Blackjack Risk of Ruin Calculator
Are you adequately bankrolled? Calculate your Risk of Ruin (RoR), N-Zero, and Expected Hourly Value based on your player edge and standard deviation.
Simulation Parameters
Advanced Settings
Simulation Results
Risk Decay Curve
What Is Risk of Ruin in Blackjack?
Risk of ruin is the probability that you lose your entire bankroll before your edge has time to pay off. It depends on three numbers: your advantage per hand, the game's variance, and your bankroll measured in betting units. A counter with a 1% edge and a 100-max-bet bankroll faces roughly a 5% chance of going broke; the same player on half that bankroll faces over 20%.
The point of the number is sizing bets to survive variance. Your edge only converts to money if your bankroll outlives the losing streaks that a fair share of even perfect play produces.
Understanding the Metrics
Risk of Ruin (RoR)
The mathematical probability that you will lose your entire bankroll before reaching an infinite bankroll. An RoR of 1% means you have a 1 in 100 chance of going broke. Most professional players aim for an RoR of less than 2%.
N-Zero (N0)
The number of hands you must play to overcome a single standard deviation of the game's inherent variance. Simply put: N0 is the point where you cross into the "long term."
Expected Value (EV)
The theoretical amount of money you will win (or lose) per hour,
calculated as:
Edge × Average Bet × Hands/Hr.
Why Bankroll Math Decides Who Survives
Card counting gives you an edge of roughly 0.5-1.5% of total action, but that edge arrives wrapped in enormous variance. A counter playing with a real advantage can lose for weeks without making a single mistake. Risk of ruin is the tool that separates "unlucky but fine" from "playing a bet size that was always going to break you." The inputs that matter are your edge, your bet spread, the game's standard deviation, and above all your bankroll in units: doubling your bankroll does not halve your risk of ruin, it squares the fraction, which is why undersized bankrolls fail so reliably.
Deep dives on both concepts: the bankroll management guide covers unit sizing and trip bankrolls, and N0 explained covers how long "the long run" actually is. New to counting entirely? Start with Card Counting 101.
The Math This Calculator Uses
The calculator uses the standard infinite-horizon risk formula from the
blackjack literature:
RoR = e^(-2 · B · w / σ²), where B is your
bankroll in units, w is your win rate (edge) per hand, and
σ
is the standard deviation per hand. N0 is computed as
σ² / w², the number of hands at which your expected win
equals one standard deviation of variance, and hourly EV is
edge × average bet × hands per hour.
These are the same relationships developed in Don Schlesinger's Blackjack Attack (the definitive treatment of blackjack risk) and Peter Griffin's The Theory of Blackjack. Two assumptions to know: the formula models a fixed edge and standard deviation per hand (a simplification of a counter's hand-by-hand reality), and it assumes you never resize bets as the bankroll swings. Resizing downward after losses, as most real counters do, lowers the true risk below the number shown; playing on unchanged after losses does not.
Frequently Asked Questions
What is a safe risk of ruin for a card counter?
Most professionals target a risk of ruin below 2%, and many play to 1% or lower. Recreational advantage players sometimes accept 5-10% on a replaceable bankroll. Anything above 10% means variance is likely to end your career before your edge pays off.
How big a bankroll do I need to count cards?
A common rule of thumb is about 100 maximum bets for roughly 5% risk of ruin, or about 150 max bets to get near 1%. With a 1-12 spread from a $10 minimum ($120 max bet), that means a bankroll in the $12,000-$18,000 range. The calculator above gives exact numbers for your specific edge, spread, and standard deviation.
What standard deviation should I enter for blackjack?
Enter it in the same units as your bankroll: multiples of your average bet. Flat-betting basic strategy runs about 1.15. A bet spread pushes it higher, typically to roughly 1.6-2 times your average bet for a 1-8 to 1-12 spread in a 6-deck shoe. Counting books often quote 3 to 4 units per hand for those spreads, but those are minimum-bet units, not average-bet units.