Math Help - 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.

Shuffle a deck of cards; then look at bottom card: probability that it's a King = ?

hmm thanks but not really answering my question.

Originally Posted by myenemy

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.