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In this video I show off a minesweeper AI that I built which can solve accurately very large games, using a significant improvement to backtracking.
github.com/yujinwunz/minesolver2
Not mentioned in the video due to how long and complicated it was:
Another thing to consider when it comes to combinations and probabilities, was that the probability of a combination depends on how many mines it includes. Combinations with mine density closer to the rest of the board are more likely. So all the calculations and algorithms are basically run many times over, with different mine count assumptions, so that this aspect could be done accurately.