Mines Calculator: Odds and Multipliers for Any Board

This mines calculator shows the exact chance of clearing any number of tiles without hitting a mine, the multiplier that would be a fair price for that risk, and how much a house edge takes off it. It works for any board from 3×3 to 7×7 and any number of mines, and on the standard 5×5 board it shows Gift Club's real Minefield ladder next to the maths.

How mines odds work

Each tile you open removes one safe tile from the board, so the odds get worse with every pick. The chance of clearing k tiles on a board of T tiles with M mines is the product of the safe share at each step:

(T − M) / T × (T − M − 1) / (T − 1) × … for k steps

On a 5×5 board with 3 mines, clearing five tiles works out to 22/25 × 21/24 × 20/23 × 19/22 × 18/21, which is 49.57%. Roughly a coin flip, even though each single pick looked safe.

How a mines multiplier is priced

A fair multiplier is one divided by the chance of getting there: 2.0175× for the example above. A game keeps its edge by paying less than that. With a house edge of e, the multiplier becomes (1 − e) divided by the chance. With 1% it is 1.9974×, with 5% it is 1.9167×.

That formula has a consequence worth knowing: every stopping point returns the same on average. Cash out after one tile or after fifteen, and the expected return is still one minus the edge. The number of mines and the tile you stop on change how often you win and how much. They do not change what the game keeps.

Gift Club's Minefield runs at a 95% target and floors each rung to two decimals, so its ladder sits just under the 5% column. On the Easy board that example pays 1.91×.

Using the calculator for a mines strategy

Since the return is fixed, a mines strategy is really a choice of shape. A few mines and a long run of picks gives many small wins. Many mines and one or two picks gives rare, larger ones. Pick a stop before you start, and use the "next tile is a mine" column to see how quickly the risk per click climbs. The mines strategy guide goes through the choices and the systems that do not work.

One thing no calculator can do is find the mines. Positions are drawn before the round starts, and no pattern of clicks changes where they are.

Frequently asked questions