Cribbage is a game in which each of two players is dealt a hand of six cards. Each player then discards two of his six cards to a four-card
"crib" which alternates between players. After the discard, the nondealer
cuts the remaining deck, and the dealer turns up the top card
of the lower portion as the starter card (American Cribbage
Congress 2025, pp. 28-29). The starter card is then
ignored until the counting round, unless it is a jack, in which case the dealer pegs
two points for "heels." Cards are then alternately
played out by the two players, with points being scored for pairs, 3s and 4s of a
kind, runs, cumulative total of 15 and 31, and playing the last possible card
("go") not giving a total over 31. All face cards
are counted as 10 for the purpose of playing out, but the normal values of 
, 
,
are used to determine runs. Aces
are always low (
).
After all cards have been played, each player counts the
four cards in his hand taken in conjunction with the single
starter card. Points are awarded for pairs, 3s and 4s of
a kind, runs, combinations of cards
giving 15, and flushes. Four held cards of the same suit
score 4 points, or 5 if the starter card is also of that
suit. In the crib, a flush scores 5 points only when all five cards
have the same suit (American Cribbage Congress 2025, pp. 12 and 15). A jack
having the same suit as a starter card is awarded an additional
point known as "nobs." The crib is then also counted and scored. The winner
is the first person to peg a certain score, as recorded on a cribbage board.
The invention of cribbage (sometimes called crib for short) is attributed to the poet Sir John Suckling (1609-1642) by his biographer John Aubrey as a derivation of the game "noddy."
The best possible score corresponds to three 5s and a jack in the player's hand with a starter 5 the same suit as the jack, giving four 5s and a jack available for counting.
This hand has 
pairs of fives (score 12), 
triplets of five totaling 15 each (score 8), four 5s available for pairing with the
jack totaling 15 (score 8), and 1 point for nobs, giving a total score of 
for the hand.
All hand scores from 0 to 29 are possible, with the exception of 19, 25, 26, and 27. For this reason, a hand scoring zero points is sometimes humorously referred
to as a "19-point" hand. The following table summarizes the possible scores
(OEIS A066354), their frequency (out of 
five-card hands,
counting the starter card as the fifth), and their probabilities.
The expected value of the score from a random
hand is 60759/12740, or about 4.7692. These probabilities
assume that the cards discarded to the crib are chosen
at random.
| score | frequency | probability |
| 0 | 1009008 | 0.07765 |
| 1 | 99792 | 0.007679 |
| 2 | 2813796 | 0.2165 |
| 3 | 505008 | 0.03886 |
| 4 | 2855676 | 0.2198 |
| 5 | 697508 | 0.05368 |
| 6 | 1800268 | 0.1385 |
| 7 | 751324 | 0.05782 |
| 8 | 1137236 | 0.08751 |
| 9 | 361224 | 0.02780 |
| 10 | 388740 | 0.02992 |
| 11 | 51680 | 0.003977 |
| 12 | 317340 | 0.02442 |
| 13 | 19656 | 0.001513 |
| 14 | 90100 | 0.006934 |
| 15 | 9168 | 0.0007055 |
| 16 | 58248 | 0.004482 |
| 17 | 11196 | 0.0008616 |
| 18 | 2708 | 0.0002084 |
| 20 | 8068 | 0.0006209 |
| 21 | 2496 | 0.0001921 |
| 22 | 444 | 0.00003417 |
| 23 | 356 | 0.00002740 |
| 24 | 3680 | 0.0002832 |
| 28 | 76 |  |
| 29 | 4 |  |
