Nine hard boards in ten ended on a coin flip

A quality review two days ago called it a genre-standard limitation, not a bug: this Minesweeper, like most versions of the game, lays its mines at random after the first tap, so sometimes the last few tiles come down to a guess. “Sometimes” was never measured. So before changing anything, a solver played a thousand first taps per board size, using only the four things players actually read: a number already satisfied frees its other neighbours; a number with exactly as many hidden neighbours as mines left flags them all; two overlapping numbers read together; and, at the end, the mine counter.

On Easy it finished 84% of random boards. On Medium, 52%. On Hard, 10.7% — nine boards in ten asked for a coin flip somewhere. Those rules are not the cleverest possible, so that is an upper bound; checked on 900 small test boards against a brute-force reader that tries every mine layout the numbers still allow, they cleared about 87% of what perfect logic clears, and never once accepted a board that perfect logic could not finish. The analytics had been saying the same thing in a different voice: in the week before, every Minesweeper run that ended, ended on a mine.

The fix is the plain one. After the first tap, the mines are dealt, the solver reads the board, and if it would ever have to guess, the deal is thrown away and made again. On Hard that is about nine deals, a few milliseconds on a fast computer and at worst about a tenth of a second on a slow phone, once per game. Faster ways exist — nudge a mine until the board works — but they tilt which boards you get; redealing keeps every board as random as before, among the ones that can be read.

The title screen now says it outright: every board can be cleared by logic, no guesses. The tests hold the game to it, with the brute-force reader as the judge.

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