Kelly + risk-of-ruin baseline
Chen and Ankenman, in Mathematics of Poker, give the closed-form for risk of ruin as an exponential function of win-rate divided by the standard deviation, scaled by the bankroll measured in big blinds. Three inputs. Two of them you do not yet know — the win-rate is a prior at this stage, and the standard deviation is roughly 100 bb/100 for 6-max NLHE cash. Your job is to set defensible priors and then update them with real data.
Chapter focus Compute risk of ruin for your current bankroll at NL10 given your win-rate prior, and set the stake-up threshold.
Load-bearing idea
Kelly says: bet a fraction of your bankroll proportional to your edge. Full Kelly maximizes long-run growth; fractional Kelly (1/2 or 1/4) trades growth for variance tolerance. Most successful poker bankroll management runs at roughly quarter-Kelly to half-Kelly. The risk-of-ruin formula above is the operationalization: it tells you the probability of going broke given current bankroll, win-rate, and variance.
The stake-up trigger is a function of your tolerance for risk-of-ruin. If you decide a 1% risk-of-ruin is the maximum acceptable, you need bankroll plus win-rate that satisfy that constraint at the next stake. NL25 has 2.5× the variance per dollar of NL10, so the bankroll requirement scales accordingly.
Retrieval prompts
- What does the risk-of-ruin formula tell you, and what assumptions does it make?
- How does fractional Kelly differ from full Kelly, and why prefer fractional in poker?
- At what bankroll size, given your prior win-rate, would risk of ruin at NL25 drop below 1%?
- What is the operational difference between a “shot-take” at the next stake and a “stake-up”?
Re-derivation log
Run the playground above with your actual current bankroll in bb. Then vary win-rate from 0 to 5 bb/100 and watch how risk-of-ruin changes. Note the inflection point — the win-rate below which risk-of-ruin becomes unacceptable. That win-rate is your stake-up threshold.