A mathematical edge is worthless if you go broke before the long run catches up. This exact Risk of Ruin calculator uses Schlesinger-Sileo formulas to determine the probability of your bankroll hitting absolute zero (detailed in our Risk of Ruin Guide).
The Risk of Ruin (RoR) is the ultimate metric for professional card counters, sports bettors, and casino advantage players. To use this calculator, you must define all values in relation to your flat bet unit (treating one “unit” as your average bet size):
I used to believe that having a positive expected value (+EV) meant my bankroll was completely safe. That was a costly misconception. High volatility can wipe out a small bankroll long before the mathematical edge has time to normalize.
To protect yourself, you need to understand the formal math behind this calculator.
The formula first normalizes your edge using your standard deviation (variance). We call this the dimensionless advantage (α):
α = Advantage / Variance = a / σ²
This ratio measures your return-to-risk ratio. A high edge with extreme variance yields a lower dimensionless advantage than a small edge with minimal volatility.
For flat-betting players with a constant edge, the probability of complete bankroll depletion over an infinite timeline is calculated using the classic Sileo formula:
RoR = ((1 - α) / (1 + α))^B
Where B is your bankroll in units. This exponential formula shows that your risk of ruin drops dramatically as your bankroll increases.
To calculate your probability of ending in profit after a set number of hands N, the tool uses a normal distribution approximation:
P(Profit) = Φ(N * a / (σ * √N))
Where Φ represents the standard cumulative normal distribution function. This shows exactly how many hands you need to play before your edge overcomes short-term volatility.
The standard industry benchmark for professional players is to maintain a Risk of Ruin under 1%.
If this calculator shows a ruin probability of 5% or 10%, you are over-betting your position.
Even though you are playing a +EV game, a bad streak of cards will easily wipe you out.
To fix this, you must either increase your bankroll or scale down your unit bet size until your infinite RoR drops under the 1% safety threshold.
If your advantage is less than or equal to 0 (a negative EV game, like standard roulette or slots), the mathematics of probability guarantee that you will eventually lose your entire bankroll if you keep playing indefinitely. No bankroll size, no matter how large, can save you from a negative expectation.
Standard deviation measures variance. High standard deviation games (like high-volatility slots or roulette single numbers) create massive swings. These swings require a much larger bankroll to absorb the downward trends compared to low standard deviation games like blackjack or pass-line craps.
The Kelly Criterion calculates your optimal bet size to maximize bankroll growth, assuming you adjust your bet size with every swing. This Risk of Ruin calculator assumes a *flat-betting* model where your bet size remains constant, providing an exact risk assessment for traditional advantage play.