Cribbage is a card game where players race to accumulate points by forming certain combinations of cards over a series of hands. Each hand consists of two types of scoring opportunities. During the 'play,' participants take turns playing cards and make combinations involving both their own cards and their opponents' cards. Once the play is complete there is the 'show,' where players make combinations involving their own cards and a single shared starter card. We describe below the standard version of Cribbage for two players; variations for three, four, and six player games also exist.

Cribbage is played with a standard deck of 52 cards. Each card is assigned a value for counting: aces count as ones, face cards count as 10, and all other cards count as their numerical value. When considering runs, all of the cards are considered in the standard order with aces low only.

The dealer deals six cards to each of the players. Each player then discards two of her cards face-down into the center of the table. These four cards form the 'crib' and will be used by the dealer during the show at the end of the hand.

After all players discard into the crib, the non-dealer cuts the deck. The dealer then turns over the top card and places it face-up on top of the discard pile. This card is called the 'starter' and will act as part of all players' hands during the show. If the starter is a Jack, the dealer immediately scores two points. This is called scoring for 'his heals.'

Starting with the non-dealer, the players alternate turns playing a single card face-up and stating the sum of the counting value of all cards played by both players. This total must not exceed 31. If a player has no cards left that will keep the total at 31 or lower then the player says "go" and her turn is skipped. The remaining player earns one point for the 'go' and must play cards so long as she is able to do so. The play then continues with the count reset to zero and with the player who called 'go' playing first in the new sequence. If a player brings the total to exactly 31 then she earns a point (this is in addition to the point for the go, which will also always be earned in this situation).

Play continues in this manner until no players have any cards remaining in their hand. When a player runs out of cards it is treated as a go. In particular, the last person to play will always score at least one point.

During the play points are also scored for completing various combinations of cards. The scoring combinations are:

In all cases, when the count is reset, all combinations are reset. For example, starting a new sequence with a card of the same rank as the last card of the previous sequence does not count as a pair.

Non-dealer plays a three and says "three".

Dealer plays a three, says "six for two" and pegs two points for the pair.

Non-dealer plays a three, says "nine for six" and pegs six points for the triple.

Dealer plays a six, says "fifteen for two" and pegs two points for the fifteen.

Non-dealer plays a five and says "twenty."

Dealer plays a four, says "twenty-four for four" and pegs four points for the straight (3,6,5,4).

Non-dealer plays a six, says "thirty for three" and pegs three points for the straight (5,4,6).

Dealer has only a seven left in his hand and says "go". The non-dealer has no cards left and therefore can make no more plays and pegs one point for the go.

The Dealer plays his seven, says "seven" and scores one point for playing the last card. Note that the dealer does not score for the (5,4,6,7) straight since the seven is part of a new sequence.

After all cards have been played the players score the points in their hands, starting with the non-dealer, then the dealer, then the crib (which is scored by the dealer). Each player's hand consists of the four cards that she did not put into the crib as well as the starter card. In the show, the scoring combinations are:

- 2 points for each combination of cards that total 15.
- 2 points for each pair of cards of the same rank. Therefore, three of a kind counts for 6 points (since there are 3 pairs of cards) and four of a kind counts for 12 points (6 pairs of cards).
- One point per card in a run of at least three cards.
- One point for a Jack (in the player's hand, not the starter card) of the same suit as the starter card. This is called one for "his nobs."
- If all four of a player's cards are of the same suit he scores four points for a flush. If the starter card is also of this suit, the player scores five points. In the crib, a flush can only be scored if all the cards are of the same suit as the starter card (in which case it is scored as five points).

Each card may be scored in multiple different combinations. For example, a hand of 10,5,5,4 with a starter card of 6 would count for 16 points: two points for the pair of 5's, three points for each of the two runs 4,5,6, two points for each of the fifteens with a 10 and a 5, and two points for each of the fifteens with a 4,5, and 6.

The first player to score 121 points wins the game. The game ends as soon a player reaches 121 points; this is why the order that points are scored can be very important, especially the fact that the non-dealer scores his hand first during the show. If the losing player fails to reach 91 points he is said to be "skunked." When playing a multi-game match, a skunking counts as two games. A player who fails to reach 61 points is said to be "double skunked."

A cribbage board is usually used to assist with keeping score. While their are a variety of different boards available, the most standard versions today have two or three parallel tracks of 120 holes. Each player has two pegs which are used to mark his score, leapfrogging the pegs each time a new score is marked (this prevents a player from loosing track of his previous score). Some boards also have an area to mark games won by each player for multi-game matches.

In the three player game, each player is dealt only five cards and one card is dealt directly into the crib. Each player then discards only one card into the crib (this leaves four cards in the crib and each player's hand). Play then continues as in the two player game, starting with the player to the left of the dealer and continuing clockwise.

All questions refer to the standard two person game. Note that until the play begins, the players have no knowledge of their opponent's hand. Therefore, from any single player's perspective, any card not in her hand has equal probability of being the starter card. For further discussion of this idea, see the problems section of the blackjack page.

- You need eight points to win the match. After discarding an ace and a king into the crib you have 5,7,8,J left in your hand. What is the probability that your hand will score at least eight points in the show?
- Since so many of the cards have a counting value of ten, fives are especially valuable cards. There are very few situations in which it is advantageous to discard a five into your opponents' crib. Consider the situation where you have A,5,8,9,9,10 in your hand. If you discard the A,5 into the crib, what is the expected value for the number of cards of counting value 10 among the two remaining cards in the crib and the starter? In this problem, assume that the dealer's discard into the crib and the starter card are chosen at random from the cards not in your hand.
- The highest score that can be earned during the show is 29 points. This occurs when you have three fives and a jack in your hand, with the jack a different suit from all of the fives, and the starter card is the remaining five. You earn twelve points for the quadruple, eight points for 15's involving the Jack, eight points for 15's involving just the fives, and one point for his nobs. What is the probability of obtaining this maximal hand?
- You are dealt a hand of 2,2,3,6,7,9 with suits such that there is no chance for a flush. What is the expected value for your hand in the show if you keep 2,2,3,6? What if you keep 2,6,7,9?

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