Strategy guides › Minesweeper
Minesweeper: where to tap first, the patterns, and when to guess
▶ Play Minesweeper🎯 Try board 15 (tap the centre first)
Two numbers left on the board, a 2 and a 2, three hidden squares between them, eleven seconds on the clock. You stare. You flag. You un-flag. Then you tap, and the field turns red. Was that bad luck, or was there something to see?
To answer that properly, we built a solver for our Minesweeper and let it play. It only opens a square it can prove is safe, and when it cannot prove anything, it computes the exact chance of a mine under every square and taps the lowest. We gave it 1,000 boards of each size, with three different first taps, and counted what it needed.
Tap the centre first
Our game guarantees that the first tap is safe, and it guarantees more than that: the mines are placed after you tap, and none of them goes on your square or on any of the eight around it. So your first square is always a 0, and it always opens an area. Where you tap decides how big that area is, and that turns out to matter a lot. Small is 9×9 with 10 mines, Medium 16×16 with 40, Large 24×16 with 70.
| Board | First tap | Squares opened | No guess needed | Solver wins |
|---|---|---|---|---|
| Small | corner | 27.5 | 80.2% | 95.2% |
| centre | 45.5 | 91.5% | 96.3% | |
| Medium | corner | 26.7 | 59.6% | 84.0% |
| centre | 64.7 | 72.9% | 88.2% | |
| Large | corner | 20.9 | 32.7% | 67.5% |
| centre | 52.6 | 44.3% | 74.2% |
Tapping the middle of an edge lands in between on nearly every measure. A common piece of advice for classic Minesweeper is to start in a corner, because a corner square is more likely to be a 0 there. In our version the first square is a guaranteed 0 wherever you tap, so that argument disappears, and the centre wins: it opens nearly twice the area and leaves a board that can be cleared without a single guess far more often.
The 1-1 against a wall
Most deductions are single-number ones: a 1 with only one hidden neighbour, or a 3 with exactly three. On Small, 648 of the 1,000 centre-first boards could be cleared with nothing more. The next step up is comparing two numbers side by side, and you will use it constantly. Here is a real example: the top of board 15 after the first tap and a few single-number moves, which place two flags and open the two 3s.
The rule behind it: if the hidden squares around one number are all also around a neighbouring number, compare the counts. Whatever is left over has to hold exactly the difference. When the difference is zero, the leftovers are safe.
1-2-1 and 1-2-2-1
Two patterns of that rule come up so often that experienced players read them at a glance. Both apply to a straight line of numbers with hidden squares on one side only.
The proof of 1-2-1 is short. If the mine for the left 1 were directly above the 2, it would also satisfy the right 1, and then the 2 would only ever see one mine. So the square above the 2 is clear, and both mines sit diagonally, one above each 1. The 1-2-2-1 works the same way from both ends.
On Small boards, patterns like these (our solver’s “compare two numbers” step) were the hardest thing needed on 170 of 1,000 centre-first boards. On Large they matter far more: only 37 of 1,000 Large boards could be finished with single-number logic, 201 needed the comparisons, and 205 more needed reasoning over a whole frontier at once, the kind where you count how the mines could be arranged.
When you must guess, guess well
Some boards cannot be cleared by logic. With a centre first tap, that was 8.5% of Small boards, 27.1% of Medium and 55.7% of Large. These are not mistakes; they are part of random Minesweeper. What you control is which square you guess.
Squares away from the numbers have a mine chance of roughly the mines left divided by the squares left. Our Large board starts at 70 mines in 384 squares, so an untouched square is a bit under one in five. Squares next to numbers can be much safer or much worse: the squares around a 1 with seven hidden neighbours share one mine, about one in seven each, which beats open ground on Large, while the squares around a 3 with four hidden neighbours are, on average, three-in-four bad. On Medium and Large, the best square our solver found when stuck had a median mine chance of 20% and 14%.
Some guesses cannot be improved. A pair of squares where one is a mine and the information around them is perfectly symmetric is a true coin flip. On Small, 58% of the forced guesses our solver met were exactly 50/50, typically two squares squeezed between the wall and a number; on Large only 25% were. If you meet one, take it early. A guess you must make anyway costs less time when you make it first.
Two last habits. Keep an eye on the mine counter at the top: near the end, the number of mines left often decides between two arrangements. And when a number already has all its mines flagged, tap the number itself: our game then opens all its other neighbours in one go.
Practice
Board 15 on Small, with your first tap in the very centre, is a no-guess board. The first tap opens 56 squares, the two 1-1 deductions above are the only comparisons it needs, and everything else falls to single numbers. The link opens the same field for everyone who taps the same first square.
Start in the middle, compare your neighbours, and save the coin flips for last.
