Check this: http://quantum-p.livejournal.com/19616.html
Any position on the board, that cant be solved intuitively with the monkey-reasoning is a matrix that could be able to solve some individual(or the whole position) squares which can lead to better solving rates. Simple random guessing didn't produce good results.
I implemented this method into my solving algorithm in C++ by adding a linear system of equations-solver. I am researching the difficulcy of Minesweeper by running tens of thousands games through the algorithm and doing statistics.
My algorithm solves upto 85% of (9,9,10) easy level minesweepers. I haven't yet ran complete tests on other difficulcy levels, but smaller tests suggest that medium level (16,16,40) has a solving rate of 55-60 % and Hard level(30,16,99) as low as 5-10%. I am going to add a few new things that would make it most optimal.
