## Home

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