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 J
5555, 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?
The required value would be 872,449,969 points.