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Classic minesweeper is not always solvable by logic. Mines are placed at random, and some positions simply do not contain enough information. What separates a good player from a lucky one is what happens then: first making sure it really is a guess, and then taking the tile with the best odds.
First: is it really a guess?
Most "guesses" are deductions nobody looked for. Before you risk anything, read every number along the edge of the open area again, check the common patterns, and count the mines that are left: near the end of a board the counter in the corner often settles a position that the numbers alone cannot.
The odds around one number
If a number still needs m mines and has t hidden tiles around it that nothing else tells you about, each of those tiles is a mine with probability m ÷ t.
Compare with the rest of the board
A tile that no number touches is not free of risk. Its odds are roughly the mines still unaccounted for divided by the hidden tiles they could be in. At the start of a board that is simply the mine density:
| Board | Mines | Odds for an untouched tile |
|---|---|---|
| Beginner | 10 | 12.3% |
| Intermediate | 40 | 15.6% |
| Expert | 99 | 20.6% |
Now the two diagrams mean something. On Expert, a tile next to that lone 1 (12.5%) is a much better guess than a random tile elsewhere (20.6%). A tile next to the lone 3 (37.5%) is much worse: leave it and open something far away instead. The rule in one line: guess where the number is small compared with the tiles around it, and stay away from big numbers.
The honest 50/50
When two tiles share one mine and every number that touches one also touches the other, no later move changes the odds. Waiting gains nothing, so take it when you get there instead of leaving it for the end: if it goes wrong, you have lost the least time. If numbers you have not opened yet could still split the pair, it is not a true 50/50: open those first.
Not all safe tiles are worth the same
Two guesses with the same odds can be very different in value. A tile in the middle of unknown ground may be an empty tile that opens a whole area; a tile wedged between numbers will only show one more number. With equal risk, take the guess that can give you the most information.
When is a guess worth it in multiplayer?
In a solo run a mine ends the board, so you guess only when you must. In multiplayer minesweeper a mine costs two points and 2.5 seconds, which you can weigh against what the guess might win. In a 1v1 duel there are 388 safe tiles and territory pays up to 12 points, so one point is about 32 tiles.
- A blind guess on that board is a mine about 17% of the time. At two points a mine, it pays for itself only if a safe result opens around 13 tiles or more on average: an opening, not a single number.
- Your first mine of a round also throws away the Flawless bonus (+2), so it really costs four points. Early in a round, do not guess for less than a big opening.
- With seconds left, the stun no longer matters and unopened tiles are worth nothing to anybody. That is the moment to gamble.
Practise without the luck
The first click in the Drill Yard always opens an area, so no run starts with a coin flip. After that it is real minesweeper: play a few boards and, every time you are about to guess, say the odds out loud first. It becomes automatic surprisingly fast.