# alternative problem concerning Minesweeper

Discussion in 'Probability' started by cellocgw, Jun 22, 2010.

1. ### cellocgwGuest

Hi, please let me know if there's a more appropriate ng to ask this
problem. Thanks.
As we all know, a typical Minesweeper game will require several
"Guesses" during play.
My question is: has anyone done some analysis to determine whether,
for a given board size and/or mine density, there in fact exists a
starting point such that an "intelligent player" (one who understands
the logic of determining all miones/not mines from the current known
field) can start at that designated square and complete the game
without any further Guesses?
I'm tempted to try an Entropy-based analysis (given that extremely low
densities and extremely high densities of mines both are pretty much
guaranteed to have such a starting point), viewing the board sort of
like a collection of magnetic spin domains.

anyway,
thanks for any help
Carl

cellocgw, Jun 22, 2010

2. ### HenryGuest

If you find yourself with a sub-position something like
* 2 2 *
2 ? ? 2
2 ? ? 2
* 2 2 *
then you will have to guess one of the question marks to go any
further. So the initial pattern
* . . *
.. . * .
.. * . .
* . . *
(or its reflection) will require a guess. You are allowed an initial
guess, but two of these patterns will force more than one guess.
There are other patterns with the same issue.

Henry, Jun 23, 2010

3. ### cellocgwGuest

Thanks-good start to the problem. So now the fun part: what's the
probability of such patterns showing up as a function of board size
and mine density? Clearly if there are only a couple mines and a big
board, that pattern can't happen. Ditto for the inverse, as you
said. Somewhere in the middle densities is where the problem gets
difficult.

cellocgw, Jun 24, 2010