Probability of Winning a Solitaire GameDate: 10/26/95 at 0:44:33 From: Anonymous Date: Wed, 25 Oct 1995 17:24:33 -0800 I am interested in finding out how to figure the probability of winning the solitaire 'clock game.' TIA Date: 11/19/95 at 15:48:42 From: Doctor Josh The probability of me personally winning the solitaire clock game is zero - I wouldn't play it. However, to figure out the probability of winning an actual played game of this form of solitaire, you should probably follow these guidelines: 1) The number of possible card combinations is 52! (that's a factorial sign, not me getting excited) 2) Winning a game is equivalent to saying that the last (52nd) card you draw is a king. Therefore, a king must be on the bottom of one of the thirteen piles; i.e. determine every possible combination with at least one king among the first thirteen cards. Remember that there can be up to four kings and that it doesn't matter which king it is. 3) Of the above possiblities of a king on the bottom, you must now figure the odds of turning that king over last. This depends on which cards have already been turned over and the positions of the remaining cards. This is a rather nasty thing to calculate, but we here at the clinic think that the odds would be pretty close to 1/13. Note that this is just a good guess. 4) So the answer (hopefully) is going to be (part 2)*(part 3)/(part 1) Let us know what you come up with. -Doctor Josh, The Geometry Forum |
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