Newsgroups: comp.ai.games
Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!news.mathworks.com!tank.news.pipex.net!pipex!newsfeed.internetmci.com!news.sprintlink.net!in1.uu.net!ncrgw2.ncr.com!ncrhub6!daynews!falcon!news
From: Dick Menninger <Dick.Menninger@DaytonOH.ATTGIS.COM>
Subject: Re: Minesweeper
X-Nntp-Posting-Host: 149.25.99.44
Message-ID: <DDs11G.8so@falcon.daytonoh.attgis.com>
Sender: news@falcon.daytonoh.attgis.com (News administrative Login)
Reply-To: Dick.Menninger@DaytonOH.ATTGIS.COM (mennid)
Organization: AT&T Global Information Solutions
X-Newsreader: DiscussIT 2.5.0.10 for MS Windows [AT&T Software Products Division]
References: <41f8m3$9sf@kernighan.cs.umass.edu>
Date: Wed, 23 Aug 1995 18:36:52 GMT
Lines: 53

The analysis below has a few inadequacies.

> ==========John McNulty, 8/23/95==========
> 
> > Has there even been an attemt to make a program that could
> play Minesweeper?
> > i.e., make the moves in the game, attempting to solve the puzzle.
> > If there has, how effective was the soultion?  And was it an
> easy problem?
> 
> Isn't minesweeper a solved problem?  Not speaking with any conviction
> here but I had the impression that the optimal strategy is known and 
> straightforward.  The only slight difficulty occurs when you know there
> is a mine in one of two cells but have no other information.  But the
> strategy is optimal there is well - you can do no better than guessing.
> 
> Another fuzzy point is when you have a clear area and a large unknown
> area and all the points along the front are ambiguous.  Depending upon
> the number of remaining mines vs the size of the unknown area, you might
> do better to pick a random cell in the unknown area rather than take
> a 50/50 (or 33/66 or whatever) chance along the frontier.

Well, the program needs to determine the probable number of mines
along the frontier (possibly it needs the pobability distribution for
the number of mines, in particular the min/max numbers).  The mines along
the frontier are not in the unknown area and thereby affect the probability
of any of the unknown cells having a mine.  Then there is the assumption
that you can pick any of them with equal effect on winnig the game.
Each may have equal probability of being an immediate loss, but
the shape of the known area and the frontier affect the value of
information provided if it is not an immediate loss.

Even along the frontier, it is not immediately clear that the actual
probability
for a cell having a mine is readily solved in closed form.  It may need some
backtracking-based calculation subsuming the whole frontier (a local solution
that precludes a full solution for the whole frontier can happen).

So there is a bit more to this than was expressed.

> 
> Have I overlooked something?  I thought the only objective was to carry
> out the above strategy as quickly as possible but for any given
> configuration,
> you either *know* where a clear cell is or you have to guess and where to
> guess is also solvable.
> 
> John McNulty


Good Day
Dick

