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Ever
played Solitaire, Patience or Klondike and wondered what the odds are of moving
all of the cards to the Ace piles? I did, and after quite a bit of research a
couple of things became quite evident. Firstly, an exact mathematical solution
does not exist; and secondly, statistical solutions based on playing a huge
number of games were impossible to find.
So… I wrote my own program (Bill's Solitaire Tester) which would play Solitaire lots and lots of times to see if I could come up with an empirical (or brute force) solution myself. The best result I have achieved so far is as follows.
On average, after playing many games of Solitaire, using the deal 3 cards and 3 times around the deck option, the frequency of moving all cards to the Ace piles is:
1 game in 11.5 played, or 8.7% of games played*
There are more statistics, discussion, and results for the other play options
such as deal 1 card etc., in the other sections of this website. I am always
happy to receive additional ideas for making the algorithms or logic more
sophisticated. Any suggestions, please send me an
email .
* The version I am simulating is also known as "Klondike" and is identical to the original Solitaire released with Microsoft Windows 3.0. Just for complete clarity, this is a statistical solution based on the optimized logic used in Bill’s Solitaire Tester V4.0 after playing 100,000,000 games (updated 7/17/2011) Result screenshot
Solitaire Related Links:
Solitaire - Wikipedia
Klondike (solitaire)
- Wikipedia
The
Odds of Winning Klondike Solitaire - The Joel on Software Discussion Group
How to Win in
Solitaire by Will Conley
Solitaire Strategy
Guide - chessandpoker.com
Vegas Solitaire
Strategy Guide - chessandpoker.com
http://winnablesolitaire.com
15seconds.com - an
examination of the VB RND() function and why you should consider using something
else
Mersenne twister -
Wikipedia - an algorithm for producing an incredibly long sequence of random
numbers
Solitaire at
search.com - a reference to the original Windows version written by Wes
Cherry
Interview with Wes Cherry at
www.b3ta.com
Solitaire: Man Versus Machine - A paper by Xiang Yan, Persi Diaconis, Paat
Rusmevichientong and Benjamin Van Roy
Lower Bounding Klondike Solitaire with Monte-Carlo Planning - A paper by Ronald
Bjarnason, Alan Fern and Prasad Tadepalli
Searching Solitaire in Real Time - A paper by Ronald Bjarnason, Prasad Tadepalli
and Alan Fern
The Mathematics of Solitaire - Persi Diaconis lecture