Mines Odds: 15 Mines on a 5×5 Board
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Fifteen mines leave fewer safe tiles than dangerous ones from the start. This changes the character of the table: even the first selection is less likely to survive than to fail.
The remaining rows cover every possible safe-run length, not a recommendation to attempt them. Comparing this table with lower-mine versions shows why changing the mine count is a volatility choice rather than a way around the edge.
Probability and return table
The “99% RTP” column assumes a 1% edge for positive picks. It is illustrative, not the actual table of Mint or any other casino.
| Safe picks | Survival | Exact fraction | Fair return | Assumed 99% RTP |
|---|---|---|---|---|
| 0 | 100% | 1/1 | 1× | 1× |
| 1 | 40% | 2/5 | 2.5× | 2.475× |
| 2 | 15% | 3/20 | 6.66666667× | 6.6× |
| 3 | 5.2173913% | 6/115 | 19.16666667× | 18.975× |
| 4 | 1.66007905% | 21/1265 | 60.23809524× | 59.63571429× |
| 5 | 0.4743083% | 6/1265 | 210.83333333× | 208.725× |
| 6 | 0.11857708% | 3/2530 | 843.33333333× | 834.9× |
| 7 | 0.02496359% | 6/24035 | 4,005.83333333× | 3,965.775× |
| 8 | 0.0041606% | 1/24035 | 24,035× | 23,794.65× |
| 9 | 0.00048948% | 2/408595 | 204,297.5× | 202,254.525× |
| 10 | 0.00003059% | 1/3268760 | 3,268,760× | 3,236,072.4× |
How the values are calculated
For K picks without replacement, P = C(25 − M, K) / C(25, K). Fair return is 1/P and illustrative return is 0.99/P when K > 0; zero picks returns 1×. Fractions use exact integer arithmetic in the calculator’s shared module. The table stops at the last safe tile; further picks have zero survival and an undefined multiplier.
Reproducible arithmetic: GitHub: mines-odds. Values are generated at build time using the tools’ shared math module.
Interpreting this configuration
A succession of safe tiles rapidly consumes the small safe pool. Later rows concern unusually selective paths through a mostly dangerous board. The fair payout increases to offset those shrinking odds, while the illustrative edge still reduces expected return on each positive-pick row by the same proportion.
Calculators and related reading
- Mines odds calculator
- Guide to the game and its odds
- Mines Odds: 1 Mine on a 5×5 Board
- Mines Odds: 2 Mines on a 5×5 Board
- Mines Odds: 3 Mines on a 5×5 Board
- Mines Odds: 5 Mines on a 5×5 Board
- Mines Odds: 8 Mines on a 5×5 Board
- Mines Odds: 10 Mines on a 5×5 Board
- Mines Odds: 24 Mines on a 5×5 Board
18+ · These results do not predict a round or guarantee a profit. Do not chase losses; only gamble money you can afford to lose. Help and limits.
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Frequently asked questions
What changes with 15 mines?
A succession of safe tiles rapidly consumes the small safe pool. Later rows concern unusually selective paths through a mostly dangerous board. The fair payout increases to offset those shrinking odds, while the illustrative edge still reduces expected return on each positive-pick row by the same proportion.
Why does the zero-pick row return 1×?
No pick has been made, so the stake is untouched. The illustrative edge applies only to positive-pick rows.
Are these actual Mint payouts?
No. These are mathematical returns with an assumed edge. Actual payouts require checking the operator’s rules.
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