Free Mines

When a round starts, the mines are placed in your browser by the first steps of a standard shuffle of the 25 tile numbers, so every possible set of mine positions is equally likely. Nothing is decided later: uncovering a tile only shows what was already there.

With m mines, the chance that k tiles uncovered in a row are all safe is the number of ways to choose k tiles from the 25 − m safe ones, divided by the number of ways to choose k from all 25. The multiplier after k safe tiles is the inverse of that chance times 99%. The house edge is therefore 1% of the bet at each of the 300 combinations of mine count and stopping point, and the test suite checks every one of them with whole-number arithmetic, with no decimals to round.

Put another way, the edge is taken once, on the bet. After the first safe tile, each further tile is an even trade on what you could cash out: the multiplier rises by exactly as much as the chance of surviving falls. That is why no stopping rule and no choice of tiles changes the average, and why the only thing they do change is the spread of results. The variance simulator shows what a wider spread does to a session at a fixed edge.

Rounding goes one way. A cash-out pays the bet times the exact multiplier, rounded down to a hundredth of a chip, and the multiplier on screen is rounded down too (to four decimal places, or two on the largest). Rounding down can cost at most 0.17% of the bet more, on the smallest bet, and never moves anything in the player's favor.

The expected figure in the session panel is the edge multiplied by the chips you have bet on finished rounds.