Is Minesweeper winnable?

This is the question posed here.

The quick answer is yes. For one, the first click is programmed not to hit a mine. For two, theoretically you can randomly click on empty squares each time and get them all.

On a practical matter, however, the answer is no. Given a perfect algorithmic system you still can often be placed in "pure guess" situations.

For example, in this game I was just playing I had two unexplored squares, one of which contained a mine. Either the space between the 4s contained the mine, or the space along the edge between the two and the one. However, both squares met the mathematical conditions expressed in the four adjacent cells.

Naturally given my 50-50 chance, I guessed wrong. I've guessed wrong facing 2 mines remaining with roughly 1/3rd of the board uncovered, so this shouldn't surprise me.