Bankroll and risk-of-ruin calculatorComing soon
Trip bankroll sizing. Risk of ruin at different units. Survival probabilities by game.
Trip bankroll sizing. Risk of ruin at different units. Survival probabilities by game.
Three numbers govern a session: the expected value per bet (negative, because the house has the edge), the variance per bet, and the number of bets you will place. From those, classical results give you everything else.
The expected loss is simply the per-bet edge multiplied by total wagers, scaled by your unit size. The standard deviation of the session result scales with the square root of bets: SD = unit × sqrt(n × σ²). The probability you end the session below your starting bankroll uses the reflecting-barrier approximation for a biased random walk, which is accurate to a few percent once n exceeds about one hundred.
For an even-money wager, the probability of busting before you double your money is the closed-form gambler's ruin formula: P(ruin) = ((q/p)^b − (q/p)^T) / (1 − (q/p)^T), where b is the starting bankroll in units and T is the target in units. On a 2:1 or 35:1 wager the ruin curve is not a clean closed form, so the density chart on the left is the better guide.
None of this tells you what you will lose. The expected loss is the amount you should plan to lose, on average, given enough sessions. Any one session can finish above or below it. The shaded red zone on the density chart shows the mass that ends below a full bust. That is the number to look at when you set a stop-loss.