How Is Mines Probability Calculated? 25-Tile Safe Odds, Survival, and Multiplier Math

Direct answer

Mines is a finite-pool sampling problem without replacement. Every safe reveal reduces the remaining tile count, so the conditional risk of the next tile changes.

Quick facts

Board

25 tiles

Mines

1–24

Survival

C(25−m,k)/C(25,k)

Multiplier

0.99/P(survive k)

01

Probability the first tile is safe

With m mines on 25 tiles, first-pick safety is (25−m)/25 and mine probability is m/25.

With 3 mines, the first tile is safe with probability 22/25=88% and contains a mine with probability 12%.

02

Probability that k picks all survive

Because safe tiles are not replaced, the probability that all k picks are safe is C(25−m,k)/C(25,k). The equivalent product is Π(i=0→k−1)(25−m−i)/(25−i).

This finite-pool model is different from incorrectly treating every reveal as an independent event with a fixed probability.

03

Risk of the next tile after k safe reveals

After k safe reveals, 25−k total tiles remain while all m mines remain unresolved. The conditional mine probability is m/(25−k), and the next safe probability is (25−m−k)/(25−k).

That is why the hazard rate rises as more safe tiles are opened in the same round.

04

The 99% RTP multiplier

If cashout is available after k safe tiles, the published model uses M(k)=0.99/P(survive k). Lower survival probability therefore corresponds to a larger multiplier.

The formula standardizes long-run expectation; it does not guarantee a 99% return in any individual round or session.

EXAMPLE

3-mine example

• First tile safe: 22/25 = 88%
• Second tile safe after one safe reveal: 21/24 = 87.5%
• First two both safe: 22/25 × 21/24 = 77%
• Two-tile cashout multiplier: 0.99 / 0.77 ≈ 1.2857×

Frequently asked questions