An edge means nothing if variance bankrupts you first. This exact Risk of Ruin calculator applies Schlesinger-Sileo formulas to give the probability your bankroll touches zero (the full background is covered in our Risk of Ruin Guide).
Risk of Ruin (Exact)
How to calculate your Risk of Ruin in 4 steps
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Risk of Ruin (RoR) is the number advantage players — card counters, sports bettors, bonus hunters — care about most. Enter every figure in terms of your flat bet unit, meaning one “unit” equals your average wager:
- Advantage per Unit (%): Your mathematical edge. Holding 1.5% over the house? Enter 1.5. Playing a negative expectation game? The value is zero or below, and ruin over an infinite timeline is a mathematical certainty.
- Standard Deviation (σ) per Unit: Volatility of the game itself. Blackjack card counters usually work with a figure near 1.15. Baccarat sits closer to 0.95. High-variance games such as dice or slots can push past 5.0.
- Bankroll (in Units): Total bankroll divided by your flat bet unit. A $5,000 bankroll at $10 per hand equals 500 units.
- Session Length (Hands/Bets): The number of wagers in your testing horizon.
The math: Schlesinger and Sileo formulas
For a long time I assumed positive expected value (+EV) made my bankroll effectively bulletproof. Wrong, and it cost money to learn. Volatility can flatten a small roll well before the edge gets a chance to express itself.
The formal math behind this calculator is what keeps that lesson from repeating.
1. Dimensionless advantage (α)
The first step normalizes your edge against variance. The result is called the dimensionless advantage (α):
α = Advantage / Variance = a / σ²
Think of it as return per unit of risk. A modest edge in a calm game can produce a higher α than a big edge wrapped in wild swings.
2. Infinite-horizon Risk of Ruin
For flat bettors holding a constant edge, the classic Sileo formula gives the probability of full depletion over an unbounded timeline:
RoR = ((1 - α) / (1 + α))^B
Here B is your bankroll in units. Because the formula is exponential, each extra unit of bankroll shrinks your ruin probability sharply.
3. Finite-horizon profit probability
For the chance of ending in profit after exactly N hands, the tool uses a normal approximation:
P(Profit) = Φ(N * a / (σ * √N))
Φ is the standard cumulative normal distribution function. Practically, it tells you how many hands it takes before your edge outmuscles short-term noise.
Strategy: Sizing your bankroll for safety
The professional benchmark: keep infinite Risk of Ruin under 1%.
A reading of 5% or 10% means your bets are too large relative to the bankroll backing them.
Even in a +EV game, a bad run of cards can take every dollar you brought.
Two fixes exist: add to the bankroll, or shrink your unit size. Do one or both until the infinite RoR lands under the 1% line.
Frequently asked questions
Why is my ruin certain if I have a negative edge? (You can configure a robust plan using our Bankroll Calculator)
With an advantage of zero or less — standard roulette, most slots — continued play eventually consumes the entire bankroll. That is not pessimism; it is how negative expectation works. No bankroll, however deep, escapes it.
How does standard deviation affect my risk of ruin?
Standard deviation is the swing factor. High-σ games (high-volatility slots, single-number roulette bets) produce deep drawdowns that demand a far larger bankroll to survive. Low-σ games like blackjack or pass-line craps let a smaller roll do the same job.
What is the difference between this and the Kelly Criterion?
Kelly computes the bet size that maximizes long-run growth rate, with stakes adjusted after every swing. This calculator instead assumes flat betting at a constant size, which delivers an exact ruin figure for traditional advantage play.