Strategy Guide
Beginner and Intermediate fields are almost always solvable by pure logic. Expert fields occasionally require a calculated guess. These techniques build from the simplest counting rules up to constraint intersection and probability analysis for those edge cases.
Fundamental Techniques
Saturation — flag when the count matches remaining unknowns
If a revealed number equals the exact count of its still-unrevealed neighbors, every one of those neighbors is an asteroid. Flag them all immediately. This is the most common source of confirmed asteroid positions in any game.
Clearance — reveal when flags satisfy the count
If the number of flags already placed around a revealed sector equals that sector's number, every remaining unrevealed neighbor is guaranteed safe. Reveal them all. These two techniques — saturation and clearance — resolve the majority of Beginner grids without anything else.
Number subtraction across overlapping constraints
When two numbers share some of the same unknown neighbors, you can subtract one constraint from the other. If cell A has 2 remaining mines among 4 unknowns, and cell B has 1 remaining mine among the 2 unknowns that overlap with A, the 2 non-overlapping unknowns of A contain exactly 1 mine between them. This narrows possibilities without full resolution.
Chain every deduction immediately
After flagging an asteroid, recheck every number that borders the newly flagged cell — its effective remaining count just decreased by one. After revealing a safe sector, check every number bordering the new cell — it may now be satisfied or nearly satisfied. Always propagate before moving on.
Advanced Techniques
Edge and corner constraints
Sectors on the grid edge have fewer neighbors — a corner cell has only three neighbors, an edge cell has five. A 1 in the corner with two unknown neighbors means one of two cells is an asteroid. A 1 with only one unknown neighbor resolves immediately. Always check edge and corner numbers first — they carry maximum constraint per neighbor.
The 1-2 pattern
A 1 adjacent to a 2 where both share a row or column of unknowns is one of the most recognizable patterns in the game. If the 1's remaining unknowns are a strict subset of the 2's remaining unknowns, the cells exclusive to the 2 must account for one of the 2's mines. This often resolves both numbers simultaneously once the shared region is identified.
Tank solving — enumerate remaining positions
When a region has a small number of unknown cells and you know the exact mine count for that region, enumerate all valid asteroid arrangements. Any cell that is an asteroid in every valid arrangement is a confirmed asteroid. Any cell that is safe in every valid arrangement is confirmed safe. This brute-force enumeration is slow by hand but decisive — use it only on small isolated regions.
Probability analysis for unavoidable guesses
Expert grids sometimes reach a state where no purely logical deduction is available. When a guess is unavoidable, calculate relative probability. If a bordered region of 5 unknown cells contains 2 known mines, each unknown in that region carries a 40% mine probability. If the global mine density (remaining mines divided by remaining unknowns) is lower, the global unknown is statistically safer. Prefer the guess with the lowest mine probability.
Maximize information from a forced guess
When you must guess, choose a sector whose reveal will produce the most new number information regardless of outcome. A sector bordered by many unrevealed cells will generate a high-value number if safe — giving you many new constraints. A corner or edge sector bordered only by the grid boundary produces fewer useful numbers even if safe. Maximize expected information, not just survival odds.