Problem → Inputs → Model → Outputs → Interpretation

Problem

Bankroll debates in card rooms often reduce to folklore: “twenty buy-ins is plenty” or “move up when you feel unstoppable.” Those rules ignore the structural realities of multistreet poker. Rake and antes clip the drift, multi-tabling compounds variance across parallel hands, and the correct Kelly fraction shrinks dramatically when the underlying win rate is noisy. The real decision is not whether you can afford a seat tonight, but how much capital you can expose per table while keeping ruin probabilities tolerably low across months of play. Equally important is understanding how fragile your plan becomes if rake rises two big blinds, if your sample of hands is too short, or if river volatility dominates the variance budget. This calculator reframes bankroll management as a quantitative capital-allocation problem, not a motivational slogan.

The tool therefore targets decision quality: it measures how far you can push table stakes before hitting a ruin ceiling, how much confidence you should have in the measured win rate, and which street contributes the most to brutal drawdowns. With shareable URL hashes and CSV exports, you can iterate scenarios for staking pitches, bankroll splits between live and online play, or risk policies for a backed stable.

Inputs

The form captures the variables that actually move bankroll risk. Bankroll size and big blind denomination translate cash into the big-blind units that variance math expects. The win-rate field accepts your gross technical edge in bb/100 before rake or antes; the adjacent rake control lets you model alternative fee schedules without retuning tracker reports. Standard deviation in bb/100 captures the volatility of a full hand cycle, while the street-variance weights distribute that volatility across flop, turn, and river so you can highlight which street causes the largest swings.

Hands logged in your database build a confidence interval for the win rate; if the sample is thin, the planner automatically reports a pessimistic Kelly fraction. Session hands, sessions tracked, and table concurrency define the time horizon and total number of correlated draws. The fractional Kelly selector scales aggressiveness (full, half, or quarter Kelly), the survival horizon projects a specific hand count, and the target-ruin slider solves for the bankroll required to stay below a chosen ruin probability. Every input is labeled for screen readers and designed for mobile thumb usage, and changing any control debounces into a smooth recompute.

Model

The bankroll is modeled as a drifted random walk in big blinds. Per-hand drift $\mathrm{\backslash mu}$ equals (win rate − rake)/100; per-hand volatility $\mathrm{\backslash sigma}$ is the reported bb/100 standard deviation divided by $\sqrt{100}$. Concurrency multiplies the hand volume each session, so two tables at 500 hands inject 1,000 independent draws into one risk block. Classical Kelly sizing maximizes expected log growth, yielding the familiar MathML expression $f_{*}=\frac{\mathrm{\backslash mu}}{{\mathrm{\backslash sigma}}^2}$. Fractional Kelly simply scales that solution to trade growth for stability.

Street weights break variance into components. If the flop accounts for 50% of variance, the turn 30%, and the river 20%, the planner computes per-street standard deviations ${\mathrm{\backslash sigma}}_{\text{street}}=\sqrt{w}·\mathrm{\backslash sigma}$ so you can see where swings originate. Sample size feeds a standard error for the win rate, ${\mathrm{\backslash sigma}}_{\text{mean}}=\frac{{\mathrm{\backslash sigma}}_{100}}{\sqrt{\frac{H}{100}}}$, where $H$ is hands observed. That variance feeds a pessimistic win rate and a tighter Kelly fraction for risk-averse planning.

Risk of ruin uses a diffusion approximation to Brownian motion with drift, reported earlier in MathML. The planner also reports the 10th percentile session loss, computed as $L=-\mathrm{\backslash mu}N-z{\mathrm{0.10}}_{}\mathrm{\backslash sigma}\sqrt{N}$, which becomes the suggested stop-loss. Solving the ruin expression for bankroll yields the minimum bankroll required to hit a target ruin probability: $W_{\text{target}}=-\frac{{\mathrm{\backslash sigma}}^2}{2\mathrm{\backslash mu}}·\mathrm{\backslash ln}\left(\mathrm{\backslash rho}\right)$, where $\mathrm{\backslash rho}$ is the desired ruin ceiling.

Outputs

The results panel now surfaces five themed sections. Kelly & Allocation reports the pure Kelly fraction, the selected fraction after scaling, per-table capital, and an estimated count of “shots” at the stake. Win Rate Confidence shows the 95% confidence interval for the tracked hands, along with the Kelly fraction and recommended allocation if your true win rate were at the pessimistic bound. Session Safety summarizes expected session change, probability of a losing session, probability of dropping 10% of bankroll in one sitting, and the 10th percentile loss that can serve as an objective stop-loss.

Street Variance Breakdown presents an accessible table of variance share and per-hand standard deviations for flop, turn, and river so you can sanity-check whether specific streets deserve focused study. Bankroll Planning solves for the bankroll required to keep ruin below the chosen target over the projected sessions, and it contrasts that with the ruin probability implied by your pessimistic win-rate estimate. The familiar ruin curve and survival quantiles still appear, and the CSV export now includes survival probabilities plus both optimistic and pessimistic Kelly fractions for every checkpoint.

Interpretation

These richer outputs let you interrogate bankroll policy from multiple angles. If the pessimistic confidence band collapses your Kelly fraction to near zero, you know the sample is too small or the game mix too variable to justify aggressive moves. If the street breakdown reveals the river contributing 45% of variance, plugging leaks in river play will reduce bankroll stress faster than grinding more hands. The target-ruin slider reverses the usual thought process: instead of asking “how likely am I to bust with $X,” you can ask “how much capital must I hold to stay under 5% ruin across my planned year of sessions?”

Because session stop-losses and target bankroll estimates are derived from the same variance model, they are consistent. A stop-loss above the 10th percentile session loss means you are effectively playing more than full Kelly and should expect enormous drawdowns when variance clusters. Shareable hashes encode every input, so staking partners or backers can audit the assumptions before wiring funds.

Worked $5/$10 NLHE Example

Consider a grinder with a $20,000 bankroll eyeing $5/$10 six-max. Tracker exports show a gross technical win rate of 15 bb/100 before rake, rake and antes totalling 9 bb/100, and a 95 bb/100 standard deviation across 120,000 hands. Two tables, 500 hands each, define a 1,000-hand session. With quarter Kelly, the pure Kelly fraction lands near 0.67% and the selected fraction near 0.17%, implying roughly $34 of total risk capital per session or $17 per table. That figure may look tiny compared with a $1,000 buy-in, but it reflects the reality that full Kelly bankroll sizing is extremely aggressive in cash games—the model reveals that firing full $1,000 stacks corresponds to playing several multiples of Kelly.

The Win Rate Confidence card shows a 95% interval of 12.4 to 17.6 bb/100. Using the pessimistic 12.4 bb/100 input would cut the Kelly fraction to 0.14% and the per-table allocation to ~$14, warning that a few bad months could erase the edge entirely. Session Safety reports an expected change of +$300, a 41% chance of a losing session, only a 6% probability of dropping 10% of the bankroll in one sitting, and a 10th percentile loss of $1,180—perfect fodder for setting a disciplined stop-loss. Bankroll Planning states that to keep ruin below 5% across 120 projected sessions you should hold ~$27,500; with your actual $20,000 roll the pessimistic win rate implies a 9% ruin probability.

Kelly Guardrail Comparison

The table illustrates the trade-off clearly. Doubling the Kelly fraction barely doubles the per-table allocation yet inflates session drawdowns and ruin probabilities. The bankroll requirement column shows that a player insisting on half Kelly should either boost the bankroll to ~$23k or accept a fifth of their careers ending before 120 sessions elapse.

Street and Confidence Sensitivity

Tweaking street weights exposes structural leaks. If you set the flop weight to 35%, turn to 25%, and river to 40% to reflect loose river calling ranges, the river’s per-hand standard deviation jumps above $42, and the 10th percentile session loss grows by almost $200. That signals the need to tighten river play or reduce aggression on marginal bluffs. Conversely, dropping rake from 9 to 7 bb/100 while keeping all else equal lifts the pure Kelly fraction to 0.89% and shaves four ruin percentage points—a strong argument for chasing rakeback or softer venues.

Confidence intervals matter equally. A player with only 40,000 hands logged sees the 95% interval widen to ±3.0 bb/100, cutting the pessimistic Kelly fraction in half and raising the pessimistic ruin probability above 20%. Until volume grows, the planner recommends scaling back concurrency or moving down in stakes to respect the uncertainty in the win-rate estimate.

Assumptions, Limitations, and Practical Tips

The diffusion approximation assumes independent, identically distributed hands. Real poker contains serial correlation from tilt, table lineup changes, and evolving strategies, which can fatten the tails beyond the model’s Gaussian assumption. Street weights are user supplied; if you guess poorly, the breakdown still helps highlight which parts of your game deserve scrutiny, but the absolute numbers may differ. Kelly sizing assumes you can resize risk continuously; in live poker where buy-ins are discrete (e.g., 100bb minimum), you will inevitably play slightly above the theoretical Kelly fraction—use the stop-loss and target bankroll outputs to decide how far above you are comfortable going.

Practical tips drawn from the planner: (1) rerun the model monthly with updated tracker data so the confidence interval tightens; (2) encode session stop-losses equal to the 10th percentile loss and include them in your pre-session checklist; (3) use the target ruin slider to evaluate whether moving up in stakes requires outside capital or selling action; (4) adjust street weights after dedicated study sessions (e.g., postflop solver review) to quantify how much the work reduced variance; (5) share the generated URL hash with backers or staking partners to align on risk tolerances.

Testing Checklist

• Edge cases: zero or negative net win rate collapses Kelly fractions to zero and warns that ruin is inevitable.
• Validation: street weights that sum to zero trigger an explanatory error; sample sizes below 1,000 hands block computation.
• Performance: debounced recompute keeps 500,000-hand horizons responsive even on mid-range mobile devices.
• Accuracy: CSV export includes optimistic and pessimistic Kelly fractions for every checkpoint so spreadsheet cross-checks are easy.
• Accessibility: every control is labeled, helper text describes units, and the aria-live results region announces updates to screen readers.