Minesweeper opening patterns

Only the edge tells you anything

A number counts the mines in the eight cells touching it. That means the only cells carrying information are the numbers sitting directly against unopened ground — the edge of the open region. A number surrounded entirely by opened cells is spent, and a cell far away from any number is unknowable.

So the habit is not to scan the board. It is to walk the boundary, one number at a time, and ask two questions at each:

1. Are its mines already flagged? If a 2 is touching two flags, every other cell it touches is safe and can be opened immediately.
2. Does it have exactly as many unopened neighbours as it needs? If a 3 touches exactly three unopened cells, all three are mines.

Those two checks alone clear a surprising amount of board. Everything below is what you do when both come back negative.

The 1-1 pattern

Two 1s side by side, with unopened cells below them and a wall or an opened cell closing off one end. On its own a 1 tells you almost nothing — but a 1 that shares its unopened cells with a neighbour is a different matter.

This is worth saying plainly because it surprises people: you can prove a cell safe without knowing where the mine is. You are not identifying the mine, you are showing it has nowhere left to be.

The pattern only works when something closes off the left-hand end — the board edge, a wall of opened cells, or an already-placed flag. Without that, the left 1 has three unopened neighbours instead of two and the argument collapses. Checking for that closed end is the mistake to avoid.

The 1-2-1 pattern

Three numbers in a row reading 1, 2, 1, with three unopened cells beneath and nothing else touching them. This one resolves completely: you learn the position of both mines and the safe cell.

The mirror image, 1-2-2-1, turns up almost as often. There the two middle cells are the mines and the outer two are safe. Both patterns run vertically as well, and both are worth recognising as a shape rather than re-deriving each time.

Subtracting flags before you compare

The patterns above assume the numbers you are reading are untouched. In the middle of a board they usually are not — there are already flags nearby. The fix is simple: subtract the flags a number already touches, and read what is left.

Do this mentally on every number before comparing it with a neighbour. A board that looks like an impassable wall of 2s and 3s often turns into a row of effective 1s once the flags are taken off, and the ordinary patterns reappear.

When there is genuinely nothing to prove

Minesweeper, unlike Sudoku, can reach positions where no cell is provably safe. That is a property of the game, not a fault in the board. When it happens, guess deliberately rather than randomly:

• Guess where the count helps you. Compare the mines left with the unopened cells left. If eight mines remain in forty unopened cells, a cell in an isolated region is far better odds than one on a tense boundary.
• Open a corner or an edge. Those cells have fewer neighbours, so whatever you learn constrains a smaller area and is more likely to be conclusive.
• Guess in the largest unopened area. A safe result there opens a big region and gives you a lot of new numbers, whereas a safe result on the boundary often gives you one number and the same problem.

Our first click is always safe, so nothing is ever lost before the board has told you anything. After that, a lost run on a large board is usually one careless flag rather than genuine bad luck — it is worth noticing which of the two happened.