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All the Perl that's Practical to Extract and Report

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  • Alright, I see a problem. Duplicates. Eg,

    K 2 2 2 2 and 2 K 2 2 2 are both the same hand, but the above considers one king-high and the other ace-high. (2s are wild.)

    Not sure how to represent the problem now.


    • When wild cards are used in poker doesn't five of a kind become the highest hand? At least that's what I vaguely recall from Hoyle.

      A brief skimming of wikipedia and the wikibooks for poker doesn't show that but then again I would think the odds of 5 of a kind shouldn't be much different than four of a kind except that it's a specific 4 cards that are needed.

      Not sure how it really affects your calculations though.

      • Well, this isn't real poker, but instead video poker, where the rules are made up and people like it that way. But five of a kind is the highest paying hand in one of these. The other, five 3-5's, five 6-k, and five aces are all separate hands, and flush comes before four 2s (four wilds). So the number of card combinations that have a chance to match as a hand does vary by game. Simply subtracting out things that overlap, like subtracting out non-royal flushes and four 2s seems to work, at least for the

    • Here is my solution to the problem.

      There are 40 hands that you are trying to emulate. All of the straight flushes for 4 suits from ten low down to ace low. To avoid duplicates I will only count ways of representing the best possible hand. That means we can immediately ignore the 4 hands with a low card of 2 because the wild card can represent a 7 instead for a better hand. Let's segment possibilities by how many wild cards there are, whether you are representing one of the 4 royal flushes, the 28 straigh

      • *sigh*. Full houses are easy. You can't have any wild cards because if you did you'd go for 4 of a kind instead. So you have 12 ways to pick the suit you're going to have 3 of a kind in, 4 choices of the cards in that kind, 11 ways to pick the one you have a pair in, and 6 choices for what the pair is. For 9504 possible full houses.

        Much harder is 3 of a kind.

        • A full house with a wild card can happen. Two pair plus a wild card gives a full house. (Terminology nit: the three of a kind does not occur in a suit, but at a rank. 3 hearts and 2 spades is not a full house. :-)

      • I skimmed this to see that you came up with basically the same final result as me and then hurriedly moved on to other things, and then got stuck again. I'm still waiting for word on whether something without a big fat E's and ()'s is acceptable.

        There's two things here... I mentioned this briefly before... but again...

        1. How many combinations of the 52 cards are recgognized as that hand by itself

        2. How many combinations of the 52 cards are recognized as that hand when other overlapping hands are tested fir