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Minesweeper Strategy: Patterns, the First Click and When to Guess

The numbers on this page come from an automatic solver playing this site's own version of the game — its boards, its first-click rule — 20,000 games or more for every figure. The solver never makes a logical mistake and, when it must guess, picks the cell with the lowest exact chance of a mine.
The short answer

Minesweeper is mostly deduction, but not entirely. A solver that never makes a logical mistake clears 96% of Beginner boards and 87% of Intermediate, but only about half of Expert: on Expert 84% of games need at least one guess. Click the centre first — on this site the first click always opens a region, and the centre opens the biggest one. Learn the patterns 1-1, 1-2, 1-2-1 and 1-2-2-1, and when you have to guess, choose the cell least likely to hold a mine rather than the one nearest your last click.

How this version works

LevelBoardMinesMine density
Beginner9 × 91012.3%
Intermediate16 × 164015.6%
Expert16 × 309920.6%
  • The first click always opens a region. The mines are laid only after it, and neither the clicked cell nor any of its eight neighbours may hold one — so the first cell is always a zero.
  • A number counts mines among its eight neighbours, diagonals included. A zero opens its whole connected area by itself.
  • Flags: right click, Ctrl/Cmd + click, or a long press on a phone. There are no question marks.
  • Chording: click an opened number that already has exactly as many flags around it as it shows, and all its other neighbours open at once. One wrong flag and you blow up.
  • You win when every cell without a mine is open; flagging the mines is not required.

Where to click first

Because the first click here is always a zero, the only question is how big a region it opens — and that depends on where it lands. A corner cell has only three neighbours, so the guaranteed-clear patch is 2×2; in the middle of the board it is 3×3.

First clickBeginner: wins / cells openedIntermediateExpert
Corner95.8% / 2884.4% / 2743.7% / 16
Middle of an edge96.4% / 3686.8% / 41about 48% / 25
Centre96.1% / 4686.7% / 6449.7% / 41

On Beginner and Intermediate the difference is within the noise. On Expert the centre is worth about six points of win rate over a corner. The classic advice to start in a corner comes from versions in which the first click is only guaranteed not to be a mine: there a corner, with fewer neighbours, is the cell most likely to be a zero. Here every first click is a zero, so the advice turns upside down.

Win rates of the solver, 20,000 games per cell of the table; cells opened is the average size of the first region.

The two rules that solve most of a board

Only numbers on the border between opened and covered cells carry information. Two rules, applied over and over along that border, do most of the work:

A 1 that already touches a flag: every other covered neighbour is safe (✓).
A 2 with exactly two covered neighbours: both are mines (✗). · marks an opened cell whose number does not matter here.

When one number says nothing on its own, compare it with its neighbour. If the covered cells around one number all lie inside those around another, subtract: the difference in the numbers is the number of mines in the cells only the second one can see. Every pattern below is this subtraction, done once and remembered.

Four patterns worth knowing by sight

Each of these was checked by trying every possible arrangement of mines in the covered cells. In the first two the left edge of the picture is the edge of the board (any opened column works the same way).

1-1 against a wall. One mine among the first two covered cells, so the third (✓) is safe.
1-2 against a wall. The 2 needs a mine the 1 cannot see: the third cell (✗) is a mine.
1-2-1. Mines sit opposite the ones (✗); the cell over the 2 and the two outer cells are safe (✓).
1-2-2-1. Mines sit opposite the twos (✗); everything else in the row is safe (✓).

These patterns appear along straight stretches of the border, which is where most of the board is solved. Spotting them at a glance is worth more time than clicking fast.

When logic runs out: guessing well

Sometimes no deduction exists: two arrangements fit the numbers equally well, and only a click will tell. How often that happens depends on the level far more than on skill:

LevelGames that need a guessGuesses per gameSolver's win rate
Beginner9.4%0.1296.1%
Intermediate29.0%0.4686.7%
Expert83.8%2.7349.4%

First click in the centre; 20,000 games per level, 100,000 on Expert.

A forced guess is rarely a good bet: the cells the solver had to pick held a mine about 32%, 28% and 18.5% of the time on the three levels. So guess as little and as well as you can:

  • First make sure it is a real guess. Look for the patterns above and for subtraction between two numbers; most “guesses” are missed deductions.
  • Prefer cells touched by few numbers. On Expert a covered cell next to no opened number held a mine 19.9% of the time when the solver had to guess, next to one number 30.9%, next to two 37.8%, next to three 48.3%.
  • But count when you can. In about nine guesses out of ten the safest cell, by exact count, was on the border after all — a number can make one of its covered neighbours much safer than the board average.
  • Corners are not safer. In guessing positions a corner held a mine as often as an edge or an interior cell (22.7%, 22.4% and 23.5% on Expert).
  • Use the mine counter at the end. With few cells left, the total number of mines often decides between two arrangements the numbers alone cannot tell apart.

Where the computer comes in

Minesweeper is the only solitaire among the games here. There is no opponent: the computer only scatters the mines at random after your first click, and on the shared score of the site a cleared board counts as your win and an explosion as the computer's. The level changes only the board and the density of mines.

What the solver's results do tell you is where the ceiling is. A board cleared on Beginner is expected; on Intermediate, losing one game in eight is about what perfect logic loses too; on Expert, winning half your games means you are playing about as well as the board allows.

The mistakes that cost the most games

  • Starting in a corner. Here it opens the smallest region and costs about six points of win rate on Expert.
  • Guessing where a deduction exists. Check every number on the border, and every pair of neighbouring numbers, before clicking blind.
  • Guessing next to a crowd of numbers. A cell touched by three or four numbers is a mine almost half the time in guessing positions.
  • Chording on an unchecked flag. One wrong flag turns the shortcut into an explosion.
  • Forgetting the mine counter in the endgame, where it settles positions the numbers cannot.

Questions and answers

Is Minesweeper luck or skill?

Mostly skill, with a level-dependent dose of luck. A solver that never errs wins 96% of Beginner boards, 87% of Intermediate and about half of Expert; the rest is lost on forced guesses, which on Expert happen in 84% of games.

Can every Minesweeper game be solved without guessing?

No. Some positions allow two or more mine arrangements that the numbers cannot tell apart. Here that happens in about 9% of Beginner games, 29% of Intermediate and 84% of Expert games, even for a perfect logical player.

Where should you click first in Minesweeper?

In this version, the centre: the first click is always a zero, and the centre opens the largest region — about 41 cells on Expert against 16 in a corner, and about six points more wins. In versions where the first click is merely safe, a corner is more likely to be a zero.

What is the 1-2-1 pattern?

Three numbers 1, 2, 1 in a row along a straight edge of covered cells. The mines are opposite the two ones, and the cell opposite the 2 is safe. Its longer cousin, 1-2-2-1, has the mines opposite the two twos.

What is the best way to guess in Minesweeper?

First make sure no deduction is left. Then pick the cell with the lowest chance of a mine: as a rule of thumb, one touched by as few numbers as possible; better still, count the arrangements, because the safest cell is often on the border next to a low number.

What is a good win rate on Expert?

About 50%. A solver that never makes a logical error and always takes the safest guess wins about 49% of Expert games here; the board itself forces guesses in 84% of games.

Is the first click always safe?

Here, yes, and more: the mines are placed after the first click, away from the clicked cell and all eight of its neighbours, so the first click always opens an empty region.

Is Minesweeper NP-complete?

Deciding whether a given Minesweeper position is consistent is NP-complete, as Richard Kaye showed in 2000. In plain terms there is no known fast method that works on every position, which is why some positions really are hard.

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Where to go from here
To cite this page: “Minesweeper Strategy: Patterns, the First Click and When to Guess”, You vs Computer, https://youvscomputer.com/games/minesweeper-strategy.html