Advanced solving techniques

Once you know the rules, the difference between a player who stalls on an expert board and one who clears it is a small set of repeatable deductions. Almost every safe square can be found by logic; the rare exceptions are true 50/50s, and even those can usually be dodged. The goal of every technique below is the same: prove a covered square is a mine, or prove it is safe, without ever clicking blind.

If you are new to the game, read the beginner's guide first, and keep the glossary handy for any unfamiliar terms. In the diagrams below, a digit is a revealed number, . is a covered cell of unknown state, F is a cell you have proven is a mine, and o is a cell you have proven is safe.

1. Counting: the two trivial cases

Every deduction in minesweeper ultimately reduces to counting. For any revealed number, look only at the covered squares it still touches and apply two simple checks.

All mines: if a number equals the count of its remaining covered neighbors, every one of those neighbors is a mine. All safe: if a number already has that many mines flagged around it, every other covered neighbour is safe.

A "2" with exactly two covered neighbors:

. . .
. 2 .      <- only two covered cells touch the 2
F . F      <- both must be mines

A "1" that already has its mine:

F . .
. 1 o      <- the 1 is satisfied; every other
. o o         covered neighbour is safe

These two cases alone clear a surprising amount of any board. Run them on every edge number after each move before reaching for anything fancier.

2. Subset elimination (comparing two numbers)

When counting alone stalls, compare two nearby numbers that share covered squares. If one number's set of covered neighbors is contained inside another's, you can subtract the smaller from the larger and learn about the leftover cells.

Suppose a 1 and a 2sit side by side and the 1's covered cells are all also touched by the 2. The 2 needs one more mine than the 1, and that extra mine has to live in the cells the 2 sees but the 1 does not. If those extra cells number exactly one, that cell is a mine.

Covered cells a b c touch the 1.
Covered cells a b c d touch the 2.

1 needs 1 mine among {a,b,c}
2 needs 2 mines among {a,b,c,d}
=> d must be a mine (the extra mine the 2 demands)

This subset trick is the engine behind most of the named patterns below — they are just subset elimination applied to common shapes you learn to recognise on sight.

3. The 1-2-1 and 1-2-2-1 patterns

These are the patterns expert players spot instantly. When you see the numbers 1 2 1 in a straight line along a wall of covered cells, the mines are under the 1s and the cell under the 2 is safe.

1 2 1      <- revealed numbers along an edge
F o F      <- mines under the 1s, safe under the 2

The cousin pattern 1 2 2 1 puts the two mines under the 2s and leaves the cells under the 1s safe:

1 2 2 1
o F F o    <- mines under the 2s, safe under the 1s

Both fall straight out of subset elimination, but memorising the shapes saves real time. Watch for them along the straight frontiers that form as a board opens up — they appear constantly.

4. Chording for speed

Chording is the single biggest speed technique. Once a revealed number has exactly the right number of flags around it, click the number itself (a left-and-right click together, or a middle-click) to instantly reveal all of its remaining covered neighbors at once. One action clears several safe squares.

Chording only saves time if your flags are correct. If even one flag around the number is wrong, chording will reveal a real mine and end the game. Flag with certainty, then chord aggressively — this is how fast players cascade through a board far quicker than clicking each square.

F . .
. 1 .   <- the 1 has its one flag; chord the 1
. . .   -> all seven other neighbors reveal at once

5. Using the total mine count

The counter above the board is itself a clue, and beginners forget it. The number of mines still to be found is global information that local numbers cannot give you. Late in a game it often resolves situations that look impossible to read from the edge numbers alone.

Two common end-game uses: if the mines remaining exactly equals the count of covered squares left, every one of those squares is a mine — you have already won, because all the safe squares are revealed. And if the mines remaining is zero, every covered square is safe — reveal them all. In between, subtract the mines you have already accounted for in one region to learn how many must be spread across the rest.

6. Surviving the 50/50

Sometimes logic genuinely runs out: two covered squares are each equally likely to hold the last mine, with no clue able to break the tie. That is a true 50/50, and it is the one moment minesweeper can force a guess. Before you accept it, make sure it is real — most apparent 50/50s dissolve once you recount a nearby number or check the total mine counter against the covered squares remaining.

When a 50/50 is unavoidable, manage the risk instead of fighting it. Resolve every other certain square first so a wrong guess costs you the fewest possible safe clicks, and guess earlier rather than later, when more of the board is still in play. You can also reduce how often 50/50s appear by clearing from the open center outward and leaving tightly boxed-in corners for last, since corners are where forced guesses most often hide.