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 The Ultimate Cribbage Hand (Posted on 2006-06-07)
In Cribbage, a hand scores as follows:

• 2 points for each set of cards that totals 15 (face cards count 10, aces count 1)
• 2 points for each pair (this means 3-of-a-kind is worth 6 points and 4-of-a-kind is worth 12 points)
• n points for each maximal straight containing n cards
• (i.e. a four card straight does not also count as two three card straights)
• n points for each maximal flush containing n cards
• (i.e. a four card flush does not also count as four three card flushes)
• 1 point for the jack of trumps

• It's easy to show that the best five card hand is J5555, worth 29 points, and, although impossible in an actual game, the best six card hand would be 445566, worth 46 points.

If the entire deck of 52 cards was considered to be a single cribbage hand, what would be its value?

 See The Solution Submitted by Jer Rating: 3.3333 (3 votes)

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 Why is J5555 only 29 pts? | Comment 1 of 21

J combined with any of the 4 5's is worth 15, as is any three of the 5's, of which there are also 4.  These 8 sets are then worth 16.

The 4-of-a-kind, as mentioned is 12 points.

Even if you don't count the 5 1-straights, or the 4 1-flushes, there must be a 2-flush, worth 2 points.

There's the Jack of trumps, worth 1 point.

Then 16+12+2+1 = 31.  Why 29?

 Posted by Charlie on 2006-06-07 14:08:00

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