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 top card in the remaining deck
is turned up. The top 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 top card. Points are awarded for pairs, 3s and 4s
of a kind, runs, and combinations of cards giving 15. A jack having the same suit
as a top card is awarded an additional point known as "nobbs." 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 players hand with a top 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 nobbs, giving a total score of 
for the hand.
All 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
A143133), their frequency (out of 
five-card hands, counting the top card
as the fifth), and their probabilities. The average score from a random hand is 511661/108290,
or about 4.7249. Of course, these probabilities assume that the cards discarded to
the crib are effectively chosen at random. Since they are presumably not, better
scores are actually more likely than indicated in this table.
| score | frequency | probability |
| 0 | 1025024 | 0.07888 |
| 1 | 101376 | 0.007801 |
| 2 | 2843456 | 0.2188 |
| 3 | 510528 | 0.03929 |
| 4 | 2874672 | 0.2212 |
| 5 | 704208 | 0.05419 |
| 6 | 1787376 | 0.1375 |
| 7 | 754144 | 0.05803 |
| 8 | 1118048 | 0.08604 |
| 9 | 353352 | 0.02719 |
| 10 | 375208 | 0.02887 |
| 11 | 42112 | 0.003241 |
| 12 | 308480 | 0.02374 |
| 13 | 15232 | 0.001172 |
| 14 | 87436 | 0.006729 |
| 15 | 8576 | 0.0006600 |
| 16 | 57272 | 0.004407 |
| 17 | 11192 | 0.0008613 |
| 18 | 2248 | 0.0001730 |
| 20 | 7828 | 0.0006024 |
| 21 | 2472 | 0.0001902 |
| 22 | 444 | 0.00003417 |
| 23 | 356 | 0.00002740 |
| 24 | 3680 | 0.0002832 |
| 28 | 76 |  |
| 29 | 4 |  |
