alternative problem concerning Minesweeper

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

  1. cellocgw

    cellocgw Guest

    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.

    thanks for any help
    cellocgw, Jun 22, 2010
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  2. cellocgw

    Henry Guest

    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
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  3. cellocgw

    cellocgw Guest

    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
    cellocgw, Jun 24, 2010
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