How to play Minesweeper without guessing

Most lost games are not bad luck. They are a deduction you did not see yet. Here are four rules that find it.

Rule 1: read a number as a counting problem

A number says how many hidden mines touch that tile. Count the hidden tiles around it. If there are exactly as many hidden tiles as the number, all of them are mines. If the number is zero, all of them are safe.

Once a number has all its mines flagged, every other hidden tile around it is safe. This one step does most of the work in the early game.

Rule 2: compare two neighbouring numbers

When two numbers look at almost the same tiles, subtract them. The tiles that only one of them sees must hold the difference.

The classic case is the 1-2-1 along a wall. The left 1 sees three tiles above it, the 2 sees the next three, and so on. The 2 minus the left 1 leaves one mine in the tile that only the 2 sees on the right; the 2 minus the right 1 leaves one mine on the left. Both mines sit above the two 1s, and the tile above the 2 is safe.

Rule 3: use the total

If the game tells you how many mines there are in all, keep count. Late in the game the total often settles a corner that the numbers cannot: if only two mines remain and two separate areas each need one, nothing else is a mine.

Rule 4: suppose, then check

When no rule gives an answer, pick a tile and suppose it is a mine. Follow what that forces on its neighbours, using only Rules 1 and 2. If a number can no longer add up, the supposition is impossible, so the tile is safe. Do the same with "suppose it is safe" to prove a mine. This is a proof by contradiction, and it is the one thing you need on the hardest boards.

Habits that help

• Scan the edges and corners first: they have fewer neighbours, so the counts are easier.
• Prefer a deduction that opens a tile over one that flags a mine. Flags only help you think; they do not win the game.
• Never guess while a deduction exists. If you cannot see one, look for the numbers that share tiles and compare them.
• If a board truly needs a guess, that is a flaw in the board, not in you (see luck or logic?).