Mines math is fully public and completely deterministic. Every multiplier you see on the Stake UI comes from a single closed-form formula; the hit probability at every step comes from a paired formula. Once you see them on one line, the whole game stops being mysterious.
The two formulas on one screen
Multiplier after k successful clears on a board with N mines: M(N, k) = 0.99 × C(25, k) / C(25-N, k). Probability of reaching that clear without hitting a mine: P(N, k) = C(25-N, k) / C(25, k). The 0.99 factor is the only edge the house keeps — the theoretical "fair" multiplier would be C(25, k) / C(25-N, k), and Stake scales it down by 1% to produce RTP 99%. No dynamic weighting, no hidden adjustments, no configuration-specific tilts. The formula applies identically from 1 mine to 24 mines, from the first click to the last.
Why every configuration has the same expected value
Multiply the two formulas and watch them cancel: P × M = [C(25-N, k) / C(25, k)] × [0.99 × C(25, k) / C(25-N, k)] = 0.99. Every configuration — 2 mines early cash-out, 12 mines full clear, 24 mines single click — returns exactly 99 cents on the dollar in expectation. A low-mine session delivers that 99% as frequent small wins; a high-mine session delivers it as rare, massive wins. The total cost to the player over enough rounds is identical.
Where the peak multiplier comes from
- C(25, k) is maximized at k = 12 and k = 13. Both equal 5,200,300. This is a pure combinatorial fact about 25-element sets. Every multiplier in Mines is a scaled version of these binomial coefficients, which is why the peak of the curve sits precisely at "clear 12 or 13 safe tiles."
- Peak multiplier = 0.99 × 5,200,300 ≈ 5,148,297. Reached by exactly two configurations: 12 mines with a full 13-tile clear, or 13 mines with a full 12-tile clear. Both produce the same monster number because binomial coefficients are symmetric around the middle.
- Peak probability = 1 / 5,200,300 ≈ 0.0000192%. Or roughly one in 5.2 million attempts. A player running 200 peak attempts per day (aggressive hunt pace) would expect one clear every ~70 years on average — but the distribution is long-tailed, and verified peak hits happen several times per year across the full Stake player base.
Provably fair — you can verify every round yourself
Each Mines round is generated from a server seed (committed in advance), a client seed (you can rotate any time), and a nonce (the round counter). After a session, rotating the server seed reveals the prior seed; feeding it back through the public verification script reproduces every safe/mine outcome exactly. The math that turns a hash into a shuffled board is documented on Stake's fairness page, and the same mechanism powers Dice, Limbo, and Plinko. The 1% house edge is the only built-in tilt and it is exactly 1% — no configuration gets a secret surcharge, no nonce gets a stealth push, and no session gets a "tune" based on balance.