Then I suggest an improved heuristics for mid-game. You can actually calculate the number of global configurations for each border configuration, they are just

Then I suggest an improved heuristics for mid-game. You can actually calculate the number of global configurations for each border configuration, they are just (n choose k) type calculations. It's somewhat more sophisticated when there are multiple disjoint border regions. Alternatively for a mid-game heuristic you can approximate the initial uniform distribution of the fixed amount of mines on the playing field with another distribution: Each square having an independent probability of having a mine or not. This could potentially simplify the calculation but it wouldn't be accurate when there are not so many mines left.