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Math Help - Clock Solitaire

  1. #1
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    Clock Solitaire

    Clock solitaire or clock patience is a card game played by one person where all 52 cards are used and dealt out in 13 piles (4 cards in each pile) with 12 piles representing the numbers on a clock (1-12) and the 13th pile placed in the middle of the clock.

    play starts by turning over a card in the middle, for example if that card was a seven you place it at the corresponding 7 pile in respect to the clock and then turn over another card from that pile, for example a jack then you would place it n the coresponding 11 pile and then take a card from that pile. this continues until you draw a king. then you begin again drawing another card from the pile in the middle.

    the game is only won if a king is last card to be turned over.

    I have been playing this game since I was pretty young and recently began wondering what the probability of winning the game is and i began to think that the probability is very low. i looked at a number of other websites that claim that the probability of winning is 1/13, where this is the probability of drawing a King last within the sequence of drawing cards.

    however, they never factor in tha tthe game cannot be won if at the bottom of a pile is the corresponding number. for example if at the bottom of the pile corresponding to 4 on the clock was a 4 card then game cannot be won.

    i hope i've explained the game properly so that you can understand.
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  2. #2
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    Shuffle a deck of cards; then look at bottom card: probability that it's a King = ?
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  3. #3
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    hmm thanks but not really answering my question.
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  4. #4
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    Quote Originally Posted by myenemy View Post
    the game is only won if a king is last card to be turned over.
    Each card has same probability of being "last card".
    Hence my last post: king has 1/13 probability.
    You're turning cards over until all 4 kings have been turned (hoping 4th is 52nd card):
    so minimun cards turned is 4 (all kings ended up in middle),
    maximum is 51 (no need to turn 52nd card: 4th king by default!).
    Anyhow, that's the way I understand your explanation of the game.
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