Mines Payout Matrix

The Greedy Click Fallacy: As you reveal more tiles, the multiplier grows, but your win probability drops exponentially. The marginal increase in payout for “just one more click” rarely justifies the massive surge in the probability of hitting a mine and losing your accumulated wins.

The math: Combinations and multipliers

To build the payout matrix, the calculator uses the formula for combinations (binomial coefficients), which calculates the number of ways to choose $r$ safe tiles out of a grid containing $M$ mines:

1. Probability of Success

The probability ($P$) of successfully revealing $r$ safe tiles without hitting any of the $M$ mines is:

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

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

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

2. Calculating the Fair Multiplier

To ensure the casino maintains its house edge ($HE$), the payout multiplier ($Multiplier$) is scaled by the probability of success:

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

Let’s audit a session where you set the game to 3 Mines ($M = 3$) and plan to make exactly 3 safe clicks ($r = 3$) on a game with a 1.00% house edge:

1. The total number of ways to pick any 3 tiles from a grid of 25 is: $C(25, 3) = 2,300$.
2. The number of ways to pick 3 tiles that are all safe (from the 22 safe tiles) is: $C(22, 3) = 1,540$.
3. Your probability of surviving 3 clicks is: $1,540 / 2,300 = 66.96%$.
4. The fair multiplier (zero house edge) would be: $1 / 0.6696 = 1.493x$.
5. Applying the 1% casino house edge gives: $1.493 times 0.99 = mathbf{1.478x}$ payout.

This audit proves that the casino’s advertised multiplier matches the mathematical combination perfectly. If a casino offers a multiplier lower than 1.47x for this setup, their house edge is significantly higher than advertised.

Frequently asked questions