From amiller @ vic.bigpond.net.au Thu Jun  3 13:47:53 CDT 1999
Article: 33989 of sci.math.num-analysis
Path: news.math.niu.edu!husk.cso.niu.edu!vixen.cso.uiuc.edu!NewsNG.Chicago.Qual.Net!207.24.245.130!nyd.news.ans.net!news.idt.net!news.maxwell.syr.edu!intgwpad.nntp.telstra.net!news2.c2.telstra-mm.net.au!not-for-mail
From: "Alan Miller" <amiller @ vic.bigpond.net.au>
Newsgroups: sci.math.num-analysis
Subject: Solitaire odds
Date: Mon, 31 May 1999 14:43:01 +1000
Organization: Telstra Big Pond Cable - Sydney Site 1
Lines: 239
Message-ID: <7it40f$ddu$1@m2.c2.telstra-mm.net.au>
NNTP-Posting-Host: 24.192.8.179
X-Trace: m2.c2.telstra-mm.net.au 928125775 13758 24.192.8.179 (31 May 1999 04:42:55 GMT)
X-Complaints-To: news@m2.c2.telstra-mm.net.au
NNTP-Posting-Date: 31 May 1999 04:42:55 GMT
X-Newsreader: Microsoft Outlook Express 4.72.3155.0
X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3155.0
Xref: news.math.niu.edu sci.math.num-analysis:33989

Someone asked about the chance of getting out the Windows
game of Solitaire.   I wrote a small Fortran program (attached) to
estimate the chance.   Using no skill, and running this program
many times, the chance seems to be about 8.1%.

If I find time, I may add some skill to see how much it lifts the chance.

The attached program can be run using Lahey's free ELF90 compiler.

--
Alan Miller, Retired Scientist (Statistician)
CSIRO Mathematical & Information Sciences
Alan.Miller -at- vic.cmis.csiro.au
http://www.ozemail.com.au/~milleraj


begin 666 Soltaire.f90
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G9&ES<&QA>0T*#0I%3D0@4%)/1U)!32!S;VQI=&%I<F5?;V1D<PT*
`
end