Expected area "sweeped" on an infinite Minesweeper board

Question

Given an average density (x/y) of x mines in y squares, is it possible to calculate the expected number of squares you can "sweep" (i.e. identify whether there is a mine or not) on an infinitely sized minesweeper game, before you have to guess- i.e. no more squares can be deduced.

Answer 1

This is not an answer, but I thought it would be interesting to do a simulation on a finite board.

So I made a bare-bones Minesweeper solver and ran a 1000 games for various mine densities on a 50x50 board and got the following:

The X axis shows the mine density (i.e. the probability that a square is a mine) and the Y axis shows the percentage of mines swept.

As can be seen, the steepness of the curve is quite large. At a density of 0.13 it is at 90% and at 0.22 it is under 10%.

To check how good (or bad) my algorithm was, I manually played 10 games of Minesweeper at expert level (where mine density is less than 0.21) and got the result of 53%. This is almost twice as good as my algorithm which got 27%. But the steepness of the curve means my primitive algorithm got 57% at the slightly lower density of 0.18.

So, even with a better Minesweeper solver I expect the basic curve shape will be the same, just shifted a bit to the right.