Bankroll & Risk-of-Ruin Calculator
The house edge tells you the average. Variance tells you the ride. Here's the realistic range for your session — and the odds your bankroll doesn't survive it.
Session
Simulated results (2,000 sessions)
Why short sessions feel lucky
The expected result grows in proportion to the number of bets, but the standard deviation grows only with its square root. Over a short session the swings dwarf the edge, so plenty of players finish ahead. Over thousands of bets the edge dominates and the chance of finishing ahead shrinks toward zero.
The figures above combine an exact formula (expectation), a normal approximation (range, chance of finishing ahead) and a Monte Carlo simulation (risk of ruin and the chart). Read Bankroll Math & Risk of Ruin for the full explanation.
The blackjack model is a simplified outcome distribution calibrated to a ~0.5% edge; slot results use our simulator's medium-volatility pay table.