# Minesweeper Probabilities



## AndyK (Jul 21, 2010)

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 (Jul 21, 2010)

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


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## tempysmurf (Jul 21, 2010)

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.


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## AndyK (Jul 21, 2010)

tempysmurf said:


> 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 (Jul 21, 2010)

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.


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## Kynit (Jul 21, 2010)

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


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## AndyK (Jul 21, 2010)

Kynit said:


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



True


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## Whyusosrs? (Jul 21, 2010)

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


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## MTGjumper (Jul 21, 2010)

AndyK said:


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




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.


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## Kynit (Jul 21, 2010)

MTGjumper said:


> 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


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## coinman (Jul 21, 2010)

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.


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## coinman (Jul 21, 2010)

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.


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## tempysmurf (Jul 21, 2010)

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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## beni (Sep 6, 2011)

AndyK said:


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


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## Posea (Oct 5, 2011)

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.


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## moogra (Oct 7, 2011)

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.


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## Xishem (Oct 13, 2011)

moogra said:


> 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]
> ...



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 .


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## MrData (Oct 13, 2011)

Xishem said:


> 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]
> ...


 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.


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## zarc (Oct 27, 2011)

*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.


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## moogra (Oct 27, 2011)

Xishem said:


> 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]
> ...




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.


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## Zaterlord (May 31, 2012)

Do you never have to guess on Beginner?


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## Georgeanderre (May 31, 2012)

I never guess on any mode until I absolutely have to. To this day I have only ever guessed on the last 2 squares of expert when its in the corner and either could be the final mine.

I have also played a very similar game called Vinesweeper, if you've played it you'll know what I mean, I have never needed to guess on that and I have scored in excess of 3million points... if you have no idea what Vinesweeper is, don't ask 

but for the meantime... big necro -.-


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## MattMcConaha (Jun 1, 2012)

zarc said:


> 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.


 
In minesweeper, the first click is NEVER a numbered spot. This means that at least you will have opened up a 3x3 hole in the board (unless you click a corner, then you get at least a 2x2.) With this 3x3 opening it is often times possible to open up the gap more until you have plenty of easy mines.

And as for the RL simulclick: The only thing that does is click on all the surrounding spaces around a number. if you RL click on a 1 that you put a flag beside, then that's the same as clicking all the spaces around the 1. However, if you put the flag in the wrong spot, then you lose. If you have the incorrect number of flags around the number, then RL clicking does nothing.


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## Bicycling Bob (Dec 14, 2013)

*My Statistics*



AndyK said:


> 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.



MineSweep: Impossible endings aginst games won.
Series No Games % Un-
#: End Won winable
1: xxxxx xxxxx xxxxx xxxx ------- 19 32 37%
2: xxxxx xxxxx ------------------ 10 25 40%
3: xxxxx xxxxx xxxxx xxxxx xxxxx xxx 18 52 35%
4: xxxxx xxxx	------------------- 9 18 33%
5: xxxxx xxxxx xxxxx xxxxx xxxxx 25 47 35%
6: xxxxx xxxxx x	------------------- 11 22 33%
7: xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 53 36% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 60 116 34% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 90 163 36% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	120 222 35% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	150 282 35% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	180 348 34% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	210 438 32% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	240 512 32% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	270 555 33% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	300 612 33% Done
8: xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 71 30% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 60 141 30% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 90 202 31% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	120 271 31% Done[/B]
9: xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 72 29% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 60 138 30% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 90 207 30% Done
10:xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 48 78% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 60 100 38% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 90 157 36% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx	120 218 36% Done	
11:xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 70 30%  Done
12:xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 70 30% Done
13:xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 64 32% Done
14:xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 64 32% Done
15:xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 30 54 36% Ongoing
xxxxx xxxxx xxxxx xxxxx xxxxx xxxxx 60 127 32% Ongoing
xxxxx xxxxx 

Games won against games guess: I replay any game I lose so this is pretty (actually extremely) accurate. As you can see it's 1/3 for every 3 games played, it's 1 game guess. 
Each x = 1 guess game in the series. "No Ending" = Guess ending. "Games Won" = Games I won

As you can see, short runs can vary a lot. Even 30 game series can vary a lot.
You can see how the #10 series started a 78% "Guess Ending" but ended at 36% "Guess Endings"
If you add up all these series you will get a pretty good (Actually very accurate) idea of what the end is. 

1 Guess game for every 3 games played.

Pretty bad competitive sport. 

Can you rely on my endgame. You bet. I'm good. Very good.


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## Bicycling Bob (Dec 14, 2013)

Bicycling Bob

Sorry about that.

All formatting was done before I posted but it didn't come out right after posting. Good luck fixing their error.


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## Game Nut (Jan 9, 2014)

I consider myself an expert minesweeper player. I don't have the fastest of times, (average of about 150 seconds) but that's just because i like to flag everything. However I believe I can play the closest anyone can get to a perfect game. I've played over 2,400 minesweeper games over the past 2 years and with probably about 100 of those games being throw away games where I didn't try. my percentage is 36%. I've since reset my statistics out of curiosity of the same question you are asking. I want to know how high I can get my percentage playing perfectly. Algorithms aren't good enough because most of them don't take into account percentages of all possibilities of selecting a set of squares along with the probability of the selecting square being beneficial to further completion of the board.


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## ~Adam~ (Jan 9, 2014)

Game Nut said:


> my percentage is 36%.



=O

Anyone know the chance of playing an expert game in which you don't have to guess at all?

Many of my games I have a 50/50 guess twice. Those darn corners.

Edit - then I read the thread and apparently I've asked the question the OP did.


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