 point hand for a total of 77.
• The highest number of points from a hand that has a potential to be a "19 hand" is 15. It is a crib hand of one suit, 46J and another ten card, with a 5 of that suit cut up. The points are 15 for 6, a run for 9, nobs for 10, and a flush for 15. Any of the following cards in an unlike suit yields a "19 hand"; 2,3,7,8,and an unpaired ten card.
• The most points that can be pegged by playing one card is 15, by completing a double pair royal on the last card and making the count 15: 12 for double pair royal, 2 for the 15, and 1 for the last card. For this to happen in a two-player game, the dealer must have two ten-value cards and two 2s, and the non-dealer must have one ten-value card and 722. The play must go: 10-10-10-go; 7-2-2-2-2. For example:

Alice (dealer)
Bob

Player	Card	Cumulative	Score	Announced
Bob		10		"ten"
Alice		20		"twenty"
Bob		30		"thirty"
Alice			1 point to Bob (30 for one)	"go"
Alice		7		"seven"
Bob		9		"nine"
Alice		11	2 points	"eleven for two"
Bob		13	6 points	"thirteen for six"
Alice		15	15 points (double pair royal, fifteen, last card)	"fifteen for fifteen"

[edit] Minimum scores

• The dealer in two-player, 6-card cribbage will always peg at least one point during the play (the pegging round), unless the opponent wins the game before the pegging is finished. If non-dealer is able to play at each turn then dealer must score at least one for "last"; if not, then dealer scores at least one for "go".
• If a player holds a 5 in his hand, he is guaranteed at least two points.
• While 19 is generally recognized as "the impossible hand", meaning that there is no combination of 5 cards that will produce a score of 19 points, scores of 25, 26, 27, and greater than 29 are also impossible in-hand point totals.^[1] Sometimes if a player scores 0 points in their hand they will claim they have a "19-point hand."^[2]

[edit] 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^[3].
• The odds of getting a perfect 29 hand in a three- or four-player game are 1 in 649,740.

Scoring Breakdown^[4]

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

[edit] Point scoring

• In a 2-person game, non-dealer can theoretically score the first 18 points on a deal: the first 7 cards played are in the order 2,A,3,5,4,7,6, and dealer's last card is 4 or larger for "go". Non-dealer scores for runs of 3, 5, and 7, plus 2 for fifteen and one for "go".
• In a 2-person game, dealer can score the first 26 points. Dealer holds 4,4,4,7, non-dealer holds 4,8,10,K, and the starter is a jack. The sequence of play is 8, 7, 4, 4, "go", 4, "go", 4; K, 10. Dealer scores 2 for his heels, 2 for fifteen, 2 for pair, 6 for pair royal, 12 for double pair royal, and 2 for 31; non-dealer then scores 1 for last.

[edit] Card combinations

• A hand of four aces (AAAA) is the only combination of cards wherein no flip card will add points to its score.
• There are 71 distinct combinations of card values that add to 15:

Two cards	Three cards			Four cards				Five cards
X5 96 87	X4A X32 95A 942 933	86A 852 843 77A 762	753 744 663 654 555	X3AA X22A 94AA 932A 9222 85AA	842A 833A 8322 76AA 752A 743A	7422 7332 662A 653A 6522 644A	6432 6333 554A 5532 5442 5433 4443	X2AAA 93AAA 922AA 84AAA 832AA 8222A 75AAA	742AA 733AA 7322A 72222 66AAA 652AA 643AA	6422A 6332A 63222 553AA 5522A 544AA 5432A	54222 5333A 53322 4442A 4433A 44322 43332
Note: "X" indicates a card scoring ten: 10, J, Q or K

[edit] References