Poker Variance Calculator for Cash Games

This poker variance calculator models cash game results from your expected winrate, standard deviation and number of hands. Compare the chance of finishing in the red with the size of a possible downswing, or check an observed winrate against a stated expectation. It supports custom inputs for NL Hold’em, PLO, full ring and heads-up games.

For example, at 5 bb/100 and SD 90, the model gives a 3.95% chance of a loss after 100,000 hands. A drop from an earlier peak is a different event and can happen even when the final result is profitable.

What is Poker Variance?

Poker variance describes the spread of results around an expected value. Winrate measures the expected profit per 100 hands; standard deviation measures the scale of fluctuations. A positive assumed winrate shifts the distribution toward profit, but individual samples can finish below expectation or below zero.

Here, bb means one big blind. A buy-in is defined as 100 bb throughout the tool. At NL50, one big blind is $0.50 and one such buy-in is $50. These units are separate from the fixed-limit convention in which “BB” can mean a big bet.

How to Calculate bb/100 from Profit

Use bb/100 = net profit ÷ big blind value × 100 ÷ hands. For example, $1,000 net profit over 20,000 hands with a $1 big blind equals 5 bb/100. Enter that result as the observed rate in the analysis tab. If your sample mixes stakes, first express each hand or session result in its own big-blind units rather than dividing the combined dollar profit by one blind size.

How to Use the Poker Variance Calculator

1. Enter an expected winrate. Use a net estimate after rake. Include rakeback only if you are consistently counting it in both the expectation and observed results.
2. Enter SD in bb/100. Prefer a value measured from a comparable game and stake. A preset is a starting scenario, not a personal measurement.
3. Choose the hand count. This sets the horizon for the final-result distribution and the simulated maximum drawdown.
4. Set the big blind. Enter 1 for NL100 or 2 for live $1/$2. This converts big blinds to dollars without changing the probabilities.
5. Run the simulation. The analytical results use the normal model. Drawdown estimates use 2,000 simulated paths; the graph displays 12 of them.

The advanced controls set hands per hour and a simulation seed. Identical inputs and seed reproduce the same paths. “New random paths” changes the seed; it does not change the analytical loss probability. Editing an input hides the old result until you calculate again.

Standard Deviation by Game Type

The presets below are illustrative scenarios retained for convenient comparison. They are not verified population averages from tracking software. Stack depth, game structure, opponents and your decisions can produce a different SD.

Playing Style & Standard Deviation

A style label or VPIP alone does not establish SD. The tool therefore does not automatically multiply volatility for “tight,” “LAG” or “maniac” play. Enter a measured value, or compare several plausible values while holding the winrate fixed. Increasing SD from 90 to 140 multiplies modeled variance by (140/90)², approximately 2.42.

PLO Variance Calculator Example

Holding winrate at 5 bb/100 and the sample at 100,000 hands, changing SD from the NL 6-max preset of 90 to the PLO 6-max preset of 140 raises the modeled chance of a final loss from 3.95% to 12.94%. This compares two chosen volatility inputs; it does not mean every PLO player has SD 140.

The Variance Formula & Confidence Intervals

Let w be winrate, s be standard deviation and T = hands / 100. With independent increments and constant inputs:

• Expected total profit: w × T bb.
• SD of total profit: s × √T bb.
• Standard error of sample winrate: s / √T bb/100.
• Central 95% total-result range: w × T ± 1.959964 × s × √T.

The normal distribution supplies the quantile used in these ranges; see the NIST normal distribution reference. Its application here is a model of aggregated poker results, not a simulation of individual cards.

Example Calculation

For 5 bb/100, SD 90 and 100,000 hands, T = 1,000. Expected profit is 5,000 bb and total SD is approximately 2,846.05 bb. The central 95% final-result range is −578.16 to 10,578.16 bb, equivalent to −0.58 to 10.58 bb/100.

This is an outcome range conditional on the assumed edge. To estimate an underlying winrate from actual results, the “Am I running bad?” tab instead centers its approximate confidence interval on your observed rate. The distinction matters: an expectation is an input, not proof of your true edge.

Probability of Loss Over Sample Size

The chance of a final result below zero is Φ(−w × √T / s), where Φ is the standard normal cumulative distribution. Every entry below uses SD 90 and the stated constant winrate.

These are endpoint probabilities. They do not describe the chance of losing 20 buy-ins along the way. At zero winrate and positive SD, the symmetric model gives a 50% chance of finishing below zero at any positive horizon.

Typical Downswing Statistics

A maximum drawdown is the largest drop from any preceding cumulative-profit peak during the chosen sample. A path that rises from zero to 3,000 bb, falls to 1,000 bb and finishes at 4,000 bb has a 2,000 bb drawdown while ending in profit.

The poker variance calculator estimates the share of simulated paths with drops of at least 10, 20, 30 and 50 buy-ins. It also reports the median and 95th percentile of maximum drawdown. There is no single “normal downswing probability” independent of hand count, winrate and SD.

Drawdowns are measured at up to 10,000 evenly spaced checkpoints per path: every 10 hands at the default 100,000-hand horizon. Samples up to 100,000 hands use approximately 10-hand spacing; longer samples use 10,000 checkpoints, giving 100-hand spacing at one million hands. Peaks and troughs between checkpoints are missed, so these are sampled-path estimates. The displayed Monte Carlo intervals measure uncertainty from using 2,000 paths; they do not include this timing limitation or uncertainty in your inputs.

Cash Game Downswing Example: 100,000 Hands

Both scenarios below use SD 90, 100,000 hands, 2,000 paths, a 10-hand grid and seed 42. Only the assumed winrate changes. One buy-in (BI) is 100 big blinds. These are reproducible sample results from version 3.1 of the tool, not measured frequencies from a population of poker players.

For the 5 bb/100 scenario, 48.30% of paths experience a 20-buy-in drawdown, while the analytical chance of finishing below zero is 3.95%. The 95% Monte Carlo interval for that drawdown frequency is approximately 46.12%–50.49%; it covers simulation sampling uncertainty only. For the 2 bb/100 scenario, the corresponding drawdown frequency is 75.30% and the analytical chance of a final loss is 24.11%.

A new seed changes the sampled statistics. A finer grid can reveal drops missed between checkpoints. The denser grid in version 3.1 also changes the seeded paths, so its drawdown numbers should not be compared with the old 100-hand-grid example as if they were the same paths.

How Long Can a Downswing Last?

The duration output is the median of each path’s longest observed period below a previous peak. It includes unfinished periods only up to the end of the sample. It is neither an average recovery time nor a deadline by which your results should improve. Converting hands to hours also requires your playing pace.

Real-World Downswings: NL50 and NL100 in Dollar Terms

The same drawdown threshold has a different dollar value at each stake. The last column repeats the 5 bb/100, SD 90, 100,000-hand, seed 42 scenario above. It is the share of sampled paths reaching at least that peak-to-trough drop, not a chance of losing the stated amount at the end.

Changing only the dollar value of the big blind leaves these model probabilities unchanged. Changing stakes can also change your actual edge and SD, so reusing the same inputs is a comparison assumption. No recovery deadline follows from this table.

Bankroll Requirements Based on Variance

The optional bankroll panel uses a separate infinite-horizon Brownian approximation: risk = exp(−2 × w × B / s²), where B is the starting bankroll in big blinds. For positive w, solving for B gives B = −s² × ln(risk) / (2 × w). This follows from the barrier-hitting result in Karl Sigman’s Brownian motion notes, section 1.8, applied to the negative of cumulative profit.

At 5 bb/100 and SD 90, the 5%, 2% and 1% model thresholds are approximately 2,426.54, 3,168.74 and 3,730.19 bb. Rounding up to whole 100 bb buy-ins gives 25, 32 and 38 buy-ins. The dollar column in this tool funds those whole buy-ins: at a $1 big blind, the 5% row is $2,500. A tool displaying the threshold in individual big blinds may instead show about 2,427 bb; that is a rounding and presentation difference. These outputs assume a known edge, fixed stakes, unlimited future play and no withdrawals. They are not finite-sample downswing probabilities or universal bankroll recommendations.

With zero or negative winrate and positive SD, no finite bankroll achieves those low eventual-ruin targets in this model. For a fuller bankroll calculation, use the risk-of-ruin tool or the bankroll requirements calculator.

How Many Hands for Statistical Significance?

Sample size determines precision, but there is no universal hand count that proves someone is a winning player. With SD fixed at 90, the approximate 95% margin around an observed winrate is:

A target margin of ±3 bb/100 requires approximately 345,732 total hands at SD 90. The formula is hands = 100 × (1.959964 × SD / margin)², rounded up. A confidence level describes the long-run coverage of the interval procedure; see NIST’s explanation of confidence limits. Estimating SD from data or changing games introduces additional uncertainty.

Hourly Rate: Where Variance Meets Volume

Expected hourly profit is winrate × big blind × hands per hour / 100. The modeled SD of one hour’s profit is SD × big blind × √(hands per hour / 100).

At 5 bb/100 and SD 90, NL100 with 400 hands per hour gives an expected $20 per hour and one-hour profit SD of $180. Live $1/$2 with 25 hands per hour gives an expected $2.50 per hour and modeled one-hour SD of $90. At live $2/$5 with the same hand count, the corresponding values are $6.25 and $225.

A 25-hand normal approximation is particularly rough because individual pot sizes matter. None of these values is a worst-hour limit. To separate rake and rakeback from your net edge, use the rake and rakeback calculator.

“Am I Running Bad?” — How to Analyze Your Results

Suppose your expected winrate is 5 bb/100, but you observe 2 bb/100 over 80,000 hands with SD 90. The standard error is approximately 3.18 bb/100 and the z-score is −0.943. Under the entered expectation, about 17.29% of equally sized samples finish at 2 bb/100 or lower.

The two-sided p-value is 34.58%. The approximate 95% confidence interval centered on the observed rate is −4.24 to 8.24 bb/100. The result is compatible with the assumed edge, but that does not establish that the edge is correct or that your decisions are good.

The poker variance calculator cannot assign a probability that “this is just luck.” Its probabilities are conditional on the model and the values entered. An unusually low or high result is a reason to examine assumptions and the sample, not an automatic diagnosis of a leak or a newly improved strategy.

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Frequently Asked Questions (FAQ)