Poker Cash-Game Risk of Ruin & Kelly Multistreet Calculator

Poker bankroll formula: Problem → Inputs → Model → Outputs → Interpretation

Poker bankroll problem

Poker bankroll planning gets distorted quickly when it is reduced to a slogan like “keep twenty buy-ins and hope the deck cooperates.” That advice misses the way rake trims your edge, how antes and deeper stacks amplify volatility, and how multi-tabling turns one volatile decision stream into several correlated ones. This calculator treats the bankroll as a capital-allocation problem in big-blind units: it estimates how much of the roll can be exposed at a given stake, how much Kelly growth is justified by the observed edge, and how sharply ruin risk rises when swings cluster over many hands. The point is not to guess whether a session will feel safe; it is to translate poker variance into a bankroll policy you can defend before you sit down.

That perspective matters most in cash games, where one rough river can undo several successful streets and where a win rate that looks healthy in tracker reports may still be fragile after rake. By framing the decision around risk-of-ruin curves, downside percentiles, and fractional Kelly sizing, the calculator helps you compare a conservative bankroll plan with a more aggressive shot-taking plan before real money is on the table.

Poker bankroll inputs

The poker bankroll inputs connect the math to your actual game. Total bankroll and table big blind size convert your roll into the units the model uses, while win rate and rake combine into the net edge that drives long-run growth. Standard deviation captures the size of the swings in bb/100, and the flop, turn, and river variance shares show which street is contributing most of that swing. Hands in your database determine how confident the calculator can be about the win rate estimate, so the confidence band tightens as your sample grows. Session hands, sessions projected, and tables at once define the exposure horizon, and the fractional Kelly selector tells the model whether you want to run at full, half, or quarter aggression.

The target-ruin input works in the opposite direction: instead of asking how likely the bankroll is to fail, it asks how large the bankroll must be to keep failure below a chosen ceiling over the projected timeline. That makes the page useful both for self-funded players and for staking conversations, because the same set of inputs can describe a cautious downswing buffer, a move-up plan, or a review of whether the current table mix is too volatile for the capital available. Every field is built for quick scenario testing, so you can compare a baseline cash-game setup against a softer, tougher, or more multi-tabbed version without changing the structure of the page.

Poker bankroll model

The poker bankroll model treats each hand as a drifted random walk in big blinds. Per-hand drift equals (win rate − rake)/100; per-hand volatility is the reported bb/100 standard deviation divided by . 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 . 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 so you can see where swings originate. Sample size feeds a standard error for the win rate, , where 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 , which becomes the suggested stop-loss. Solving the ruin expression for bankroll yields the minimum bankroll required to hit a target ruin probability: , where is the desired ruin ceiling.

Poker bankroll outputs

The poker bankroll outputs are organized around decisions rather than raw statistics. Kelly & Allocation shows the pure Kelly fraction, the selected fraction after scaling, the suggested capital per table, and how many shots the current roll supports at the chosen stake. Win Rate Confidence shows the 95% confidence interval for the observed win rate and then recomputes Kelly at the pessimistic edge so you can see how much of the apparent advantage survives uncertainty. Session Safety translates the math into expected session change, the chance of booking a losing session, the chance of losing 10% of the bankroll in one sitting, and a percentile-based stop-loss that can be checked against your discipline.

Street Variance Breakdown isolates the flop, turn, and river so you can tell whether the variance problem is coming from early aggression, turn pressure, or river decisions. Bankroll Planning answers the practical question of whether the current roll is large enough to stay under the chosen ruin ceiling across the projected session count, and it contrasts that with the ruin implied by your pessimistic win-rate estimate. Taken together, the output cards let you compare a normal day, a downswing-heavy stretch, and a move-up shot without leaving the page.

Poker bankroll interpretation

Read the poker bankroll interpretation as a set of guardrails, not a prediction that every session will match the curve exactly. If the pessimistic confidence band pushes Kelly near zero, the sample is either too small or the game is too volatile to justify much aggression. If one street accounts for a large share of variance, that is usually the first place to look for strategic leaks, because reducing river volatility often protects the bankroll faster than adding extra tables. If the target-ruin bankroll sits well above the bankroll you actually have, the calculator is telling you that the move-up plan needs more capital, less concurrency, or a much lower tolerance for drawdowns.

The same logic works in reverse when you set a stop-loss. A stop-loss above the 10th percentile session loss is usually a conservative checkpoint that allows ordinary variance to play out, while a stop-loss below that level can force you out during a routine downswing. Use the ruin curve, the percentile losses, and the pessimistic Kelly estimate together when deciding whether to sit, stay, or step down in stakes, because those three views are all looking at the same poker bankroll from different angles.

Worked $5/$10 NLHE bankroll example

For this poker bankroll calculator, 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.

Poker bankroll Kelly guardrail comparison

The comparison makes the trade-off plain. Doubling the Kelly fraction barely doubles the per-table allocation, yet it pushes session drawdowns and ruin odds noticeably higher. The bankroll requirement column is the clearest reminder that a player who wants to run at half Kelly either needs a larger roll or must accept a materially higher chance of being forced down before the projected session count is complete.

Poker street variance and confidence sensitivity

Tweaking the street weights shows whether the bankroll pressure is coming from the flop, the turn, or the river. If you set the flop weight to 35%, turn to 25%, and river to 40% to reflect looser river calling ranges, the river’s per-hand standard deviation jumps above $42 and the 10th percentile session loss grows by almost $200. In practical poker terms, that points toward cleaning up river bluff selection or reducing thin value spots where the bankroll is taking the biggest hits. Conversely, dropping rake from 9 to 7 bb/100 while keeping everything else equal lifts the pure Kelly fraction to 0.89% and shaves four ruin percentage points, which is why even a small rake improvement can matter more than another marginal study session.

Confidence intervals matter just as much as street weights. A player with only 40,000 hands logged sees the 95% interval widen to ±3.0 bb/100, which cuts the pessimistic Kelly fraction in half and pushes the pessimistic ruin probability above 20%. Until the sample gets larger, the safest response is usually to scale back concurrency, reduce stake size, or treat the current win rate as provisional rather than bankable. That is especially important in poker because a short-term heater can make a fragile edge look much more stable than it really is.

Poker bankroll assumptions, limits, and practical tips

The bankroll model assumes hands are independent and identically distributed, which is a useful simplification even though real poker is messier than that. Tilt, table changes, seat selection, and strategy adjustments can create streaks that are fatter-tailed than a clean Gaussian model, so the output should be read as a disciplined approximation rather than a promise. Street weights are also user supplied; if you estimate them poorly, the breakdown still helps you think about where the swings come from, but the exact dollar figures may drift away from reality. Kelly sizing also assumes you can resize risk smoothly, whereas live poker buy-ins are discrete and table caps can force you slightly above or below the ideal fraction.

Practical use of the calculator is straightforward. Re-run the page whenever your tracker sample meaningfully changes so the confidence band stays current. Use the 10th percentile loss as a candidate stop-loss when you want a rule that respects ordinary variance rather than your mood. Check whether moving up in stakes requires outside capital, a smaller table count, or a lower Kelly fraction before you make the jump. If a study block makes one street less volatile, update the street shares so the calculator reflects the new distribution of risk. And when you want a second opinion, copy the scenario hash and compare the baseline roll against a tougher or looser game mix before committing to the next session.

Poker bankroll testing checklist

• Edge cases: zero or negative net win rate should drive Kelly toward zero and make it clear that the bankroll is being asked to survive without a measurable edge.
• Validation: street weights that sum to zero should trigger an explanatory error, because the flop, turn, and river shares need at least one positive value to separate variance.
• Performance: the debounced recompute keeps large hand samples responsive, which matters when you are comparing several poker bankroll scenarios in one sitting.
• Accuracy: the CSV download lets you cross-check ruin checkpoints, survival probabilities, and Kelly fractions in a spreadsheet if you want a second look.
• Accessibility: the labeled controls, unit hints, and live results region make it easier to test poker bankroll assumptions on both desktop and mobile.

How to use this poker bankroll calculator

1. Enter Total bankroll as the amount of poker capital you want to protect.
2. Enter Table big blind size for the cash-game stake you are considering.
3. Enter Win rate (bb/100 hands) from your tracker, then set rake to match the game if you already track a gross rate.
4. Run one poker scenario, then compare it with a second setup for stakes, table count, or Kelly fraction before you move up.