Rust Mines Probability Calculator and Odds Guide

The Mines probability formula

Suppose a game has N tiles, M mines and no tile can be selected twice. The chance that the first K distinct picks are all safe is:

P(survive K picks) = C(N - M, K) / C(N, K)

The same calculation can be entered without combination notation:

((N-M)/N) × ((N-M-1)/(N-1)) × … × ((N-M-K+1)/(N-K+1))

That second form works as a manual calculator. Start with 1, multiply one fraction for every planned pick, then multiply by 100 to express the result as a percentage. Do not raise the first-pick probability to the power of K; that would incorrectly treat later picks as if the board reset.

Worked calculator: 25 tiles

The table below assumes a fixed 25-tile example board and distinct selections. It is editorial arithmetic, not a paytable or claim about a live operator.

For three mines and three successful picks, the calculation is 22/25 × 21/24 × 20/23 = 0.669565…, or about 66.9565%. The chance of hitting at least one mine during those three picks is the complement: 100% - 66.9565% = 33.0435%.

Audit a displayed multiplier

If a successful cashout pays a total multiplier X, including the returned stake, its expected return at that step is survival probability × X. A fair-break-even multiplier before any edge would be 1 / survival probability.

Using the three-mine, three-pick example, the break-even multiplier is approximately 1 / 0.669565 = 1.4935×. A displayed 1.45× would imply an illustrative expected return of 0.669565 × 1.45 = 0.97087, or 97.087% under those inputs. The implied edge would be about 2.913% if—and only if—the rules, multiplier definition and settlement contain no additional condition.

Keep at least six decimal places until the last step. Rounding each fraction first can create a visible mismatch that is only a calculation artefact.

What changes the calculation

The formula assumes a fixed mine layout for the round, distinct picks and immediate loss when a mine is selected. A live rule may differ. Check whether the board resets, whether a revealed safe tile can be selected again, whether bonus tiles exist, whether the displayed payout includes the original stake, and how an interrupted round settles.

Auto-pick does not change the combinatorial probability if it selects uniformly from the same remaining tiles. A provably fair record can help reconstruct which cells were assigned as mines, but it does not prove that the multiplier table offers a particular return. Read the provably fair guide as a separate audit.

A repeatable Mines worksheet

Compare the result with the broader house-edge methodology and the game-type taxonomy. Mines belongs in the house-banked column only when the operator supplies the paytable and settles the result against its own schedule.

For one public-source example of an operator that names the format, use the RustSnowball review; the review does not claim that a particular Mines configuration matches this worksheet.