Higher variance
Doubling standard deviation quadruples the variance term and materially increases modeled risk.
Poker Risk of Ruin Calculator
Estimate bankroll failure risk under a fixed positive-edge Brownian approximation, or solve for bankroll at a chosen target. The poker risk of ruin calculator makes unit and validity conditions explicit rather than presenting a certainty.
Brownian bankroll-failure approximation
The approximation assumes a fixed positive edge, independent increments and unlimited time; all bankroll values are in big blinds.
How the result is built
More Bankroll Reduces Risk but Does Not Remove Variance
Under a fixed positive-edge Brownian approximation, modeled risk declines with bankroll but remains conditional on win-rate and variance assumptions.
Current bankroll3,000 bb
Estimated current risk2.35%
Target risk5%
Modeled target bankroll2,397 bb
| Bankroll (bb) | Estimated risk |
|---|---|
| 0 | 100% |
| 750 | 39.16% |
| 1,500 | 15.34% |
| 2,250 | 6.01% |
| 3,000 | 2.35% |
| 3,750 | 0.92% |
| 4,500 | 0.36% |
| 5,250 | 0.14% |
| 6,000 | 0.06% |
The exponential model
Risk falls exponentially with bankroll and win rate, and rises with squared standard deviation. All values must use compatible big-blind scales.
Non-positive win rate breaks the premise
At zero or negative expected growth, the positive-edge formula cannot produce a protective bankroll target. The tool reports the condition instead of returning a misleading finite number.
Infinite-horizon approximation
Changing stakes, stopping rules, withdrawals, estimation error, and non-independent sessions alter actual failure probability. This is a comparative planning model.
Test sensitivity instead of trusting one forecast
The estimated chance of depletion is only as stable as the win-rate and variance assumptions behind it. Recalculate with a lower edge and a higher standard deviation, then compare the suggested reserve across those cases. A large change signals model uncertainty that one headline percentage would hide.
Worked examples
Target risk of zero
The infinite-horizon formula requires unbounded bankroll for literal zero risk.
Frequently asked questions
Why does the model require positive win rate?
Its decay in ruin probability depends on positive expected drift.
Is a 5% result a guarantee?
No. It is conditional on assumptions that can fail.
Why is standard deviation squared?
The Brownian approximation uses variance, which is standard deviation squared.
Can I solve for bankroll instead?
Yes. Select the target-risk mode.