Mines Odds: 3 Mines on a 5×5 Board
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Three mines are a useful middle reference when comparing short Mines rounds. There are many safe opening choices, yet each extra selection exposes the same stake to another chance of losing the whole round.
The table separates the fair return from an illustrative return with an assumed edge. That makes it possible to discuss the cost of a payout haircut without pretending to reproduce an operator’s multiplier schedule.
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 | 88% | 22/25 | 1.13636364× | 1.125× |
| 2 | 77% | 77/100 | 1.2987013× | 1.28571429× |
| 3 | 66.95652174% | 77/115 | 1.49350649× | 1.47857143× |
| 4 | 57.82608696% | 133/230 | 1.72932331× | 1.71203008× |
| 5 | 49.56521739% | 57/115 | 2.01754386× | 1.99736842× |
| 6 | 42.13043478% | 969/2300 | 2.37358101× | 2.3498452× |
| 7 | 35.47826087% | 204/575 | 2.81862745× | 2.79044118× |
| 8 | 29.56521739% | 34/115 | 3.38235294× | 3.34852941× |
| 9 | 24.34782609% | 28/115 | 4.10714286× | 4.06607143× |
| 10 | 19.7826087% | 91/460 | 5.05494505× | 5.0043956× |
| 11 | 15.82608696% | 91/575 | 6.31868132× | 6.25549451× |
| 12 | 12.43478261% | 143/1150 | 8.04195804× | 7.96153846× |
| 13 | 9.56521739% | 11/115 | 10.45454545× | 10.35× |
| 14 | 7.17391304% | 33/460 | 13.93939394× | 13.8× |
| 15 | 5.2173913% | 6/115 | 19.16666667× | 18.975× |
| 16 | 3.65217391% | 21/575 | 27.38095238× | 27.10714286× |
| 17 | 2.43478261% | 14/575 | 41.07142857× | 40.66071429× |
| 18 | 1.52173913% | 7/460 | 65.71428571× | 65.05714286× |
| 19 | 0.86956522% | 1/115 | 115× | 113.85× |
| 20 | 0.43478261% | 1/230 | 230× | 227.7× |
| 21 | 0.17391304% | 1/575 | 575× | 569.25× |
| 22 | 0.04347826% | 1/2300 | 2,300× | 2,277× |
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
Early survival does not lock in the original odds for later clicks. After every safe reveal, all three mines remain hidden while fewer tiles remain. Compare adjacent rows to see the cost of extending a surviving round; comparing only the displayed multipliers misses the probability sacrificed.
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: 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: 15 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.
See what a staking level needs, with example numbers.
Frequently asked questions
What changes with 3 mines?
Early survival does not lock in the original odds for later clicks. After every safe reveal, all three mines remain hidden while fewer tiles remain. Compare adjacent rows to see the cost of extending a surviving round; comparing only the displayed multipliers misses the probability sacrificed.
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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