Mines Payout Matrix

How combinatorics drives the 5×5 grid

Casino Mines uses 25 covered tiles. Before the round starts you pick how many mines hide beneath them — anywhere from 1 to 24 — and place your bet. Each coin you uncover raises the payout multiplier and gives you a decision: bank the win or click again. One mine ends the round and takes the whole stake.

A stubborn myth says some squares are “hot.” They aren’t. The outcome is pure combinatorial probability: after every safe reveal, the mine-to-safe ratio on the remaining board worsens, so the danger of the next click climbs fast.

The math: Combinations and multipliers

The matrix is built from binomial coefficients — the count of ways to select $r$ safe tiles from a board holding $M$ mines:

1. Probability of Success

The probability ($P$) of uncovering $r$ safe tiles without touching any of the $M$ mines is:

P(Success) = C(25 - M, r) / C(25, r)

With the combinations function $C(n, k)$ defined as:

C(n, k) = n! / (k! * (n - k)!)

2. Calculating the Fair Multiplier

The operator then scales the fair odds by the house edge ($HE$), producing the payout multiplier ($Multiplier$):

Multiplier = (1 - House_Edge_Percentage) / P(Success)
Multiplier = (1 - House_Edge_Percentage) * C(25, r) / C(25 - M, r)

Step-by-step audit: Auditing 3 Mines, 3 Clicks

Take a round set to 3 Mines ($M = 3$) with a planned cashout after exactly 3 safe clicks ($r = 3$), on a game advertising a 1.00% house edge:

1. Total ways to choose any 3 tiles from 25: $C(25, 3) = 2,300$.
2. Ways to choose 3 tiles that avoid all mines (22 safe tiles): $C(22, 3) = 1,540$.
3. Survival probability across 3 clicks: $1,540 / 2,300 = 66.96%$.
4. Fair multiplier at zero edge: $1 / 0.6696 = 1.493x$.
5. After the 1% house edge: $1.493 times 0.99 = mathbf{1.478x}$ payout.

The audit confirms the advertised figure matches the combinations exactly. If a site pays less than about 1.47x for this setup, its real edge exceeds the stated 1%.

Frequently asked questions