The formula
For a player with positive win rate, the standard approximation is:
RoR ≈ exp(−2 × WR × BR / SD²)
Where WR is win rate in BB/100, BR is bankroll in big blinds, and SD is standard deviation in BB/100.
Worked examples
Example 1: A 5 BB/100 NLHE winner
WR = 5, BR = 3,000 BB, SD = 100. Compute:
RoR ≈ exp(−2 × 5 × 3,000 / 100²) = exp(−3) ≈ 0.0498 = ~5%
5% risk of ruin — right at the standard professional target. A 5 BB/100 winner with 30 buy-ins (3,000 BB at 100bb buy-in) and normal SD is in the comfortable zone.
Example 2: Doubling the bankroll
Same player, 6,000 BB bankroll (60 buy-ins):
RoR ≈ exp(−2 × 5 × 6,000 / 100²) = exp(−6) ≈ 0.0025 = ~0.25%
Doubling the bankroll dropped risk of ruin from 5% to 0.25% — a 20× improvement. This is the exponential decay people miss when thinking about bankroll size.
Example 3: PLO with the same bankroll
Same WR = 5, BR = 3,000 BB, but SD = 150 (PLO):
RoR ≈ exp(−2 × 5 × 3,000 / 150²) = exp(−1.33) ≈ 0.264 = ~26%
The same nominal bankroll runs 26% risk of ruin in PLO — totally different territory. This is why variance is the variable most players ignore and why PLO bankroll requirements are much higher than NLHE.
What target should you set?
- Below 1% — conservative / professional. Appropriate when poker income pays rent. Requires a comfortable bankroll buffer.
- Below 5% — moderate / standard. The typical serious-player target. Standard 30 buy-ins for NLHE cash lands here.
- Below 10% — aggressive. Acceptable if you can move down stakes immediately when bankroll drops below threshold. Not acceptable if you cannot.
- Above 10% — dangerous. Going broke is a real risk, not a tail risk.
The exponential intuition
Risk of ruin is exponential in BR/SD². The practical translation:
- Doubling bankroll squares the RoR — 5% becomes 0.25%.
- Halving bankroll square-roots the RoR — 5% becomes 22%.
- Doubling SD quadruples the exponent's denominator, so RoR jumps from 5% to roughly 50% at the same bankroll.
- Doubling win rate doubles the negative exponent — 5% becomes 0.25%.
Common mistakes
- Treating RoR as static. RoR updates as your bankroll moves and as your realized win rate clarifies. Recalculate at least monthly.
- Using assumed SD instead of measured SD. If your tracker measures SD = 140 but you assume SD = 100, your real RoR is much higher than you think.
- Calculating RoR with a win rate from a tiny sample. A 5 BB/100 realized winner over 5k hands might actually be a 0 BB/100 player. RoR with the wrong input is fiction.
- Ignoring stake-up RoR. RoR for your current stake is fine — but if you are about to move up, run the math for the new stake before you do.
How StackEdge handles this
StackEdge measures your realized win rate and standard deviation from your session log and updates risk of ruin live. The app surfaces stake-down warnings when RoR rises above your target, and stake-up opportunities when bankroll growth makes the next stake comfortable. Use the free bankroll calculator to model hypothetical scenarios without the app.
