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50/50s in Minesweeper

A 50/50 is a spot where two squares are equally likely to hide a mine and no number on the board can tell them apart. On a random board it is the most common way to lose a game you were playing well. The percentages in the pictures are worked out by trying every arrangement of mines that fits the numbers; none of them are estimates.

Two squares in the corner, one mine

The 5 already has four flags and the 2 has one, so each still needs exactly one mine — and both touch the same two hidden squares and nothing else hidden. The mine can sit in either square and every number stays true. Two arrangements, one mine each: 50% for each square. No amount of looking changes that. This is a true 50/50.

Two separate pairs

Each pair is its own 50/50 and nothing links them, so you have to guess twice. The chance of getting through both is one in four. Pairs like these, left between flags near the walls, are why random expert boards so often end on luck.

Three squares in a corner, one mine

Only the 5 touches these three squares, and with four flags around it, it needs one more mine. That allows exactly three arrangements, one mine each, so each square hides the mine one time in three. It is still a guess, but not a coin flip: a guess here goes right two times out of three.

Looks like a guess, but isn't

Three hidden squares and the 1 in the bottom-left corner touches all of them, which looks like a one-in-three guess. But the 1 two squares to its right touches only the two squares on the right of the three, and it also needs one mine. So that mine is the corner 1's mine too, and the square on the left edge is safe. Then the 3 at the top has only one hidden square left for its last mine. That comparison is the 1-1.

Before you guess

Why you will not meet one here

Every board on this site is solved before you see it, and a board that would need a guess anywhere is thrown away and drawn again. The pictures on this page are the shapes that filter removes.

How boards are checked, and how many it throws away

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