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Speaking as the same sort of person (96 secs on expert :-) ), I agree that the most useful strategy is to click in the middle. This is because the cost of restarting is practically nothing for your first few clicks (no sunk time costs), so what you should really be optimizing is trying to get the most information about the board as soon as possible. All the more so because optimally your whole game will proceed logically from that first cascade. Bigger cascades are less likely to dead end, meaning you'll be less likely to have to guess at random again later (when you actually will have sunk time costs).

I'd say it really depends on what you're optimizing for.

When I'm going for a high score, I want the fastest time (and lost games don't count for anything). So I guess a lot, especially in the first few seconds, looking for good spreads and free information.

When I'm in the mood for a logic puzzle, I go for the best completion rate (percentage of games won). Then I click a single corner and work with whatever I get, guessing again only if my remaining options are guesses anyway. (The corner eliminates at least one bad endgame).

When I just want a fun experience, I go for most games completed in a session. In that case, I click all four corners to start to eliminate bad endgames. Those aren't a fun experience.

Wouldn't bigger cascades be more likely to deadend, due to the average density of what's leftover increasing?

My fault for being ambiguous about the word "bigger", thanks for pointing this out. It's true that you're not looking for a large area per se. What you want is a large perimeter. The best starting click would be a whole lot of thin tentacles stretching out across the board, not a giant square-ish clump.

That is, you're trying to maximize information. A large rectangular area doesn't give you nearly as much information about the board as a tentacle-y one, because most of the squares don't tell you anything but their own value.

This is a definite problem on expert. I had a few female friends in college who were insanely good at Minesweeper, able to clear expert more often than not and insanely fast (under 100 seconds). When I was trying to get better and would get excited to get a big cascade, they'd just chuckle knowing that it was just going to make my chances that much more slim.

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