# Minesweeper Probabilities

#### AndyK

Hey everybody, I'm a minesweeper nut and have been using Google to try and figure out what percentage of Expert minesweeper games are winnable without guessing (specifically without having to guess a 50:50 case). So far I haven't found this calculation anywhere and seeings how there are quite a few math/probability geniuses here I figured I'd ask.

One possible explanation for me not finding this calc yet is because it is impossible to compute.. Minesweeper is NP-complete when considering mine placement, but I think that calculating a percentage of winnable games (without guessing) is a different issue and thus possibly not NP-complete.

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#### keemy

##### Member
When you say winnable do you mean winnable without having to guess?

#### AndyK

All of them are potentially winnable.

I'm assuming you're trying to find out how many games there are where you don't have to guess. Here's a start... http://www.minesweeper.info/forum/viewtopic.php?f=15&t=107 and you might even want to ask them.
Ha! Woops, yeah that is what I meant, I'll edit my post

I checked out that link and vomited a little bit after seeing all the math. I don't see how those calculations reveal anything about percentage of winnable games without guessing though.

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#### MTGjumper

##### Member
Not knowing much on the subject, but isn't the first click a guess? You have no indication of whether you'll hit a mine or not.

#### Kynit

##### Member
I thought the board was generated after the first click, so that you can never hit a mine on your first click.

#### AndyK

I thought the board was generated after the first click, so that you can never hit a mine on your first click.
True

#### Whyusosrs?

##### Member
minesweeper is cool. I used to play that a ton. I hate it whenever you have to guess on that last mine or two

#### MTGjumper

##### Member
I thought the board was generated after the first click, so that you can never hit a mine on your first click.
True

Yeah, that makes sense. Didn't know that was the case, and I've never played minesweeper enough to know this was the case. But does the first click always give enough information (for example, revealing only a 1) which would then surely lead to subsequent guessing.

#### Kynit

##### Member
Yeah, that makes sense. Didn't know that was the case, and I've never played minesweeper enough to know this was the case. But does the first click always give enough information (for example, revealing only a 1) which would then surely lead to subsequent guessing.
I think that's the question that the topic is asking

#### coinman

##### Member
So what is your best times?
On this computer it's 3 seconds for easy, 43 seconds by Oliver Perga for the middle level, I have to beat his time soon and 161 for expert.
On my old computer where i used to play it a lot i think the times was 4, 36 and 121. I also crashed at sub 110 seconds times on 50/50 chances a few times at expert level.

#### coinman

##### Member
I also notice that the game is somehow different on Windows Vista then on older windows versions, not only the design.

I think a good improvement of the game would be if it always was winnable without guessing.

#### tempysmurf

##### Member
Use minesweeper clone or minesweeper x instead of the windows versions. My best time is 82 seconds on expert without using flags.

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#### Posea

##### Member
Not sure if there is a way to work it out mathmatically, but with:
1524 expert games 28%;
759 medium games 94%;
100 beginner games 100%

You usually dont have to guess on the medium.. but it does happen.

#### moogra

##### Member
What do you mean? You have potential to guess on all of them
Let's take this as an example you're down to 3 mines left:
[ ][1][0]
[ ][3][1]
[ ][ ][1]

You're going to have to guess.

It might be easier to start by finding all the 50/50 cases.

#### Xishem

##### Member
What do you mean? You have potential to guess on all of them
Let's take this as an example you're down to 3 mines left:
[ ][1][0]
[ ][3][1]
[ ][ ][1]

You're going to have to guess.

It might be easier to start by finding all the 50/50 cases.
This situation won't happen. You're going to have some hints coming from one of the directions. It depends where this case is located. For example:
[?][?][0]
[ ][1][0]
[ ][3][1]
[ ][ ][1]

You're going to have those numbers, unless this case is hugging the top left corner, in which case you would have numbers below it.

It's just that this is not an example of a 50/50 guess.

I've been playing Minesweeper a lot this past week, primarily intermediate, and my best time is 35. I need to start playing expert .

#### MrData

##### Member
This situation won't happen. You're going to have some hints coming from one of the directions. It depends where this case is located. For example:
[?][?][0]
[ ][1][0]
[ ][3][1]
[ ][ ][1]

You're going to have those numbers, unless this case is hugging the top left corner, in which case you would have numbers below it.

It's just that this is not an example of a 50/50 guess.

I've been playing Minesweeper a lot this past week, primarily intermediate, and my best time is 35. I need to start playing expert .
In my experience, that situation happens a lot in the corners. In this case, the numbers below it wouldn't matter because you know the two below the 3 are mines and either of the two left can be the remaining mine. There is no way to know for sure which it is and you do have to guess.

#### zarc

##### Member
used to

I used to play alot of minesweeper in my college days, true that the first click is always a wild guess, then the next few clicks would also be a guess but if you got 1 area open wide, that's the time to simultaneously click left and right click right? to know which one is the mine and which one is not.

#### moogra

##### Member
This situation won't happen. You're going to have some hints coming from one of the directions. It depends where this case is located. For example:
[?][?][0]
[ ][1][0]
[ ][3][1]
[ ][ ][1]
You're going to have those numbers, unless this case is hugging the top left corner, in which case you would have numbers below it.

It's just that this is not an example of a 50/50 guess.

I've been playing Minesweeper a lot this past week, primarily intermediate, and my best time is 35. I need to start playing expert .

There are 50/50s NOT in the corner too. I used to play a lot (nearly 10k games on beginner, 1k games on intermediate, 5k games on expert on windows, probably around 2k games of intermediate on clone -- only played intermediate for fun NF). Got tired of it after a while especially since my mouse was too whack (too fast on 1 setting, too slow on 1 setting below).

Also let's say the first number you opened up was a 1 and was not an island.
[ ][ ][ ]
[ ][1][ ]
[ ][ ][ ]
You know nothing else about the board. There's still a low chance you'll hit a mine if you do indeed go around the mine and if you don't, you'll have to guess anyhow.