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.
| Level | Board | Mines | Mine density |
|---|---|---|---|
| Beginner | 9 × 9 | 10 | 12.3% |
| Intermediate | 16 × 16 | 40 | 15.6% |
| Expert | 16 × 30 | 99 | 20.6% |
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 click | Beginner: wins / cells opened | Intermediate | Expert |
|---|---|---|---|
| Corner | 95.8% / 28 | 84.4% / 27 | 43.7% / 16 |
| Middle of an edge | 96.4% / 36 | 86.8% / 41 | about 48% / 25 |
| Centre | 96.1% / 46 | 86.7% / 64 | 49.7% / 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.
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:
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.
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).
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.
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:
| Level | Games that need a guess | Guesses per game | Solver's win rate |
|---|---|---|---|
| Beginner | 9.4% | 0.12 | 96.1% |
| Intermediate | 29.0% | 0.46 | 86.7% |
| Expert | 83.8% | 2.73 | 49.4% |
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:
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.
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.
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.
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.
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.
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.
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.
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.
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.