GoodRun

BANKROLL & RISK · ADVANCED · LIVE CASH ONLY

Compare cash stakes with Kelly.

See how your assumptions change a bankroll-based stake reference.

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Illustrative inputs throughout, including an ASSUMED live SD of 120 BB/100. Change them for your game. There is no universal measured “normal live SD”. This compares bankroll exposure, not how much to bet or shove in a hand.

Your bankroll and live cash game
Money allocated to this poker scenario, in the same currency as the stake.
The actual money per big blind at the game you are comparing.
One representation is editable at a time. Your actual depth is derived, never silently fixed at 100 BB.
Already after rake and mandatory playing fees. This page never deducts them again.
Illustrative live NLHE input: ASSUMED, not measured. SD is not variance or standard error.

ASSUMED · Live NLHE example · not measured

SD starting points and evidence limits

Reference and evidence limits →

Currency is a unit label. No exchange rates, saved inputs or automatic fee subtraction.

Growth is a different question from ruin.

Kelly targets expected logarithmic wealth growth under an assumed distribution. It does not maximize the chance of winning the next hand or eliminate drawdowns. A short observed win rate is not proof of a true edge.

Proportional stake rebalancing differs from keeping one fixed stake, making withdrawals or needing a minimum buy-in. This page gives no Kelly ruin probability, drawdown forecast, shot-taking rule or tournament sizing. Fixed-stakes risk of ruin has its own model →. Check rake and direct playing fees separately →; enter the resulting net edge here without subtracting fees again.

The cash-poker approximation

Time t is in 100-hand blocks. With assumed true edge w BB/100, SD s BB for a 100-hand result, bankroll B and monetary big blind b, let a = b/B. The continuous model is dB/B = a × w × dt + a × s × dW. Its expected log-growth rate is g(a) = a × w − a² × s² / 2.

The derivative g′(a) = w − a × s² and g″(a) = −s² give full exposure aK = w / s². A fraction c uses ac = c × w / s², so modeled BB = B × c × w / s². For your entered depth k, bankroll fraction per buy-in = c × k × w / s², reference buy-ins = s² / (c × k × w), and bankroll threshold at entered BB bi = bi × s² / (c × w).

This assumes continuous rebalancing, constant edge/SD/depth across stakes, independent increments and no withdrawals or financing. It is a diffusion approximation to discrete cash poker. Mean and SD alone do not identify an exact discrete Kelly solution. Changing depth changes the buy-in description at unchanged edge/SD, but real game distributions can change with it.

Hourly inputs are converted once: w/hour = w/100 × hands/hour / 100 and SD/hour = SD/100 × √(hands/hour / 100). Mean divided by variance is unchanged by a consistent unit conversion; SD never scales linearly with time.

Fractional growth and volatility, within this model

With fixed assumptions, g(c)/g(1) = 2c − c². Half Kelly has 75% of full modeled log growth, 50% of log-return SD and 25% of log-return variance. Quarter has 43.75%, 25% and 6.25%, respectively. These are model ratios, not promised outcomes or drawdown limits. This tool does not implement a risk-constrained Kelly optimizer.

Sources and evidence limits

Edward Thorp on the Kelly objective; David Aldous, Berkeley: mean/variance approximation and uncertainty; Busseti, Ryu and Boyd: fractional versus risk-constrained Kelly. These sources explain the objective and limitations; none measures your edge or establishes a universal poker bankroll. The cash-poker unit derivation is stated above. Sources checked 1 November 2026.

The live NLHE/PLO SD starting points share the variance tool’s source and evidence labels. The defaults are assumed examples, not a measured live population.

Keep context for your next comparison.

Record sessions, stakes and expenses in GoodRun, then choose your own assumptions when comparing games.

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