Minesweeper Strategy

Minesweeper strategy involves pattern recognition and learning basic logic, where to make the first click, how to guess effectively and how to play Minesweeper efficiently. This guide explains the rules of the game and shares tips, tricks and tactics so you can win Minesweeper.


Windows Minesweeper
Minesweeper on Windows XP with 10 mines solved in 8 seconds

The Rules

Minesweeper is a game of logic where mines are hidden in a grid of squares. Clicking on a mine ends the game. Safe squares contain numbers telling you how many mines touch each square. These numbers can be used as clues to solve the game.

Windows Minesweeper makes the first click safe. You open squares with the left mouse button and place flags on mines with the right mouse button. You can also place questionmarks by pressing the right mouse button a second time. When you open a square that touches no mines, squares will open in every direction until the opening is surrounded by numbers. A common strategy for starting games is to click randomly until you get a big opening with lots of numbers.

Chording is when you press both mouse buttons at the same time. If you flag all the mines touching a number you can chord on the number to open the other squares. However, if you place the correct number of flags on the wrong squares, chording will end the game.

The three difficulty levels are Beginner (8x8 or 9x9 with 10 mines), Intermediate (16x16 with 40 mines) and Expert (30x16 with 99 mines). The game ends when all safe squares have been opened. A counter shows the number of unflagged mines and a clock shows your solving time. Minesweeper saves your best time for each difficulty level.

You can also play custom games up to 30x24 with a minimum of 10 mines and maximum of (x-1)(y-1) mines.


Basic Gameplay

When a number touches the same number of squares those squares must be mines.

Minesweeper pattern

The 1 on the corner touches 1 square so it must be a mine.

Minesweeper pattern

The 2 touches 2 squares so they must both be mines.

Minesweeper pattern

The 3 touches 3 squares so they must all be mines.

Minesweeper pattern

The 4 touches 4 squares so they must all be mines.

Minesweeper pattern

The 5 touches 5 squares so they must all be mines.

Minesweeper pattern

The 6 touches 6 squares so they must all be mines.

Minesweeper pattern

The 7 touches 7 squares so they must all be mines.

Minesweeper pattern

The 8 touches 8 squares so they must all be mines.

A simple trick involves pressing both buttons on a number to depress (but not open) the squares it touches. This will show you how many unopened squares touch that number. A common mistake is to fall for a fake 1 corner where the 1 already touches a mine.

Finding Minesweeper patterns

The pink 2 touches three squares and cannot be solved. The yellow 2 touches two squares and can be solved.

Finding Minesweeper patterns

The yellow 2 touches three squares and cannot be solved. The pink 3 touches three squares and can be solved.

Avoiding common mistakes

The 1 in the corner is already touching a mine. The pink square is not a mine.

Avoiding common mistakes

The 1 in the corner is already touching a mine. The pink square is not a mine.


Famous Patterns

A pattern is a common arrangement of numbers with one solution. Memorising patterns is important because thinking wastes precious time.

The two most famous patterns are 1-2-1 and 1-2-2-1 and you should memorise these immediately.

Minesweeper 1-2-1 pattern

The 1-2-1 pattern has one solution.

Minesweeper 1-2-2-1 pattern

The 1-2-2-1 pattern has one solution.

The 1-2-1 and 1-2-2-1 patterns are actually combinations of a single more important pattern. When you see 1-2-X on a row the X is always a mine.

Take some time to understand how this pattern works. There are two mines in three squares (because the 2 touches three squares) and there is one mine in the first two squares (because the 1 touches two of the three squares). The third square must contain the other mine.

Minesweeper 1-2-1 pattern

The 1-2-1 pattern has one solution.

Minesweeper 1-2-1 pattern

Apply the 1-2 pattern from the left.

Minesweeper 1-2-1 pattern

Apply the 1-2 pattern from the right.

Minesweeper 1-2-2-1 pattern

The 1-2-2-1 pattern has one solution.

Minesweeper 1-2-2-1 pattern

Apply the 1-2 pattern from the left.

Minesweeper 1-2-2-1 pattern

Apply the 1-2 pattern from the right.


Simple Logic

Minesweeper is a game of logic. Numbers are clues and your mission is to find the arrangement of mines consistent with those clues.

A common example is 1-1-X on a row starting from a border. The first 1 touches two squares and the second 1 touches three squares. Both clues are true so the third square must be empty. This logic is similar but opposite to the 1-2-X pattern which always has a mine in the third square. On corners the X in 1-1-X can wrap around a corner.

Minesweeper logic using 1-1-X

The pink 1 means there is one mine in the three squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The third square from the border must be empty.

Minesweeper logic using 1-1-X

The pink 1 means there is one mine in the three squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The third square from the border must be empty.

Minesweeper logic using 1-1-X

The pink 1 means there is one mine in the five squares it touches. The yellow 1 means the mine is in the subset of two yellow squares. The pink squares must be empty.

Minesweeper logic using 1-1-X

Each pink 1 means there is one mine in the five squares it touches. Each yellow 1 means the mine is in the subset of two yellow squares. The pink squares must be empty.

Sometimes a mine belongs to a subset of squares so the remaining squares must be safe.

Minesweeper logic using subsets

The pink 1 touches seven squares and the yellow 1 touches a subset of four squares. The mines must be in the yellow squares so the pink squares are safe.

Minesweeper logic using subsets

The pink 1 touches five squares and the yellow 1 touches a subset of two squares. The mines must be in the yellow squares so the pink squares are safe.

Minesweeper logic using subsets

The pink 2 touches four squares and the yellow 2 touches a subset of two squares. The mines must be in the yellow squares so the pink squares are safe.

Minesweeper logic using subsets

The pink 2 touches four squares and the yellow 4 (effectively a 1) touches a subset of two squares. The mine must be in the yellow squares so the pink squares are safe.

Sometimes instead of safe squares we can find mines.

Minesweeper logic finding mines

The 3 touches four squares. The yellow 1 touches a subset of two squares. The second and third mines must be in the pink squares.

Minesweeper logic finding mines

The 4 touches five squares. The yellow 1 touches a subset of two squares. The second, third and fourth mines must be in the pink squares.

Minesweeper logic finding mines

The 3 touches five squares. Each yellow 1 touches a subset of two squares. The third mine must be in the pink square.

Minesweeper logic finding mines

The pink 4 touches five unopened squares. One is flagged so there are three mines left in four squares. The yellow 2 touches a flag so there is one mine left in two yellow squares. The two pink squares must be mines.

You can combine these examples to form chains of logic alternating between finding mines, using 1-1-X and using subsets. It's not a coincidence that one of the earliest Minesweeper games was called Relentless Logic!

Combining Minesweeper strategies

Find the two mines and use 1-1-X to open the third square then open the pink squares.

Combining Minesweeper strategies

Find the three mines and use 1-1-X to open the third square then open the pink squares.

Combining Minesweeper strategies

Find the mine and use 1-1-X to open the third square then open the pink squares.

Combining Minesweeper strategies

Find three mines. The 4 effectively becomes 1 and the 2 effectively becomes 1. Use 1-1-X to open the third square then open the pink squares.


Pattern Reduction

Complex mine arrangements can be reduced to known patterns.

Subtract known mines from each number. For example, if you have flagged a mine touching a 3 it becomes a 2.

Reduced Minesweeper 1-2-1 pattern

1-2-1

Reduced Minesweeper 1-2-1 pattern

1-2-1

Reduced Minesweeper 1-2-2-1 pattern

1-2-2-1

Reduced Minesweeper 1-2-2-1 pattern

1-2-2-1

The next few examples are more complicated because you need to solve the situation in your head to see the pattern. If you do not see the patterns take turns reducing numbers and using 1-2-X to solve these examples.

Complicated Minesweeper patterns

1-2-1

Complicated Minesweeper patterns

1-2-2-1

Complicated Minesweeper patterns

1-2-2-1 and 1-2-1

Complicated Minesweeper patterns

1-2-1 and 1-2-1


The First Click

So where is the best place to make the first click?

You need an opening surrounded by numbers to start solving. Most players start games with two or three random clicks. Clicking in the middle produces bigger openings thus more numbers and an easier start to the game. However, openings in the middle are less common than openings near edges.

The Beginner (8x8) and Intermediate (16x16) levels on Windows Minesweeper generate a limited number of games that repeat in board cycles. In 2002, Tim Kostka generated every board and calculated the probability and average size of openings for each square. The probability of an opening increases towards edges but the size of openings increases towards the middle of the board. Similar calculations were performed for Expert.

Minesweeper first click openings

Average opening size on Beginner ranges from 18 to 32 squares.

Minesweeper first click openings

Average opening size on Intermediate ranges from 27 to 66 squares.

Minesweeper first click openings

Average opening size on Expert ranges from 16 to 41 squares.

Minesweeper first click probability

Opening probability on Beginner ranges from 0.19 to 0.60.

Minesweeper first click probability

Opening probability on Intermediate ranges from 0.21 to 0.60.

Minesweeper first click probability

Opening probability on Expert ranges from 0.12 to 0.50.

You might notice that the four squares in the top left corner produce the fewest and smallest openings. Windows Minesweeper makes the first click safe by shifting the mine to the first empty square on the top row starting from the left corner.

Windows Vista introduced guaranteed openings on the first click in which case you should always start in the middle. New players should start in the middle on all versions because despite losing more games in the first few clicks they will finish more games. For experienced players the best place to start is more complicated and depends on personal preference. Do you mind losing thousands of games an hour in the first three clicks to get bigger openings?


Guessing

Sometimes in Minesweeper you are forced to guess.

New players guess because it is easier than solving, but sometimes guessing is unavoidable. The optimal guessing strategy depends on whether your goal is to win or to win quickly.

The first strategy is to guess quickly. This is the best approach when there is no possibility of obtaining further information. It can also be effective if you are happy losing in order to win fewer games more quickly. Solving the rest of the board can often eliminate the guess but many professionals guess immediately to avoid incurring time moving the mouse to an easier location.

The second strategy is to guess only when you are forced to guess. If the squares touch other unopened squares solve the rest of the board first in the hope that approaching from a different direction will eliminate the guess.

A third strategy is to practice playing with no flags so you become better at looking for empty squares. Players who enjoy flagging often make the mistake of guessing mines when it is equally important to open safe squares.

Minesweeper guessing strategy

This 50:50 guess is unavoidable. The best strategy is to guess quickly.

Minesweeper guessing strategy

The pink squares are a 50:50 guess. The first strategy guesses quickly. The second strategy solves the rest of the board and hopes new information eliminates the guess.

Minesweeper guessing strategy

There could be 1, 2 or 3 mines in these four squares. The second strategy solves the rest of the board to determine the number of mines. If there are 1 or 3 mines no guessing is needed.

Minesweeper guessing strategy

You cannot deduce the mines. The third strategy forgets about mines and opens the safe pink squares. If each pink square is a 1 the blue squares can also be opened.

A fourth strategy makes the most useful guess. Sometimes one option eliminates another guess or makes the rest of the board easier to solve. For example, when there is a 33:66 situation on a row it is more useful to open the right or left squares. Opening the middle square forces you to make a second guess.

A fifth strategy considers probability. The mine density on Beginner (8x8) and Intermediate (16x16) is 0.156 and on Expert (16x30) is 0.206. When there is a 50:50 guess it is safer to open a random square! Remember that edges are more likely to be openings than squares near the middle. A special case is the top left corner where the probability of being a mine nearly doubles after the first click due to mine shifting.

Minesweeper guessing strategy

Avoid unecessary guesses. Instead of opening three squares in a row open the yellow squares first so you have time to react if the middle square is a mine.

Minesweeper guessing strategy

If you open the middle square you need to make another guess. The fourth strategy opens the blue square to eliminate the guess.

Minesweeper guessing strategy

There are multiple 50:50 guesses. The fourth strategy opens a useful square. If the blue square is a 3 or 7 it eliminates guessing. If the green square is 3 or 6 it could also eliminate guessing.

Minesweeper guessing strategy

There are multiple 50:50 guesses. The fifth strategy opens a "random" square. On Expert the blue square is 20:80, does not touch a 50:50 and is on an edge so might be an opening.

The sixth strategy is to calculate probability. This is the best strategy for winning games but can be complicated and time consuming. Local probability is easy to calculate but global probability is much more difficult. For example, it is easy to calculate that one mine in two squares is 50:50 but what if probability depends on all possible mine arrangements for the rest of the board? Sean Barrett has written an excellent guide to Minesweeper Advanced Tactics.

The following example considers all six strategies. The first strategy is to guess quickly and hope for the best. This approach will give the best score if you survive. The second strategy is solving the rest of the board to determine the number of mines remaining. There are 79 possible mine arrangements but only 1 solution has 9 mines. The third strategy opens a safe square but in this case there are none. The fourth strategy makes a useful guess. In this case there is one square (I) that solves the board if it is a 4 or 7. The fifth strategy guesses a square that does not touch a number (B, C, F, G) hoping Expert density of 0.206 comes to the rescue. The sixth strategy calculates global probability which ranges from 0.392 (D, K) to 0.798 (J).

Minesweeper complex guessing strategy

Three local 50:50 guesses.

Minesweeper complex guessing strategy

Three local 66:33 guesses.

Minesweeper complex guessing strategy

Preparing to calculate.

Minesweeper complex guessing strategy

Global probabilities.


No Flags

Minesweeper is won by opening all safe squares. Flagging every mine is a waste of time. On Intermediate a NF player needs to open 216 safe squares but an inefficient Flagger also needs to flag 40 mines. However, remember that chording can open multiple squares.

NF players look for openings instead of mines. Openings propagate in all directions until they are surrounded by numbers. The statistic for board difficulty is 3BV which counts the minimum number of left clicks required to clear a board. Numbers surrounding openings are not counted because clicking on border numbers is redundant. Low 3BV boards favour NF players because there are more openings with the mines grouped into islands. The perfect board for a NF player would only consist of openings with all numbers being borders. When a NF player identifies multiple safe squares the ones known to contain numbers which might be borders are opened last.

The special skill of NF technique is "seeing" mines in order to use logic such as 1-1-X and subsets to search for openings.

Minesweeper NF technique

The only reason to flag the pink squares is to make them look pretty.

Minesweeper NF technique

The NF technique "sees" the two mines touching the left 3 and uses 1-1-X twice to open the blue squares.

Minesweeper NF technique

The NF technique "sees" the two mines touching the 3 and uses 1-1-X to open the 1. The yellow squares will be numbers but the blue square could be an opening.

Minesweeper NF technique

The NF technique "sees" the three mines touching the 4 and uses 1-1-X to open the 1. The yellow squares will be numbers but the blue square could be an opening.

Minesweeper NF technique

Pink squares are mines and yellow squares will be numbers. The blue squares might be openings.

Minesweeper NF technique

Pink squares are mines and yellow squares will be numbers. The blue squares might be opening.

Minesweeper NF technique

Pink squares are mines and yellow squares will be numbers. The blue squares might be openings.

Minesweeper NF technique

The pink squares are 50:50 guesses so the yellow squares will contain numbers. A NF player should guess a blue square.


Efficiency

Fewer clicks means less time.

The first rule is never flag a mine unless you are going to chord.

The second rule is to chord efficiently. New players flag then chord multiple times on all nearby numbers. Practice slowly being careful to chord only on numbers that will clear squares. Also practice chording on the number in each case that will open the most squares. This practice will improve your chording efficiency during normal speedplay.

The third rule is to use 1.5 Click technique when you chord. The inefficient way to chord requires four actions. You press and release the right mouse button to flag then press and release both buttons to chord. The efficient way to chord involves three actions. You press the right mouse button to flag, start pressing the left mouse button as you slide onto a number then release both buttons to chord. This reduces time spent chording by 25%.

Minesweeper efficiency

There is no reason to flag this mine because no squares can be opened by chording.

Minesweeper efficiency

Chording on a 2 opens one square but chording on a 1 opens two squares. Use the 1.5 Click to flag and slide onto the 1 to chord.

Minesweeper efficiency

Use the 1.5 Click to flag and slide onto the yellow 1 to open four squares. Do not chord the pink 1.

Minesweeper efficiency

Do not flag the pink squares because you cannot chord on them. Use the 1.5 Click to flag and slide onto the yellow 1 to chord. Do not chord the pink 2.

The fourth rule is to switch between flagging and NF for local efficiency. Flaggers need to practice NF to eliminate the short pause that occurs when switching to a less familiar playing style. Practice slowly being careful to choose the most efficient solution for every local situation. The global rule is that high 3BV favours flagging because there are more numbers while low 3BV favours NF because there are more openings. The local rule is that high numbers (5,6,7,8) favour NF because there are fewer squares to open while low numbers (1,2,3,4) favour flagging because chording opens more squares.

Minesweeper efficiency

Play NF and solve with one click. Flagging takes between 1.5 and 4 clicks depending on efficiency.

Minesweeper efficiency

Play NF and solve with one click. Flagging takes between 2.5 and 3.5 clicks depending on efficiency.

Minesweeper efficiency

An efficient Flagger uses the 1.5 Click to flag and chord. A NF player takes three clicks. An inefficient Flagger uses three flags and chords three times.

Minesweeper efficiency

A NF player hopes for openings and takes 3 to 6 clicks. An efficient Flagger uses the 1.5 Click three times. An inefficient Flagger uses three flags and chords five times.

Minesweeper efficiency

An efficient Flagger uses the 1.5 Click once to flag and chord. Total 1.5 clicks.

Minesweeper efficiency

A NF player clicks the yellow square hoping for an opening. Total 1 to 4 clicks.

Minesweeper efficiency

An efficient Flagger uses the 1.5 Click once then chords again then opens the yellow square. Total 3.5 clicks.

Minesweeper efficiency

A NF player clicks the yellow squares and hopes for an opening. Total 3 to 6 clicks.

The fifth rule is to shorten your mouse path. The mouse should not move unless there is a purpose. New players move the mouse when their eyes move and they jump around the board looking for easy patterns. Experienced players solve several moves in advance and scan the board while continuing to solve locally. In addition, most players prefer moving the mouse in certain directions and often move the cursor further than needed to solve from their favourite direction. Practice solving from your weaker directions so you become better at choosing the most efficient route during normal speedplay.

The statistic for efficiency is IOE which measures total clicks divided by 3BV. A board with a 3BV of 50 can be solved in 50 left clicks for an IOE of 1.00. However, it is possible to solve a board in fewer clicks than 3BV with efficient chording. Use a version such as Minesweeper Arbiter that saves IOE records and practice playing slowly for efficiency. This practice will gradually improve your efficiency during normal speedplay.

Minesweeper efficiency

A new player will jump to an easier part of the board. An experienced player instantly sees the pink mine and safe yellow squares and does not waste time moving to another location.

Minesweeper mouse path efficiency

Do you naturally start at the top or from the bottom? Practice the opposite direction.

Minesweeper mouse path efficiency

An extremely efficient mouse path on Expert. Flags are green and chords are purple while left clicks are blue.

Minesweeper mouse path efficiency

An inefficient mouse path on Expert. Flags are green and chords are purple while left clicks are blue.


Final Thoughts
  • Open the game menu and untick the option to use questionmarks. You can now remove flags with one click instead of needing two clicks.
  • Instead of using the smiley face or game menu to start games use the [F2] button. Keeping one finger on the keyboard is the fastest way to start games.
  • If you accidentally click on a mine slide the cursor onto a safe square before releasing the mouse button.
  • Ignore the timer. Looking at the clock wastes times and makes you nervous.
  • Look with your eyes not your mouse. New players follow their eyes with the mouse cursor.
  • Players who flag should practice NF to make switching between styles for efficiency second nature.
  • Play custom games with more mines to practice solving. Your speedplay will benefit from improved pattern recognition.
  • Occasionally play as fast as possible without caring about mistakes. Pushing your speed boundary improves your average speed.
  • Play in a warm room and heat your hands. This increases blood flow and reaction time.
  • Take breaks and exercise. This increases blood flow and reaction time.
  • Listen to music to distract your brain. Reducing conscious thinking saves time and reduces mouse handling errors.
  • Buy an ergonomic mouse that fits your hand and avoid resting weight on your wrist. Carpal Tunnel Syndrome has forced many great players to retire.
  • Open your mouse and clean the lint off the rollerball...if you still live in the 1990s!

Historical Links

Minesweeper Guide (1992)
First mention of the 1-2-1 and 1-2-2-1 patterns.

Minesweeper Page (1996)
Short introduction to the rules of the game.

Minesweeper For Beginners (1996)
Introduction to logic with an early mention of random guessing and a recommendation to start in the middle.

Hall of the Minesweeper (1996)
Basic gameplay and the 1-2-1 pattern.

Minesweeper Tips (1997)
Detailed examples of 1-1-X and 1-2-X with a brief mention of reduction ("equivalency").

The Minesweeper Page (1997)
Detailed guide with many examples of patterns, reduction, basic logic and guessing strategies.

A Mathematical Introduction to the Game of Minesweeper (1997)
Theorems and notation for the 1-2-1 pattern and its reduction ("Relative 1-2-1 Theorem").

Minesweeper Strategies and Tactics (1999)
List of tips for playing Minesweeper including guessing strategies and how to play efficiently.

Minesweeper Strategy (1999)
Short introduction to basic gameplay with an early mention of NF style.

Minesweeper Advanced Tactics (1999)
Detailed analysis of global probability.

Intermediate Hall of Fame (2001)
Introduction to patterns and reduction ("hidden patterns") discussing efficiency and guessing quickly.

First Click (2002)
Detailed analysis of opening size and probability for each Minesweeper level.

Minesweeper Advanced Play (2003)
Theoretical reasons for openings being more likely in the middle of the board.

The Minesweeper Handbook (2003)
Basic gameplay including 1-1-X ("partial determinism") and efficient chording.