Provably-fair game math

Casino Math Toolkit

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.

Setup
same $ amount every bet
Configure the game and press Run simulation.
Solve for
Drives revenue (edge × turnover). Not what drives ruin.
Ruin is driven by exposure per unit of bankroll, and that comes from two independent directions. At high multipliers the danger is one rare huge payout, so max win governs. At low multipliers each adverse event is small but frequent, so a losing streak governs and max bet is what matters. Capping only one leaves the other open — so risk here is always computed on the max bet.
Binding constraint
Risk matrix — max bet × multiplier
Risk of ruin at your bankroll and RTP. Risk climbs on both axes; no safe corner is reachable by controlling only one.
Sensitivity
Bankroll required, by target