For example you can use a particle filter to approximate the distribution of mines. Every time you obtain new information you update the filter so that only distributions compatible with constraints remain.
Once you have an approximation to the distribution of mines you can calculate the probability of each spot being a mine. You can also calculate statistical indicator like the Information Gain of each action.
A good strategy is therefore to play low mine probability with highest information gain. But there is a trade-off, when the mine probability is non-zero. So you need to look-ahead.
Fortunately thanks to the mine distribution approximation you can also simulate any actions and their consequences, because you can use your approximation of the distribution to predict which number will be revealed upon a click.
So an even better strategy is to unroll the game tree for the best few candidate moves based on some heuristics, and calculate the cost gain probabilities after a few moves.