For a standard Mines model with 25 tiles and a fixed number of uniformly placed mines, the chance of surviving several distinct picks is a combinations problem. The table below is calculated from that model, not copied from a casino payout display. Different board sizes or mechanics require a different calculation.
Define the model before reading the odds
Assume a round starts with 25 tiles, M of them mines, placed uniformly without replacement. You choose k different tiles without information about hidden locations and cash out only if every chosen tile is safe. The mine count remains fixed during the round.
The probability of surviving k picks is P = C(25 − M, k) / C(25, k), where C(n, k) counts combinations. Equivalently, multiply the successive safe fractions: (25 − M)/25 × (24 − M)/24 and so on for k factors.
Exact-model survival table
Percentages below are rounded to six decimal places. The fair total-return multiplier is 1/P and includes the original stake. It would have zero house edge before rounding or other rules. It is not a claim about any operator's advertised multiplier.
| Mines | Safe picks required | Chance of all picks being safe | Fair total-return multiplier | ||
|---|---|---|---|---|---|
| 1 | 1 | 96.000000% | 1.041667x | ||
| 1 | 3 | 88.000000% | 1.136364x | ||
| 1 | 5 | 80.000000% | 1.250000x | ||
| 1 | 10 | 60.000000% | 1.666667x | ||
| 3 | 1 | 88.000000% | 1.136364x | ||
| 3 | 3 | 66.956522% | 1.493506x | ||
| 3 | 5 | 49.565217% | 2.017544x | ||
| 3 | 10 | 19.782609% | 5.054945x | ||
| 5 | 1 | 80.000000% | 1.250000x | ||
| 5 | 3 | 49.565217% | 2.017544x | ||
| 5 | 5 | 29.181254% | 3.426858x | ||
| 5 | 10 | 5.652174% | 17.692308x |
Worked example: three mines and five picks
There are C(22,5) safe five-tile selections among C(25,5) possible five-tile selections. Their ratio is approximately 0.495652174, or 49.565217%. The complementary probability of hitting at least one mine before completing those five picks is 50.434783%.
The zero-edge total-return multiplier is approximately 2.017544x. If an illustrative paytable targeted 99% return for that cash-out point, its multiplier before rounding would be 0.99/P ≈ 1.997368x. A $1 stake would have expected total return $0.99 and expected net loss $0.01 under those assumptions.
The next pick has different conditional odds
After four safe picks on a three-mine board, 21 tiles remain: 18 safe and three mines. The next pick is safe with probability 18/21, approximately 85.714286%. That is a conditional probability after survival, not the chance of completing all five picks from the start.
If the board is uniformly generated and hidden, a corner, diagonal or repeating pattern does not improve those probabilities. What changes is the number of remaining safe tiles and mines, not the shape traced by your clicks.
Calculate the edge from the actual multiplier
If the posted total-return multiplier at a chosen cash-out point is m, the model's expected return per unit stake is P × m. The house edge is 1 − P × m. Check whether the display includes the returned stake; a net-profit multiplier requires different interpretation.
A common constant-edge formula is only a model, not a universal promise. Operators may round multipliers or use different rules. Compare the actual game instructions and payout table with the probability assumptions.
Verification does not predict the mines
A supported provably fair system can let you reconstruct a completed board from disclosed inputs and an algorithm. It does not reveal the next board in advance or turn prior boards into a signal. Keep the seed commitment and verification procedure separate from the payout mathematics.
Choosing fewer picks changes the distribution of outcomes, but under a constant-edge paytable it does not remove the house edge. A losing round does not make the next board safer.
Frequently asked questions
What are the odds of five safe picks with three mines?
Under the 25-tile uniform model, C(22,5)/C(25,5) = 49.565217% after rounding.
Does a tile pattern improve Mines odds?
Not under the stated uniform hidden-board model. Every unselected tile has the same conditional risk.
Are the table's fair multipliers the payouts I receive?
No. They are zero-edge mathematical benchmarks; the game's actual multipliers can include a house edge and rounding.
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Sources
Numerical scenarios are illustrative unless explicitly attributed to a named primary source.
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