Probability of Winning a Solitaire Game

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

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