Speaking as someone who has spent WAY too much time playing minesweeper -- Early on I came to a similar conclusion (though without doing the actual math) and started clicking on corners initially. I soon discovered, as most people do, that corners are much more likely to expand out into a tiny opening that you can only follow for a short time before you're forced to make a "coin toss" move. If the goal is to make a _usable_ blob, clicking in the middle is best.
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.
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.
Yeah. On 'advanced' I got to the point where I'd click all four corners (and if that didn't work I'd try again) because it massively reduced the chances of coming to a '50/50 guess', which was the biggest difficulty of the game and most often happened near the corners...
A corner may be more likely to expand at least one square, but a middle click is more likely to have an immediately actionable open square. This is somewhat related though to the type of play one uses.
I started out as a flagging user (the usual right-click to mark known mines), and then I always started in the lower right corner. Then (after a few years break) I started playing non-flagging (that is no right click allowed) and I find that a middle click is much more likely to give an "easy" opening.
My usual opening consists of several middle clicks spread out until I get an opening (or failure).
Added: The cost (in seconds) of clicking corners until an opening is too high compared to the risk of getting a coin toss in a corner. Prudence isn't fast enough :)
