Cribbage (statistics)

Some cribbage statistics are

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.$\{52\; choose\; 4\}\; imes\; 48\; =\; 12,994,800$
* 1,009,008 (approximately 7.8%) of these score zero points.cite web
url= http://www.crhc.uiuc.edu/~steve/humor/cribbage.html
title= Amusing Cribbage Facts
accessdate= 2008-03-03
author= Steven S. Lumetta
date= 2007-05-15]
* Not accounting for suit, there are 13428 unique hands.cite web
url= http://washwithcare.com/math/cribbagehands.php
title= All Possible Cribbage Hands
accessdate= 2008-08-05
author= Tim Wood
date= 2008-08-05]

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. This can happen in two ways in A a two-player game. Either the dealer must have two ten-value cards and two 2s, and the non-dealer must have one ten-value card and 722, in which case the play must go: 10-10-10-go; 7-2-2-2-2. For example:

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.

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:

References