The formula
risk of ruin = exp(−2 × μ × B / σ²)
bankroll for risk r = −σ² × ln(r) / (2 × μ)
μ is the win rate per unit (bb per 100 hands, or ROI × buy-in per tournament), σ the standard deviation per the same unit, B the bankroll in the same units. The model assumes results are roughly normal and that you keep playing the same stakes.
Reference table (cash, σ = 90 bb/100)
| Win rate | Bankroll for 5% RoR | Bankroll for 1% RoR |
|---|---|---|
| 2 bb/100 | 61 buy-ins | 93 buy-ins |
| 5 bb/100 | 24 buy-ins | 37 buy-ins |
| 8 bb/100 | 15 buy-ins | 23 buy-ins |
| 12 bb/100 | 10 buy-ins | 16 buy-ins |
Reference table (tournaments, σ = 7 buy-ins)
| ROI | Bankroll for 5% RoR | Bankroll for 1% RoR |
|---|---|---|
| 10% | 734 buy-ins | 1,128 buy-ins |
| 20% | 367 buy-ins | 564 buy-ins |
| 30% | 245 buy-ins | 376 buy-ins |
| 50% | 147 buy-ins | 226 buy-ins |
Tournament variance is brutal, which is why most players move down in stakes during downswings rather than holding a bankroll of a thousand buy-ins. That behaviour, not the formula, is what keeps real players solvent. The rake calculator shows how much of a win rate rake takes before the bankroll question even starts.
Frequently asked questions
What is risk of ruin?
The probability of losing the entire bankroll before the win rate has time to work, assuming you never move down in stakes. The formula is RoR = exp(−2 × win rate × bankroll / σ²), with all quantities in the same units.
What standard deviation should I use?
For no-limit cash games 80–100 bb/100 is typical; 6-max runs higher than full ring. For tournaments the standard deviation in buy-ins depends on field size: about 3–5 for sit-and-gos, 6–8 for small MTTs, well over 10 for large fields.
How many buy-ins is enough?
With a 5 bb/100 win rate and 90 bb/100 standard deviation, 5% risk of ruin needs about 24 buy-ins of 100 bb; 1% needs 37. Tournament players with 20% ROI and 7 buy-in standard deviation need roughly 370 buy-ins for 5%.