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Exact Risk of Ruin

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).

Risk of Ruin (Exact)

For +EV players (advantage gamblers, card counters, value bettors). All inputs are per UNIT bet — i.e. treat one "unit" as your flat bet size and express everything against that.
Dimensionless advantage α = a/σ²
Risk of ruin (infinite horizon)
Expected win over N hands
σ of win over N hands
P(end in profit) after N hands

How to calculate your Risk of Ruin in 4 steps

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):

  1. Advantage per Unit (%): Your expected mathematical edge. If you have a 1.5% edge over the casino, enter 1.5. If you are playing a game with a negative expectation, this value is 0 or negative, and your ruin is 100% mathematically guaranteed over time.
  2. Standard Deviation (σ) per Unit: The measure of game volatility. For blackjack card counting, this is typically around 1.15. For baccarat, it’s roughly 0.95. For high-variance games like dice or slot machines, it can exceed 5.0.
  3. Bankroll (in Units): Your total bankroll divided by your flat bet unit. For example, if you have a $5,000 bankroll and bet $10 per hand, your bankroll is 500 units.
  4. Session Length (Hands/Bets): The total number of wagers you plan to place during your testing horizon.
Infinite vs Finite Horizon: This tool calculates two types of risk. The infinite horizon is the probability of going broke at *any* point in your lifetime, even if you play forever. The finite horizon calculates the probability of ending in profit after your specified session length.

The math: Schlesinger and Sileo formulas

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.

1. Dimensionless advantage (α)

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.

2. Infinite-horizon Risk of Ruin

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.

3. Finite-horizon profit probability

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.

Strategy: Sizing your bankroll for safety

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.

Frequently asked questions

Why is my ruin certain if I have a negative edge? (You can configure a robust plan using our Bankroll Calculator)

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.

How does standard deviation affect my risk of ruin?

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.

What is the difference between this and the Kelly Criterion?

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.