Minesweeper
Minesweeper Probability — When You Have to Guess
6 min read · Burmly
Not every Minesweeper position is solvable without guessing. Roughly 20–30% of intermediate games and up to 35% of expert games require at least one guess somewhere. Understanding probability won't make the uncertainty disappear — but it tells you where to guess, and how bad the odds actually are.
The 50/50 — the worst case
A true 50/50 is when exactly two unknown cells have exactly one mine between them, and no other information can distinguish them. Both cells are equally likely to be the mine. You guess and accept the 50% survival rate.
Common 50/50 setups:
- Two unknowns at the end of a 1-1 pattern with no additional neighbors
- Two diagonal unknowns touching only each other's common numbered cell
- Isolated corner pairs late in the game
Don't try to outthink a true 50/50. Both options are genuinely equal. Click one and move on.
The global mine count method
Your mine counter shows how many mines are left unflagged. This gives you a global probability even when local patterns don't resolve a position.
Expert board: 99 mines total
You've flagged 87. Mines remaining: 12
Unknown cells remaining: 30
Base probability for any random unknown cell: 12/30 = 40%
Now compare local constraints: a cell touching a 1
that has 4 unknown neighbors → local probability ≈ 25%
Click the locally constrained cell, not the isolated unknown.
How to estimate local mine probability
For each unconstrained unknown cell, use the global rate. For cells constrained by numbers, you can often estimate better:
- A cell is the only unknown neighbor of a 1: 100% mine
- A cell is one of 4 unknown neighbors of a 1: ~25% mine (from that number)
- Cross-reference with other adjacent numbers — if another number also constrains the cell, combine the information
Opening probability
At the start of a game before any moves:
- Beginner (9×9, 10 mines): 10/81 ≈ 12.3% per cell
- Intermediate (16×16, 40 mines): 40/256 ≈ 15.6% per cell
- Expert (30×16, 99 mines): 99/480 ≈ 20.6% per cell
This is why clicking corners is bad (fewer neighbors = less new information) and clicking near the center is better (more cells revealed per click).
Unavoidable guesses
Some board configurations are genuinely unsolvable without guessing regardless of skill. These typically happen when:
- Two symmetric regions have the same mine count, and no number touches only one region
- The remaining mines could be distributed in multiple valid configurations
- A 50/50 exists in a corner with no other constraints touching it
Recognizing an unavoidable guess quickly — rather than staring at it — is itself a skill. When you've checked all neighboring numbers and no deduction resolves the ambiguity, it's time to guess using the best available probability.
If you must guess: pick the position that exposes the most new cells if you survive. A guess in an isolated corner gives you one result. A guess near contested territory might open a large region.
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