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by James Robertson.
Original Post: Advanced Minesweeper - Don't Guess!
Feed Title: Michael Lucas-Smith
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Feed Description: Smalltalk and my misinterpretations of life
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No matter how much we have to do sometimes we're still bored. It is in these moments that we make great breakthroughs of humanity in fields such as: crossword puzzles, mazes, solitaire.. and of course Minesweeper
I've been trying to perfect my new minesweeper artform, which I liken to counting cards in poker (except that this is legal and I unfortunately cannot make money off it). It is counting the squares where mines could go and discovering what could not possibly be possible.
This never requires a leap of faith, except right near the end of the game - but sometimes you get lucky. We'll see how we go this time. Lets begin our game:
We've got a fairly good set up. But it's square. Any body who knows minesweeper knows that square edges are a bad thing. Already some people would take a guess and randomly shoot for somewhere else in the field. Don't do it! There's still a lot we can discover about this field. I've marked out the squares of interest in cyan and green and they reveal that the top two 2's must occupy those spaces with at least one mine. Therefore, the first blue smiley must be a safe click. Following on from that, the next two 1's must also be occupied with at least one mine, therefore there cannot be a mine next to the fourth 2. Lets take the next step:
This is a big jump. I just play out all the clicks as they come. Anything that is 'obvious' I go for it. Well, picking out those first few initial observations has given us nearly the entire board. (For non-advanced minesweeper players, you will probably stuff up many many times at this step).
What cna we do from here? We continue with our logical counting. We have another set of two 2's that we can target. There must be a mine at one of those locations, which means the second 2 must have a mine to its right. Bam, that is a definite mine. If that's a definite mine than the 1 above it says that to the left has to be safe. We therefore now know the location of two mines and we haven't yet clicked. To the right of the 1 must also be safe, therefore we have another mine to the right of that safe place to satisfy the 2.. taking that further there are a couple more safe places to click as well.
Uh oh, square edges again. Not to worry. We can attack this board from both the top and the bottom. Starting at the top, we see that a 2 next to a mine must have a mine there. If it did, then the 1 above it must have a safe click. Similarly, down the bottom, we once again attack the two 2's, there must be a mine on either side of them, therefore the is a safe click under one of the mines.
Unfortunately, the bottom of the board didn't reveal much to us - but the top of the board did! It told us there is 1 in our safe spot. Our safe spot continues to tell us that there must be either a mine above or below. If that's the case, that 1 is already satisfied. Any other square around it must be safe. Three free clicks for us!
We've been given a gift! Another one that shares the same to 'potentially occupied squares'.. therefore we can do another three safe clicks.
We still know that those two squares must contain a mine. Now we know that the top one, thanks to the two and the one, must contain at least one mine. Therefore because the 1 must be taken by one of the two spaces, we have two more free clicks we can take.
Thanks not to our luck, but our observation and counting skills, we now have most of the top. We'll leave those two squares alone because we don't have enough information to discover their true configuration. Instead, lets attack the 3, 2, 1 scenario on the top left. There has to be a mine next to the 1, and the 2 is already touching another mine, therefore, the square under the 3 must be a safe click.
Bummer, that didn't tell us much at all. Okay, time to think on this a bit.. if the lower section must contain a mine and the next vertical section must contain a mine, and the 2 next to the 3 already touches a mine, then the square under the 3 must be safe!
Joy! it's a 2. This means we still know there must be a mine on either side, and the 2 is already touching one mine. We effectively have the free clicks around a 1 example again. So lets take out three free spaces and see what that gives us.
It gives us a 1, a 1 right next to an area we know must be occupied with a mine. This gives us another four free clicks and reveals the locations of the mines all the way down our vertical drop.
Once again we can attack the board from the bottom and the top. Well, the middle this time. Down the bottom we can see two mines butted up against a 3, therefore the two empty spaces have to contain one mine. If they contain one mine, than the 2 next to the three must have a mine to its right. If it has a mine to its right then there's only one other place to satisfy the 3 next to it.. to its right as well.
Up the top, we see a 1 that must contain a mine. If there is a mine there, than the top 3 is satisfied. Down below, there mus tbe a mine along the side of the two vertical 3's, which would satisfy the top vertical 3, but not the bottom - leaving only one place that a mine could live.
Unfortunately we didn't get much information out of that. So we're going to have to think a little harder on this one. Back to our one-scenario. We already know that the 2 we revealed before must get one of its mines from the left or the right, therefore it has to get its second mine from that gap next to the 1. If we fill a mine in there, a few more locations free up and...
We reveal the entire top of the board. We're down to our final leg now. We have just the bottom of the board to complete. Those young children can almost go play in the mine riddled paddock again.
We can see we have two 1's butted up against a wall, this is a dead give away. There's only one combination this can work in with the three there, so we take it.
Uh oh.. a square. We're running out of obvious information. Lets take the one mine we know about, which is next to that three, and see if anything obvious springs to mind.
Right. I've officially been beaten by this board. There's no way I can get the right answer by deduction alone. I must make some educated guesses. There are some nice shapes we have here.
We know there are 11 mines left on the board and we can account for seven of them. If we account for seven of them then there are roughly 11 squares on the board we could click in and perhaps hit one of the four.
Now it's time to guess...
We've discovered that some of our assumptions are probably right. I've marked out some likely candidates - only problem is there are still 2 mines missing and I've got no 'proof' that my red slashes are where the mines are.
It turns out that once you're down to this level of analysis of the board, you shouldn't guess! You should go with the likely positions you've chosen. Of my intuited positions I had -one- wrong. Had I taken my intuition over a statistical guess, I'd have won this board.
So, I hope you've learnt some of the tricks I use to play minesweeper. It makes the game a battle of the wits instead of a random slog fest. Oh, and one piece of advice:
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