Minesweeper-O-Rama




Minesweeper Tips

Y ou're probably better off visiting some of the websites listed on the MineLinks page to find strategy and tips for playing Minesweeper, but I really have noticed a few things while playing. So, hopefully, a few of the tips below will help you improve your time and enjoy the game.

This page is broken up into three main areas - use the links below to go directly to that section, or just scroll down the page:
  • Playing Tips - General tips and strategy for playing Minesweeper
  • Minesweeper Quiz - A few sample boards, to see how much you learned from the tips
  • Level Statistics - Information on how the different levels relate to each other in terms of difficulty


Playing Tips

Starting Out
When I first started playing, I always started each game by just randomly clicking squares until something opened up. This does seem to work, and without doing some serious statistics, I'll say it works just as well as any other method.

However, I don't do this anymore. Currently, every time I start a game, I click the square in the top left corner. This will uncover a 1, 2 or 3 numbered square. If you see a 3, then you know each square touching it is a mine. If I get a 1 or 2, I next click the third block down on the left.

Starting Move:
Top left corner

Starting position: top left corner
2nd Move: 3rd square
down on left side

Second move: third square down on left side

From there, I keep going down the left side, clicking every other block, until something opens up. If I make it all the way to the bottom, then I start back at the top and click every other square going right along the first row. By doing this, you either get a good opening to start with, or else you hit a mine and start over.


Playing: What to look for
It occurred to me that, while playing, corners are your friends. Since these areas have fewer covered squares, it's easier to tell where the mines are. Below are a few examples of corners telling you exactly where mines are:

Corner with 1
A 1 square in a corner
Corner with 2
A 2 square in a corner
Corner with 3
A 3 square in a corner
Corner with 4
A 4 square in a corner

Likewise, there are a few other common circumstances that can tell you exactly where the mines are (or are not). Each situation is different, depending on the numbered squares involved, but once you understand these, you'll see them in every game you play. And, once you're able to recognize them, they will certainly increase your speed, since you won't have to reason out as many situations.

A row of 1's In this group of 1's, you know that the square below the third 1 from the left is not a mine. This is due to the first 1 only touching two squares, which means the mine must be under one of them. Since the second 1 also touches these same two squares, any other square the second 1 touches cannot hide mines.
1's and 2's together When there are a couple 1's next to a couple 2's, you can usually immediately identify one mine and one non-mine square. In this case, we know that, of the three squares below the first 2 from the left, two of them must be mines. Since the second 1 from the left touches two of them, we know that one of these squares must be a mine, and that the third square that 2 touches (the square below the second 2 from the left) is a mine. Also, since we know that one of the two squares that both the second 1 and first 2 touch is a mine, then the rest of the squares that the second 1 touches cannot be mines.
A 3 in the open Here, you can see the 3 has covered squares only on one side of it. This means that it touches only three squares, all of which must be mines. Additionally, since there is a 2 on each side of the 2, each of which touch two of the squares below the 3, you know that none of the other squares that those 2's touch can be mines.
A 2 between two 1's A 2 between two 1'sWhen in the open, a 2 between two 1's will always mean that the two squares below the 1's hide mines. (see right). This is because, of the three squares touched by the 2 between the 1's, only two of them can be mines. Since the 1's each touch two of these squares, the mine cannot be in the square that is overlapped.
Drilling in off a 1 Drilling in off a 1 Drilling in off a 1 When you have a 1 that is set in to the covered squares, it is usually a good place to drill into the covered squares. In this case, you know that there is a mine under one of the covered squares touched by the second 1 down on the left. Since the 1 immediately to the right of that 1 touches both of these squares, all of the covered squares to the right are safe to uncover. Then, since there is another 1 to the right, then the surrounding covered squares are also safe.


Using Flags
I use flags heavily - in fact, more than I should. I like them because it keep sme from having to remember where the mines are. Also because after you flag a mine, you can both-click (click both mouse buttons at the same time) on the numbered squares around the flag to uncover more non-mine squares.

The reason I say I might use it too heavily, though, is because using flags can slow you down. It takes time to flag a mine, which adds to your overall game time. I think this is why an Expert score o 99 seems so far out of reach to me. I'm sure that the people who get those scores only flag the mines they have to, and not every one, like me.

For example, none of the flags below needed to be set. They are obviously mines, and therefore just wasted time. Further, in the image on the right, the group of four covered squares in the lower left can even be easily cleared without setting any flags. Using flags sparingly should improve your time, once you get the hang of it.

Flags that did not need to be set More flags that did not need to be set
Blind Guessing
If you play more than a few games, you're bound to run into a situation where you cannot logically determine where a mine is. Sometimes, you'll have a choice of two covered squares, either one of which could hide a mine. What it boils down to is that, sometimes, you'll guess right, and sometimes you won't.

2x2 block guessing This particular situation is probably the most common blind-guess situation. When I run into on of these during a game, I usually pass it by and come back to it at the end of the game. Basically, though, all four squares have an equal chance of hiding a mine, so you just have to guess, based on experience. In this case, I would guess the mines are under the top left and bottom right (I was wrong - bottom left and top right).
Guessing to find help Guessing to find help Guessing to find help Often during the game, you'll hit a point where there are no safe squares to uncover. In this case, since you have to guess, try to guess somewhere that will most likely help you (providing you don't uncover a mine). I usually look for numbered squares that touches a group of covered squares, where only one of the covered squares can be a mine. Then, if the square you uncover is a 1, you're all set, because any other squares that 1 touches cannot be a mine, giving you safe squares to uncover.


Minesweeper Quiz
Minesweeper Quiz #1 Minesweeper Quiz #2
Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Minesweeper Quiz #1 Minesweeper Quiz #1 uses the board at left as if you were playing a game in progress. The object is to click on a "safe" square - one that doesn't cover a mine. Click on any of the covered squares to see if you can figure out which are safe, and where the mines are. Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Click to see if this is a 'safe' square Minesweeper Quiz #2 Minesweeper Quiz #2 is the same idea, but a little more difficult (or easier, depending on how you look at it). Again, click on any of the covered squares to see if you can uncover more numbered squares and locate the mines.


The Levels
Minesweeper has four levels that can be played - Beginner, Intermediate, Advanced, and Custom. While playing a lot, I started to wonder whether the Intermediate and Expert levels were harder just because they were bigger, or because there was a higher percentage of mines (I suspected the latter). And, I thought that if I could figure out the ratio of mined-to-unmined squares, then I could make Custom boards that where the same difficulty level as the three standard levels, but just bigger. So, I set up an Excel spreadsheet, and this is what I found:

  Beg. Int. Exp.
Height 9 16 16
Width 9 16 30
Total (HxW) 81 256 480
#/Mines 10 40 99
Difficulty 0.12 0.16 0.21
Change - 0.03 0.05


In the table above, I assigned the "Difficulty" rating simply by dividing the number of mines by the total number of squares. "Change" refers to how much more difficult the next level up is, compared to the one before it. It seemed to me, then, that the next level beyond Expert would have a Change of 0.07.

I used the Custom board to create this next level, as indicated in the table below. Plus, indicated in the table below, based on Difficulty, are the dimensions (width, height, #/mines) to make the largest possible Custom boards with the same difficulty ratings as each of the three standard levels (you know, in case you really like the Beginner level, but the games are just too short). Also, at the end, I worked out the difficultly rating for the maximum settings on the Custom board (which, it turns out, is incredibly hard).

  Beg. Int. Exp. Custom
(next)
Custom
(Beg.)
Custom
(Int.)
Custom
(Exp.)
Custom
(Max.)
Height 9 16 16 24 24 24 24 24
Width 9 16 30 30 30 30 30 30
Total (HxW) 81 256 480 720 720 720 720 720
#/Mines 10 40 99 199 89 113 149 667
Difficulty 0.12 0.16 0.21 0.28 0.12 0.16 0.21 0.93
Change - 0.03 0.05 0.07 - - - 0.65


Finally, I wondered just what was the likelihood of clicking on a mine on your second click. With Minesweeper, no matter where you click first, it won't be a mine. The second click, though, could be a safe square or a mine. To figure out what the chance of clicking on a mine with the second click, I just divided the number of remaining safe squares by the total number of squares
  Beg. Int. Exp. Custom
(next)
Custom
(Beg.)
Custom
(Int.)
Custom
(Exp.)
Custom
(Max.)
Total (HxW) 81 256 480 720 720 720 720 720
#/Mines 10 40 99 199 89 113 149 667
#/Safe Squares 70 215 380 520 630 607 571 52
Difficulty 0.12 0.16 0.21 0.28 0.12 0.16 0.21 0.93
Chance of clicking a safe square 88% 84% 79% 72% 88% 84% 79% 7%
Chance of clicking a mine 12% 16% 21% 28% 12% 16% 21% 93%


Note that the percentages for the three standard boards are the same as the Custom board equivalent. If you are so inclined, you can check my math by downloading my Excel spreadsheet.


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Updated 5/7/05
by bherzog@kent.edu
©2005 Brian Herzog
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