How many points is 4 fives in cribbage?

First, you score up the pone’s hand, and the dealer’s follows. After you score both hands, the dealer scores up the crib.

The significance of this order of scoring is that toward the end of the game, each player scores three hands in a row (two as the dealer and then one as the pone), which can have a significant impact on the strategy of the game. Because Cribbage is a game of “first past the post,” if both players are close to pegging out, you can score up your hand and win as the pone, while the dealer is impotently waiting to score up his huge hand.

The points that you score in the hand and the crib, as dealer, by and large, come from the same categories as those for which you scored points in the play, but a couple of modifications complicate matters. For example, you can use cards, including the starter, in more than one combination.

Cribbage scoring chart

Cribbage scoring examples and tips

8-9-10-10

• 3 for one run of 8-9-10
• 3 for the run using the other 10
• and 2 for the pair of 10s

3-3-4-5

You score the crib hand in exactly the same way as your own hand, except for the restriction on four-card flushes. Consider flushes to be a last resort; unless you can’t do anything else, let them go. With all the cards in the same suit, you have no possibility of making pairs. Plus, they don’t count during gameplay.

Some numbers in Cribbage are impossible to score — 19, 25, 26, and 27. Because you can’t score 19, referring to a hand as being worth 19 points is a humorous way of referring to a hand worth nothing.

A 0-point hand must have five distinct cards without forming a run or a fifteen combination. If such a hand includes a 5, it cannot hold a 10 or a face card. It also cannot include both an A and a 9; both a 2 and an 8; both a 3 and a 7; or both a 4 and a 6. Since four more cards are needed, exactly one must be taken from each of those sets. Let us run through the possible choices:

• If the hand includes a 9, it cannot hold a 6, so it must hold a 4. Having both a 4 and a 9, it cannot hold a 2, so it must hold an 8. Holding both a 4 and an 8, it cannot hold a 3, so it must hold a 7. But now the hand includes a 7-8 fifteen, which is a contradiction.
• Therefore, the hand must include an A.
  • If the hand includes a 7, it now cannot contain an 8, as that would form a 7-8 fifteen. However it cannot hold a 2, as that would form a 7-5-2-A fifteen. This is a contradiction.
  • Therefore, the hand must include a 3. Either a 2 or a 4 would complete a run, so the hand must therefore include a 6 and an 8. But this now forms an 8-6-A fifteen, which is a contradiction.

Therefore, every set of five cards including a 5 has a pair, a run, or a fifteen, and thus at least two points.

Interestingly, a hand with two 5s also can score at least two points; an example is 2 5 5 7 9, which would be most likely a crib hand, and would not score a flush because of the pair, although said hand can be a non-crib four-card flush if either 5 is the starter. A hand with three 5s scores at least eight points; a hand with all four 5s scores 20 points and is improved only with a 10, J, Q, or K (scoring 28 except for the 29 hand previously described.)

It is also true that holding both a 2 and a 3, or an A and a 4 (pairs of cards adding up to five) also guarantees a non-zero score:

• If a hand includes both a 2 and a 3 and is to score 0 points, it cannot have a face card, an A, a 4, or a 5. This requires three cards from the 6, 7, 8, and 9, and any such selection will include a fifteen.
• If a hand includes both an A and a 4 and is to score 0 points, it cannot have a face card or a 5. It also cannot have both a 2 and a 3; both a 6 and a 9; or both a 7 and an 8. If the hand includes a 2, it cannot have a 9 (9-4-2 fifteen). Thus it must have a 6. It then cannot have an 8 (8-4-2-A fifteen) or a 7 (7-6-2 fifteen). If, however, the hand includes a 3, it cannot include an 8 (8-4-3 fifteen) or a 7 (7-4-3-A fifteen). These are all contradictions, so every hand containing both an A and a 4 scores at least two points.

• The table below assumes the card(s) discarded to the crib are randomly chosen. Given this assumption, the odds of getting a 28 hand in a two-player game are about 1 in 170984, and a perfect 29 hand 1 in 3,248,700.[3]

• However, if we assume that the player will always keep J555 if those cards are included in the hand, the odds of getting a perfect 29 hand starting with a six-card hand are 1 in 216,580, while the odds after discarding from a five-card hand are 1 in 649,740.[4]

Scoring Breakdown, assuming random discard(s) to the crib[1]

Note that these statistics do not reflect frequency of occurrence in 5 or 6-card play. For 6-card play the mean for non-dealer is 7.8580 with standard deviation 3.7996, and for dealer is 7.7981 and 3.9082 respectively. The means are higher because the player can choose those four cards that maximize their point holdings. For 5-card play the mean is about 5.4.

Slightly different scoring rules apply in the crib - only 5-point flushes are counted, in other words you need to flush all cards including the turn-up and not just the cards in the crib. Because of this, a slightly different distribution is observed:

Scoring Breakdown (crib/box hands only)

As above, these statistics do not reflect the true distributions in 5 or 6 card play, since both the dealer and non-dealer will discard tactically in order to maximise or minimise the possible score in the crib/box.

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