Advanced Minesweeper

I would say the goal is not to have the highest probability of triggering a cascade, but rather, some combination of:<p>- high probability of triggering a cascade<p>- high probability of that cascade being "useful", that is, of being able to work outward from the cascade you opened. (Clicking on the empty corner and getting 1-3-1 on its borders means you still have to guess to escape the corner.)<p>- high probability of <i>not</i> leaving difficult areas for the end. (Coin flips are most likely to occur in corners and edges; in the middle of the board, you usually have information from multiple directions. It's still possible to be forced to guess in the middle, but it happens far less often.)<p>As a result, the strategy I've chosen on expert boards (based on experience, without particularly robust statistical backing) is to click the corners sequentially until I get one that allows me to open up more than a few squares. I occasionally lose a game on the second or third click this way, but I don't lose very many on late coin flips.

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.

Although I have no idea since I have never seen the code, I'm pretty sure there's no way to hit a bomb on your first click. I'm played enough (MS Windows) Minesweeper and have never, ever hit a bomb on the first click.<p>As a side note, Minesweeper the first game I ever programmed was for my intro C class in college using SRGP[1] as the graphics library. Thinking back, it was a tough project. The Minesweeper logic wasn't so bad but doing the graphics was the most work. In hindsight, it shouldn't have taken more than a couple hours to code but took everyone a fair amount of time. Of course we didn't know what they hell we were doing. Fun stuff.<p>EDIT: After searching around it appears there is code to prevent the first-click bomb in a rather novel way[2].<p>[1] <a href="http://www.niksula.cs.hut.fi/~tik86120/X_srgp.html" rel="nofollow">http://www.niksula.cs.hut.fi/~tik86120/X_srgp.html</a> [2] <a href="http://www.sanchitkarve.com/blog/2009/01/does-minesweeper-cheat/" rel="nofollow">http://www.sanchitkarve.com/blog/2009/01/does-minesweeper-ch...</a>

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.<p>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.<p>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.

This seems totally wrong to me. Of course the probability of surrounding squares being <i>all</i> safe is higher in the corner simply because there are <i>fewer surrounding squares</i>!<p>To make it more fair, calculate the probability that 3+ adjacent squares would be safe, since that's how many you get in the corner. Then the math shows that center is better because there are more neighboring squares that could be potentially blank.<p>More useful would be the probability of having a cascade continue on past adjacent squares to squares adjacent to those, with the "winner" being whichever location is most likely to make the largest exposed bubble.<p>My strategy is generally click a few places in the center quickly. If I die, I don't have much invested and just start over. If I find a large bubble, then I can play.

I think it's nowhere near that simple. You don't just want to open up a cascade, but a _quality_ cascade that gives enough information to work with to identify which cells are mines, or, failing that, won't involve a risky guess. A '1' in the corner means each neighboring cell is a 1 in 3 risk, while a '1' in the middle is only 1 in 8.<p>shameless plug: a minesweeper solver I wrote [<a href="http://mrgris.com/projects/minesweepr/demo/player/" rel="nofollow">http://mrgris.com/projects/minesweepr/demo/player/</a>]

Someone ought to write something to empirically test this assertion by clicking on the various possible locations.

My shortest time on the advanced mode of windows version is 62 seconds. I'm sure many of you'd beat that.

Would it be possible to make a 3D Minesweeper game inside Minecraft?

There're some gems on DataGenetics' blog. Highly recommended.