A related question here is whether and when the mine placement is fully determined. I think it is definately true that the mine placement is NOT determined until AFTER you click the first space. However, I’m not entirely convinced that it’s then fully determined at that point either. I could swear, but the program seems to punish uninformed guesses at a more than random rate, even when the patterns don’t seem to mandate that there must be a mine at a cetain location.
Do you guys start in corners or in the middle? I always start in the corner because I feel like there’s a greater chance of getting many squares to go away, and it’s easier when I see a 1 diagonal from a block to say “Hey, that’s a mine!” Is there any mathematical proof that either is better?
I saw once on the SDMB that a couple of posters had beaten the expert level in under 100 seconds! I thought that I was quite the expert player, with my best at 139 seconds. I can’t imagine getting it down to less than 100.
I always start in the corner. Not because I get a better “clear”, but because the corners can be such a biznatch sometimes. I figure three corners are better than four.
I always clear out the four corners as my first four moves and work from there.
Back in my university days I used to spend an inordinate time in front of a win3.1 machine running minesweeper. After a lot of practice I managed indeed to do it in under 100 seconds. (I believe that my record was 96 seconds.) It involved clicking all four corners and somewhere in the middle within the first couple of seconds. Which of course often led to a very early explosion, but once in a while it opened up quite a lot of the playing field.
Then it’s all pattern matching and luck.
If you aren’t concerned with losing, corners are a good bet.
For the smallest possibility of losing initially (and my logic may well be faulty) it is better to start toward the center.First off, if you get a 1, it’s 1 mine out of eight squares, rather than out of three (corner) or five (side).
Second, it’s best to make the next guess in a diagonally adjacent square. It is actually irrelevant on the first pick, but if the square reveals 2 or greater, then you know that your next pick is less likely to be a shared mine
For example with
?3?
?1?
???
you would logically rule out the four squares that are adjacent to the 1 and the 3 for the next pick, since there’s a good chance that the 1 and 3 ‘share’ a mine. This narrows your choices down to the three at the bottom (of which you can ‘safely’ pick both bottom corners or just the bottom center), and makes you that much more likely to have to pick another square at random elsewhere on the board.
Whereas with
??3
?1?
???
you can pick the other three corners as necessary.
Once a chunk of the board is revealed, it’s playable. Otherwise, I go diagonally from the 1s, avoiding squares that are also adjacent to revealed 2s or higher (since Expert has a 1/4.84848… chance of a mine in any given square, it is better to guess at random elsewhere rather than click an uncertain square adjacent to a 2).
Beyond that… I usually lose. Yes, the random factor bites at times. The way I figure, though, it’s more fun to survive farther into the game 
If you happen to get a 1 in the middle, that’s better than a 1 in the corner, but the flip side to that is that you’re much less likely to get a 1 in the middle. And a 0 is very helpful no matter where it is, and that’s significantly more likely in a corner. I always start in one corner and work from there, and my best time for Expert is 80-something (though I’d probably have to get a new mouse before I could replicate that). If I get a 0 on my first move, I’ll clear some area, and probably be able to make an actual deduction on my next move. If I get a 1, then any of the three adjacent spots has a 2/3 chance of safety, slightly better than a random spot on the board, so I go in one of them (typically also on the edge). If it’s a 2 or 3, then I skip over one, and pick the next one on the edge, so I have some shared squares and therefore at least some information about the arrangement.
My best expert time is 81 seconds, and if I’m trying for a record time I’ll start by randomly clicking until I’ve opened up one or two good-sized blank areas. This causes lots of quick losses but allows for fast games when it works.
And as Chronos mentioned, having a good mouse and being able to click quickly makes a difference. There are lots of patterns that you can recognize faster than you can click.
For us computer-ignorant types, what is NP-complete?
Apos, I don’t think it punishes random guessing. I don’t think it’s an advanced enough program, for one thing; you just remember the bad outcomes more than the good ones.
FWIW, just to brag, my best time on the expert is 78 seconds, which I’ve managed to repeatedly replicate but haven’t broken since I set it 3-4 years ago. It’s a question of a good mouse, knowledge of the patterns involved, and years and years of time wastage.
Thanks to all of you, guys. Yesterday I managed my fisrt expert game in the astonishing time of 719 seconds.
Think I have to practice a bit :rolleyes:
I never even continue a game unless I can open a blank field of sqaures in the first few clicks.
Oh, and the fast times probably come from the feature where, once you have placed the indicated number of flags around a numbered cell, you click both mouse buttons simultaneously on the number, and the remaining cells all open up (even the ones containig the mines you erroneously thought were in another square. I had been playing for a shamefully long time before someone pointed it out to me, but it’s right there in the Strategies and Tips in the Help file.
:eek: :eek: :eek: :eek: 
Basically, the set of NP-complete problems are the hardest problems to solve out of the set of problems that allow quick verification of an answer.
which of course ends the game, if that happens
If you overassign–set two flags next to a one, and double-click, for instance–nothing will happen, even if there are adjacent nonflagged squares.
Depends upon what you mean by “hard”
An NP complete problem may be easy to solve–straightforward, even–but what is hard is finding a way to do it quickly.
In this case, problem A is harder than problem B iff there exists a polynomial-time reduction from an instance of B to an instance of A. That’s what I mean by “hard” here.
The World Record for Expert Minesweeper currently stands at an astonishing 41 seconds (according to this site: http://metanoodle.com/minesweeper/ ).
All I can say is: unbelievable!
Not the 41 seconds, the amount of time and effort you’d have to invest to approach this mark. For those who want to, this site offers tips: http://www.frankwester.net/winmine.html
The guy with a 41-second best time on the expert also has a best time of 1 second on the beginner level, as do a bunch of other ranked people. That has to be luck, as you don’t have time for more than a couple of clicks in a second.
BTW, Minesweeper (and P vs NP) featured prominently in the plot of the second episode of Numb3rs. I don’t think it’s going to save it though.