From spallone@mail1.sas.upenn.edu Mon Nov 6 16:04:48 CST 1995 Article: 47611 of sci.math Path: muir.math.niu.edu!mp.cs.niu.edu!vixen.cso.uiuc.edu!uwm.edu!msunews!netnews.upenn.edu!mail1.sas.upenn.edu!spallone From: spallone@mail1.sas.upenn.edu (Steven T Spallone) Newsgroups: sci.math Subject: Solitaire probability Date: 2 Nov 1995 19:23:44 GMT Organization: University of Pennsylvania Lines: 6 Message-ID: <47b5s0$moj@netnews.upenn.edu> NNTP-Posting-Host: mail1.sas.upenn.edu X-Newsreader: TIN [version 1.2 PL2-upenn1.3] I heard somewhere that the chances of winning a fair game of Solitaire, like the one on Windows, is about one out of thirty. How does one go about calculating this? -- -Steven From jpl@stat.mps.ohio-state.edu Mon Nov 6 16:04:55 CST 1995 Article: 47669 of sci.math Path: muir.math.niu.edu!mp.cs.niu.edu!vixen.cso.uiuc.edu!uwm.edu!math.ohio-state.edu!not-for-mail From: jpl@stat.mps.ohio-state.edu (John P Lawrence) Newsgroups: sci.math Subject: Re: Solitaire probability Date: 3 Nov 1995 01:33:21 -0500 Organization: The Ohio State University Lines: 18 Message-ID: <47cd3h$j42@osustat.mps.ohio-state.edu> References: <47b5s0$moj@netnews.upenn.edu> NNTP-Posting-Host: osustat.mps.ohio-state.edu In article <47b5s0$moj@netnews.upenn.edu>, Steven T Spallone wrote: >I heard somewhere that the chances of winning a fair game of Solitaire, >like the one on Windows, is about one out of thirty. How does one go >about calculating this? This was discussed in rec.games.abstract about a year ago. I'm not familiar with the windows game, but the version that i played most often gives the player about one chance in 6 of winning, as I recall. There's a book on solitaire that describes the chances of winning for the different versions. I don't remember the title, but you might find more knowlegeable people in the games newsgroup. John From rusin@vesuvius.math.niu.edu Wed Jun 19 10:39:54 CDT 1996 Article: 75954 of sci.math Path: muir.math.niu.edu!rusin From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Solitaire Mathematics Date: 19 Jun 1996 05:14:55 GMT Organization: NIU Mathematical Sciences Lines: 32 Message-ID: <4q82cf$b8p@muir.math.niu.edu> References: <4q1ect$dgn@risc.agsm.ucla.edu> <4q4jd5$i8r@muir.math.niu.edu> NNTP-Posting-Host: vesuvius.math.niu.edu Status: R In article <4q4jd5$i8r@muir.math.niu.edu>, I wrote: >Agreed. I did entertain my computer by having it play a few million >hands of the game (modelled after the Windows-supplied version which >costs $52 to play and returns $5 for each card raised to its suit >pile). I think it tended to lose about a dollar a hand with the >strategy I taught it. My recollection was that the stumbling block >was the great number of times when no cards (or maybe just a few) >could be raised -- once a reasonable fraction of them had gone up, >there was often a way to move them back and forth to complete the >win. So you could estimate your odds pretty well by "simply" counting >the odds that no card at all could be raised, that just one could be, >etc. (quit when tired and call it an estimate). OK, I found my notes (some of them now at http://www.math.niu.edu/~rusin/uses-math/games/solitaire/ ) According to the data I have, my simple-minded strategy lost me an average of $1.68 per game (the game costs $52 to play and has a maximum net profit of $208 per game). I was able to win completely about one game out of every 30. It was rarer than I remembered to get completely zonked: in only about one game out of every 150 did I never find an Ace. But as hinted at in my previous post, there are a heckuva lot of games in which just a few cards could be moved up -- the median number so moved was 7, and being able to raise only 6 was even more common (about 10% of the games). The average net loss is small enough that I would not be surprised if someone produced a winning strategy. On the other hand, since relatively few games really present any opportunity for creativity, being able to make such gains would be difficult. dave