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Posers and Puzzles

Posers and Puzzles

  1. Standard member royalchicken
    CHAOS GHOST!!!
    22 Jul '03 20:01 / 2 edits
    Seven intrepid RHP-ers conene for an evening of entertainment. ChessNut supplies the snacks, Dr. Brain the beer, T1000 the humour and the glorified rodents, Kirksey the wisdom, Rwingett the raccoons with poker faces, Genius the music, and Rhymester the cards and the bears. They arrange themselves around a table, and Rhymester sets down a brand-new deck of cards, just out of the package. They are arranged in the standard manner. It is decided that Kirk deals. Upon recieving the cards, Kirk does not shuffle; as an Apostle and perfect adherent to tradition, he points out that on the first hand played with a new deck of cards, the cards are cut once and not shuffled. So he gives them to Genius to cut. Genius removes the top card (a 2 of clubs, since it is a brand-new deck), and places it on the bottom. Kirk then deals the first card to each of them, of course dealing himself last. He then deals a second card to each, but takes his from the bottom of the deck. He then deals the third card to each with no irregularities. He repeats his cheating on the fourth card, and then deals the fifth and last card normally to each person. Through a foggy haze created by the effects of Dr. Brain's fine gifts, T1000 notices something is wrong...his speech is slurred, but he makes Kirk's foul cheating known. The jolly RHP-ers agree that Kirk must draw five new cards from the top of the deck. Fegining indignation, Kirk throws his illicit hand to the table, which contained three of a kind. The others laugh knowingly. Then ChessNut (the first to be dealt to) looks at his cards. A full house. Dr. Brain checks his. A full house as well. T1000. FUll house. Rwingett. Full house. Genius. Same. Rhymester has a full house. Kirk lifts his new hand, mumbles some unintelligible incantation, and the betting ensues. Laughing at his percieved mastery of the situation, ChessNut demands Kirk show his cards. Kirk complies with a laugh, and wins with a royal flush.

    The question is: What happened, and for what percentage of possible cuts of the deck will Kirk's strategy win with a straight flush?

    EDIT While obtaining your answer with a deck of cards is Apostle-worthy cheating (), it is a cool phenomenon with a simple explanation.
  2. Standard member Toe
    23 Jul '03 12:29
    without actually solving anything: there are 13 cards per suit. Two deals of 7 would be 14, one out-of-step with the suits. However, the 'cheat' every second card avoids drawing the 14th card, thus putting you back onto 13, so the cards will stay in alignment.

    And as for how many cuts work out: well, that depends on whether or not you removed the jokers and the rule card...
  3. Donation ChessNut
    Lightly Salted...
    23 Jul '03 14:24
    I'm just happy to have been invited! Must have some party as I don't remember much of it... it's a bit of a haze... Dr. Brain must have brought some strong stuff. Sort of brings back memories of college.

    Cheers!
    The Nut.
  4. Standard member royalchicken
    CHAOS GHOST!!!
    23 Jul '03 16:46 / 1 edit
    Originally posted by Toe
    without actually solving anything: there are 13 cards per suit. Two deals of 7 would be 14, one out-of-step with the suits. However, the 'cheat' every second card avoids drawing the 14th card, thus putting you back onto 13, so the cards will ...[text shortened]... s on whether or not you removed the jokers and the rule card...
    You understand the basic way it works; it's not very complicated. But excluding jokers etc., what percentage of origianl cuts preserves the win for Kirk?

    ChessNut, of course you were invited...Dr. Brain's Elixir works best with something salty.
  5. 23 Jul '03 21:53
    Originally posted by royalchicken
    Seven intrepid RHP-ers conene for an evening of entertainment. ChessNut supplies the snacks, Dr. Brain the beer, T1000 the humour and the glorified rodents, Kirksey the wisdom, Rwingett the raccoons with poker faces, Genius the music, and Rhymester the cards and the bears. They arrange themselves around a table, and Rhymester sets down a brand-new de ...[text shortened]... eck of cards is Apostle-worthy cheating (), it is a cool phenomenon with a simple explanation.
    It's difficult enough just coping with the idea of being in the same room as that motley collection of vagabonds, nevermind actually thinking about the question posed

  6. Donation richjohnson
    TANSTAAFL
    23 Jul '03 22:04
    Originally posted by royalchicken
    You understand the basic way it works; it's not very complicated. But excluding jokers etc., what percentage of origianl cuts preserves the win for Kirk?

    ChessNut, of course you were invited...Dr. Brain's Elixir works best with something salty.
    9/13?
  7. Standard member royalchicken
    CHAOS GHOST!!!
    24 Jul '03 00:48
    Maybe......expound....my lips are sealed.

    T1000: you've perfectly hit the reason I didn't put myself in there (kidding).
  8. Donation richjohnson
    TANSTAAFL
    24 Jul '03 01:23
    Originally posted by royalchicken
    Maybe......expound....my lips are sealed.

    T1000: you've perfectly hit the reason I didn't put myself in there (kidding).
    It is clear that cutting the deck by taking the 1st card on the top and placing it on the bottom is equivalent, in these circumstances, to taking the top 14 cards off the top and placing them on the bottom.

    Therefore, there are 13 different types of cut which can be made.

    The 5 cards pulled by the dealer at the end will be sequential, and unless the 1st card pulled is a J, Q, K or A (note that A2345 would only be a straight, since the A would have a different suit), the dealer will have a straight flush. If there are only 4/13 ways not to get one, there must be 9/13 ways to get a straight flush by the above method.

    Did I miss anything?
  9. Standard member royalchicken
    CHAOS GHOST!!!
    24 Jul '03 17:20
    No, your'e right on. Good job .
  10. Standard member genius
    Wayward Soul
    25 Jul '03 10:05
    Originally posted by ChessNut
    I'm just happy to have been invited! Must have some party as I don't remember much of it... it's a bit of a haze... Dr. Brain must have brought some strong stuff. Sort of brings back memories of college.

    Cheers!
    The Nut.
    yeah-must have been wild-i mean-kirk? cheating?!? and anyway-i'm a minor (well, actually, i'm not according to scotts law, but i still can't drink!...) and i can remeber diddly-squat!...
  11. Subscriber phil nutley
    Quantum Theorist
    25 Jul '03 12:11
    Afraid I lost the will to live after the first sentence.
    Any one got a padded room they can lend me for a while??