Two calculators sharing one model: what happens to the player’s bankroll bet by bet, and what bankroll the house needs to survive its own paytable. Runs entirely in your browser — no dependencies, no network.
The house wins the stake B on a losing bet and pays out max win W on a winning one, so its net loss on a win is (W − B). Win probability follows from the paytable:
Note that p × W = RTP × B regardless of W. The house edge per bet is always B × (1 − RTP) — max win never changes expected profit, only volatility. That is the entire point of this calculator.
Risk of ruin comes from the Lundberg coefficient r, the positive root of:
This is used instead of a normal approximation because the house’s risk here is rare large payouts rather than smooth diffusion — a Gaussian model materially understates the tail. Ruin probability decays exponentially in bankroll, so every additional ln(2)/r of capital halves it.
Exposure per unit of bankroll can arrive two ways, and capping one leaves the other open. At high multipliers p is tiny and each win is enormous, so ruin is a single-event risk and max win governs. At low multipliers each win costs little but happens most of the time, so ruin arrives as a losing streak and max bet governs.
A worked case: bet 10,000 at 1.1× gross with RTP 99% means p = 90%. Each win costs the house only 1,000 — but on a 10,000 bankroll, ten consecutive wins clears it, and P(ten in a row) is 34.9%. True risk of ruin is 82.3%. No payout cap helps here; only a lower max bet does.
A useful sanity rule independent of multiplier: keep max bet under roughly 1–2% of bankroll, then layer the multiplier and absolute-payout caps on top for the high-multiplier tail.
A common approximation, r ≈ 2(1−RTP)/(RTP·W), is a diffusion limit valid only when wins are rare. At 50× and above it is accurate to about 1%; at 2× it is off by a factor of 2, and at 1.1× by a factor of 10. This tool always solves the exact equation above, so it stays correct across both regimes.
Solving for max win inverts the same relation numerically: risk of ruin increases monotonically with W (bigger ceiling, fatter tail), so the solver bisects on W until the resulting ruin probability matches the target.
This is an indefinite horizon — over a finite operating window the real figure is lower. It assumes no withdrawals; if you pull profit out, the bankroll stays flat and true risk is higher. And ruin means zero, whereas your real constraint is the drawdown that triggers a covenant or forces you to shut the game off. Treat every number here as a floor.