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### Probability of Winning a Solitaire Game

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Date: 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
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```
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

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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Associated Topics:
High School Probability

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