(This is based on my earlier MSE question that has been stagnant for just over a week, since the
best answer only addresses the case of two mines and does not even completely resolve that.)
What is the computational complexity of playing 1-dimensional Minesweeper in a way that
maximizes the probability of winning, where the board length is given in unary, the number
of mines is known, and their position is chosen uniformly from among all possibilities?
I believe the reasoning used in the proof of $\:$IP $\subseteq$ PSPACE
shows that the complexity is at most PSPACE.