Another priority with the first click is that you won't be entirely surrounded by mines and wires, wires being indeterminate, entangled chains of unrevealed spaces.
I'm pretty sure a probability can be worked out for rate of occurrence and length of a wire - but with the corner strategy, you're minimizing the likely amount of perimeter by 3/4. That's got to make a "coin flip" situation more likely, which has to be weighed against the more likely reveal.
If you don't get a reveal on the first click, you end up just clicking again a few times and restarting if you reveal a mine. Doesn't waste more than a second in any case. Not sure if that's really meaningful unless there's a no restart rule, or you're being graded by the percentage of games finished that are started.
Paper on minesweeper configurations being NP-complete. Wires in the paper are wires when approached from all directions, but I'm abusing the term a bit when I also include entangled squares around the perimeter of a minesweeper opening - which have only been approached from one direction.
I think of minesweeper as a bunch of soap bubbles that are popped until you reach wires, which if they connect board boundary to board boundary, or connect to another wire that does that, or connect to themselves, end the skill game and create a probability game. Been meaning to play around with 2D areas that are surrounded by wire rings, but too lazy.
The idea of randomness carved by rules creating stable shapes intrigues me. I play minesweeper too much. Expert: 78, 95 non-flagging, lawl.
I'm pretty sure a probability can be worked out for rate of occurrence and length of a wire - but with the corner strategy, you're minimizing the likely amount of perimeter by 3/4. That's got to make a "coin flip" situation more likely, which has to be weighed against the more likely reveal.
If you don't get a reveal on the first click, you end up just clicking again a few times and restarting if you reveal a mine. Doesn't waste more than a second in any case. Not sure if that's really meaningful unless there's a no restart rule, or you're being graded by the percentage of games finished that are started.