Minesweeper Solver

Every deduction in Minesweeper comes from two sentences. A number tells you how many mines touch it, counting all eight neighbors. When flags already cover that count, every other neighbor is safe. When the unknown neighbors exactly equal the number, all of them are mines.

Chain those two rules and most boards start solving themselves. A 3 with three flags around it opens its whole neighborhood at once. A 1 touching a single covered cell flags it without further thought. Beginners stare at the grid. Strong players read a list of small counting facts and let the clicks follow.

The solver does that chaining exhaustively. It takes the numbers and flags you enter, derives every certainty, updates the board, and repeats until nothing new falls out. What survives that loop is honest ambiguity, and only there does it switch from proof to probability.

Deriving everything from the two rules works, and it is slow. Experienced players memorize packaged shapes instead, the same few number rows that resolve whole regions on sight. The solver checks these shapes on every pass, which is why it spots in milliseconds what takes a human eye several seconds.

Each pattern is just the base rules in costume. That matters when memory fails mid-game: any forgotten pattern can be re-derived from the two rules on the spot. Nobody needs to carry a textbook. The rules rebuild every pattern given ten seconds of thought.

The 1-2-1 family deserves drilling first. It appears constantly along walls and it settles several cells in one glance. Learn to see it and entire borders stop being work.

Chording is the move casual players never discover. When a number already touches enough flags, clicking that number opens every remaining neighbor at once. One click can clear seven cells. Along a solved wall, two chords finish what a cell-by-cell player is still aiming at.

Flag discipline is the other half of speed. Unflagged numbers force constant recounting, and recounting is where seconds and accuracy both leak. A fully flagged board reads at a glance, and a readable board chords cleanly. The solver flags every certain mine for exactly this reason: flags are the interface the rest of the logic runs on.

Invert the habit. Stop scanning for safe-looking cells and start reading number groups, resolving them, and clicking after. Eyes on the numbers, not the empty grid. That single inversion is the difference between hesitant play and fast play.

Nearly every board stalls somewhere. A pocket of cells where two arrangements fit the numbers equally well, and no counting rule can pick between them. That pocket is the ambiguous core. How it gets played separates careful players from lucky ones.

The solver answers the core with arithmetic, not instinct. It computes each remaining cell's mine probability from the live constraints and points at the safest click. A menacing corner cell can carry a small chance while an innocent middle cell carries a large one. The board's appearance means nothing. The constraint math means everything.

Internalize that and endgames change character. Stop asking which cell looks safe. Ask which cell the numbers constrain least. One habit, applied everywhere, and the coin-flip regions start costing far fewer games.

Beginner runs 9 by 9 with 10 mines, intermediate 16 by 16 with 40, expert 30 by 16 with 99. The counting never changes across them. What changes is how many deductions stay live at once. Expert keeps dozens of chains open simultaneously while a human holds maybe three, which is exactly where manual play starts leaking time.

Density is the real variable. Sparse beginner boards resolve in long clean chains. Packed expert boards stall into probability cores earlier and more often. Adjust expectations accordingly: a beginner loss usually means a missed deduction, while an expert loss often means a lost coin flip played correctly.

Most versions protect the opening click, so it never hits a mine. Use that free information aggressively. A wide opening area hands you a border full of numbers to work with, and the solver's first pass over a good opening often clears a third of the board untouched.

Corners and edges carry fewer neighbors, which makes their numbers stricter. A corner 2 with three covered cells is nearly solved by definition. Beginners treat edge numbers as background. Strong players start there, because fewer neighbors means each flag teaches more.

Openings also behave differently at the rim. An opening that touches a wall gives you a long clean border to chord along, while a center opening scatters numbers in every direction. Neither is better in itself. The point is to read what the border offers instead of clicking wherever feels central.

The solver weights these constraints the same everywhere, which is worth copying. No cell gets special treatment because of where it sits. Every number is a small equation, and the rim equations are simply shorter.

Play a real board until it stalls, enter the position here, and study what got missed. The gap between your stall point and the solver's is a syllabus. Each overlooked deduction is a pattern not yet absorbed, and a few sessions of this makes 1-2-1 walls leap off the grid.

Diff finished boards the same way. Run a solved game through and check whether every guess was forced. Finding a guess that was not, a risk taken where logic had an answer, teaches more than ten clean wins.

Accept the true coin flips. Some endgames are honest fifty-fifties and the solver simply picks a side. Losing those is not failure. It is the game working as designed, and the correct response is a new board, not a new theory.