Minesweeper with no guessing
Every board here is checked before you see it. If any square on it cannot be worked out by reasoning, the board is fixed or replaced until every square can. You will never be asked to flip a coin.
What goes wrong in the ordinary game
Minesweeper is counting. Each number tells you how many mines touch that square, and the whole game comes out of that. Until you reach something like this.
Both clues read one. Both of them are touching A and B, and neither is touching anything else that is still covered. So exactly one of the two is a mine, both clues say so, and the board ends there, which means there is no third clue anywhere that could break the tie.
You can play forty moves correctly and arrive here. Then you pick one and find out. About half the time, a board you solved properly ends in a loss you had no way to avoid.
Players call it a fifty-fifty. It is the single most common reason a good game of minesweeper ends badly, and it is not a mistake you made.
How this site prevents it
Before any board is handed out, a solver plays it.
It starts where you would start, at the opening square and the cascade around it, and it works only from what a player could see at that point. It does not read the mine layout to decide its next move. The only thing it asks the board is what number sits under a square it has already proved is safe, which is exactly what you learn by clicking one.
It has two ways of reasoning, and they are the two you use. First: a number whose mines are all accounted for makes every other neighbour safe, and a number with exactly as many covered neighbours as it has mines makes all of them mines. Second: when two numbers overlap, the difference between them can be settled on its own. That second rule is what solves the 1-2-1 and the 1-2-2-1, and it is what most players mean when they say a board needs no guessing.
Then it checks what is left. If a single covered square remains that neither rule can decide, the board is not handed over.
What happens next is the part worth knowing, because it is not what you would guess. The board is not thrown away. A stuck corner is a local fault on a board that is otherwise perfectly good, so one mine beside the sticking point is moved somewhere else and the whole proof is run again. That can happen up to two hundred times on a single board. Only when repair keeps failing is the board abandoned, and a fresh one built from the next seed.
One deliberate omission is worth knowing about. The solver is not allowed to count the mines remaining. A solver that counts can certify more boards, but it would be promising something only to players who are also counting. Boards that need the mine counter to break a tie are thrown out here along with the rest.
One you can play
This board went through everything above. Nine by nine, ten mines, and the generator had to move one mine before it would certify — this is a repaired board, not a lucky one. Clearing it takes the overlap rule twice; neighbourhood counting alone will not finish it.
There is an answer, and every step to it is a deduction. If you hit a mine, undo and carry on.
The rest of the game
The full game runs at the three classic sizes, with a fourth tier graded on how often the overlap rule is needed. Losing is recoverable: hitting a mine is recorded and then you carry on, because a board you have been reading for ten minutes should not be lost to one slip of the hand.