Calculator
Approximation: ROR = e^(-2 × edge × bankroll / variance), where edge is decimal per hand.
What Risk of Ruin Means
Risk of ruin (ROR) is the probability that you will lose your entire bankroll before it grows indefinitely. Even with a positive edge, short-term variance can wipe out an underfunded bankroll. ROR quantifies exactly how likely that is.
The classic formula is: ROR = e(−2 × edge × bankroll / variance), where edge is your average advantage per hand (as a decimal), bankroll is measured in betting units, and variance is the variance per hand in units squared. The formula assumes a fixed bet size — in practice, your bet spread changes the effective variance.
A 5% ROR means there is a 5% chance you will go broke. A 1% ROR means a 1% chance. No bankroll is ever 100% safe — but you can make the probability of ruin acceptably small.
Understanding Each Input
Bankroll (units)
Your total bankroll measured in minimum bet units. If you play $10 tables and have $5,000 set aside for blackjack, your bankroll is 500 units. Only count money you have specifically dedicated to blackjack — not your rent money or emergency fund.
Player Edge per Hand (%)
Your average expected advantage per hand, including all hands played at every count. For a Hi-Lo counter using a 1-8 spread at a decent 6-deck game, this is typically 0.5% to 1.0%. Basic strategy players have a negative edge (the house has the advantage), so this calculator is primarily for counters.
Getting your edge right is critical. Overestimating your edge by even 0.2% dramatically underestimates your risk. If you are unsure, use the Blackjack 3000 simulator to estimate your edge for your specific rules, spread, and penetration.
Variance per Hand (units²)
The variance of your results per hand. For flat-betting basic strategy, variance is approximately 1.3 units² per hand. With a bet spread, effective variance increases because your larger bets contribute more to overall swings. A 1-8 spread might have an effective variance of 5-8 units², and a 1-12 spread could be 10-15 units².
If you do not know your exact variance, use 1.3 for flat betting or estimate based on your spread. Many simulation tools (like CVCX or the Blackjack 3000 sim) can calculate this for your exact game conditions.
Practical Bankroll Scenarios
| Bankroll (units) | Edge | Variance | ROR | Assessment |
|---|---|---|---|---|
| 200 | 0.8% | 1.3 | 8.5% | Aggressive, expect some busts |
| 500 | 0.8% | 1.3 | 0.04% | Very safe for flat betting |
| 500 | 0.8% | 7.0 | 32% | Spread increases variance significantly |
| 1000 | 0.5% | 7.0 | 24% | Modest edge with wide spread |
| 1000 | 1.0% | 7.0 | 5% | Good edge, acceptable risk level |
| 2000 | 1.0% | 7.0 | 0.3% | Very comfortable bankroll |
Notice how variance from bet spreading dramatically changes the picture. A bankroll that looks very safe for flat betting (500 units at 0.8% edge → 0.04% ROR) becomes risky when you add a realistic spread (500 units with spread variance 7.0 → 32% ROR).
How to Lower Your Risk of Ruin
There are only three levers:
- Increase your bankroll. The most straightforward approach. Doubling your bankroll roughly squares the ROR (e.g., 10% becomes 1%).
- Increase your edge. Better game selection (deeper penetration, better rules) improves your hourly edge. Every 0.1% matters.
- Decrease your variance. Use a smaller bet spread. A 1-6 spread has much lower variance than 1-12, but also less expected hourly profit. This is the fundamental trade-off in bankroll management.
The Kelly criterion suggests sizing your top bet so that your edge divided by variance is optimized. Full Kelly is the maximum growth bet but comes with roughly a 13.5% ROR. Most professional counters use half-Kelly or less for a more comfortable ride.
Common Mistakes
- Using flat-bet variance with a spread. If you bet 1-8, your effective variance is much higher than 1.3. Using the flat-bet number makes your ROR look artificially low.
- Overestimating your edge. Your theoretical edge assumes perfect play, correct counting, and correct deviation execution. In reality, fatigue, distractions, and speed pressure reduce your effective edge. Be conservative.
- Not counting expenses. Trip costs, tipping, and meals come out of your bankroll. If you travel to play, your effective bankroll is smaller than your chip stack.
- Playing through a losing streak “because the math says I should win.” ROR is calculated before you start. Once you have lost half your bankroll, your new ROR is higher because you have fewer units. Reassess if your bankroll shrinks significantly.
Frequently Asked Questions
What ROR should I target?
Professional counters typically target 1-5% ROR. Recreational players who can replenish their bankroll might tolerate 10-20%. A 0% ROR is impossible — you can only make the probability very small. Choose a level that lets you sleep at night.
Does ROR account for my bet spread?
Only if you input the correct effective variance. The calculator uses a simplified exponential formula. For a spread bet strategy, your effective variance is higher than flat-bet variance. Input the spread-adjusted variance for an accurate result.
Can I use this for sports betting or poker?
The ROR formula works for any game where you have a quantifiable edge and variance. The inputs are the same: bankroll, edge per bet, and variance per bet. The formula does not account for opponent adaptation, changing bankrolls, or non-stationary edges.