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Game Mathematics

How BoredGamez calculates Mines survival probability and multipliers

The exact without-replacement probability model behind Mines, explained with a 25-tile, five-mine worked example.

Author
BoredGamez Engineering
Published
Published July 9, 2026
Reading time
7 minute read

Part 1

A board is fixed at round start

When a player starts Mines, the server validates the grid and mine count, selects unique hidden indexes, and stores them with the active round. Supported grids contain 25, 36, 49, or 64 tiles. Mine locations are not re-rolled after each click and are not returned to the browser while the round is active.

Because picks are made without replacement, the probability changes after every safe reveal. With 25 tiles and five mines, the first pick has 20 safe possibilities out of 25. After one safe reveal, the second has 19 safe possibilities out of 24 remaining tiles.

Part 2

Multiplying conditional survival chances

The chance of surviving several picks is the product of each conditional safe chance. Three safe picks on that example board are (20/25) x (19/24) x (18/23), which is approximately 49.6%. The function works the same way for every supported grid and mine count.

BoredGamez converts survival probability into a multiplier by dividing a 0.96 theoretical-return factor by that probability, then rounding down to the nearest hundredth of a multiplier. This produces a consistent model across configurations while preserving the product's current 96% factor.

  • One safe pick: 80.0% survival.
  • Three safe picks: approximately 49.6% survival.
  • Every unrevealed position is symmetric under the generator.

Part 3

Why tile position is not a strategy signal

A corner, centre, or recently adjacent tile does not have a different hidden probability in this implementation. The server chooses unique indexes uniformly and the interface does not attach position-based weights. A streak of safe corners is history, not evidence that future corners have become safer.

The decisions a player controls are configuration, entry size, and when to stop. Larger mine counts make each reveal less likely to survive, while a successful stop settles the current multiplier. The public guide publishes concrete tables for one setup and labels that setup so readers do not apply those figures to every board.