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The Ultimate Cribbage Hand (Posted on 2006-06-07) Difficulty: 4 of 5
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)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    re: some help from the computer (spoiler) | Comment 10 of 21 |
    (In reply to some help from the computer (spoiler) by Charlie)

    Also, we only count 'his nob' if we hold a jack of the same suit as the turn-up card. In this example we are using all of the cards in the deck so presumably we have a fifty-one card hand and turn up the fifty-second card. If this is a Jack, we or our opponent score two points depending on who turned it up, but these points are not added to our hand total, so in 12 of 13 fifty-two card hands we will not count 'his nob'. Of course, this also means our opponent has zero cards or something else. In any event, the straights sure make this a valuable ultimate cribbage hand.

      Posted by Eric on 2006-06-07 23:15:06

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