Roulette Risk of Ruin
Risk of ruin is the probability that you go broke before reaching some target - a session length, a profit goal, or a bankroll doubling. It is the practical measurement of how survivable a strategy is.
Different strategies have wildly different risk of ruin even at the same expected loss.
The flat-bet formula
For flat betting on an even-money bet with house edge e in decimal form, starting with K base-bet units and betting until ruin or doubling the bankroll:
P(ruin) = 1 − ((1−e)/(1+e))K
| Units (K) | European (e=0.027) | American (e=0.053) |
|---|---|---|
| 20 | 67.4% | 84.5% |
| 50 | 47.4% | 65.0% |
| 100 | 49.4% | 75.6% |
| 200 | 24.7% | 55.5% |
| 500 | 6.2% | 20.3% |
For a $1,000 bankroll with $10 base bets (K=100), risk of ruin before doubling is roughly 49% on European.
How bet sizing changes risk
Doubling base bet quartiples short-session bust probability. Halving base bet halves bust probability over the same target spin count.
Practical: smaller bets, longer sessions, lower bust risk. The math of this is exact.
Risk by strategy
Approximate bust rates across 200 spins of $10 base on $1,000 bankroll, European:
| Strategy | Bust rate |
|---|---|
| Flat red | ~0% |
| D'Alembert | ~1-2% |
| Fibonacci | ~3-5% |
| Martingale | ~5-8% |
| Labouchere (1,2,3,4) | ~8-12% |
| Single number flat | ~5% |
| James Bond (scaled to $20/spin) | ~3% |
| James Bond (classic $200/spin) | Bust on first 1-12 streak |
These are aggregate numbers from thousands of simulated runs. Your own runs will vary.
Why progression bust rates are higher
Progression systems multiply stake during losing streaks. The same losing run that flat betting absorbs as -10 units, Martingale absorbs as -127 units (10+20+40+…).
Risk of ruin scales with the maximum bet size required, not just average bet size. Aggressive progressions have very high tail risk.
Reducing risk of ruin
- Smaller base bet (most impactful).
- Shorter session.
- Stop-loss rule (e.g. stop at −30% of bankroll).
- Avoid catastrophic-tail systems (Martingale, aggressive Labouchere).
- Choose European or French over American.
Estimating from the tester
Run any setup 20-50 times in the Roulette Strategy Tester. Count the busts. That ratio is a practical risk-of-ruin estimate for your specific setup.
More simulations = tighter estimate. The exact formula is for flat betting only - progression systems are best evaluated empirically.