How to Estimate Poker Variance and Downswing Risk

Poker variance measures the spread of results around their expected value; a downswing is a decline in cumulative results from a peak to a subsequent trough. Neither a final loss nor a deep drawdown alone proves bad play or bad luck. To assess them, use comparable data, a calculation with explicit assumptions and a separate review of your decisions.

The poker variance simulator shows which outcomes a selected model allows. A positive win rate entered into the calculator is an assumption, not evidence that you have an edge over your opponents.

What data do you need?

For a cash-game calculation, you need a win rate and standard deviation from the same comparable sample of actual results, plus the number of hands to model. Mixing different playing conditions makes the calculation harder to interpret.

These terms describe different things:

Here, bb means big blind. The examples assume one cash-game buy-in is 100 bb; that is a model assumption, not a universal rule. See the win rate definition for more detail.

In your tracking software, filter for one format, one stake level and a comparable period. Changes in rake, opponents, table load or tilt can affect both average results and their spread. Your win rate should be net of rake; do not add rakeback if the other data you are comparing excludes it.

Use actual results with the same filters to obtain standard deviation. Do not substitute the standard deviation of all-in equity adjusted winnings: that is a different data series.

A game-format preset in the calculator is only a starting assumption. It does not measure your standard deviation or verify your personal win rate.

What does a 5.7% probability of loss mean?

With an assumed true win rate of 5 bb/100 and standard deviation of 100 bb/100, the model gives approximately a 5.7% probability of finishing 100,000 hands below zero. This is the probability of a final loss, not a drawdown or ruin.

The calculation assumes independent 100-hand blocks with normally distributed results and constant parameters. Each block has a mean result of 5 bb and a standard deviation of 100 bb. For the full sample:

SD_N = SD_100 × √(N/100)

For 100,000 hands, the expected result is +5000 bb, and the standard deviation of the total result is 3162 bb after rounding. The conditional 95% outcome range is −1198 to +11,198 bb.

The cash-game SD convention is displayed as bb/100, but the model treats 100 bb as the standard deviation of a 100-hand block. Variance is the square of that spread, not another name for the same number.

If the big blind is $1, the expected monetary result is +$5000. This is the model's mean, not a promise of profit.

The figures are rounded. The final value does not mean a loss is mathematically impossible. Every row is conditional: if your true win rate is lower than the input or playing conditions change, these probabilities no longer describe your play.

As the number of hands increases, the absolute standard deviation of total results grows in proportion to the square root of the volume. At the same time, the error in estimating the average win rate decreases. Neither fact means earlier losses must be recovered.

How do you repeat the calculation in the simulator?

Select cash-game mode, enter the example parameters and then run the simulation. You do not need a poker-room account or a connection to tracking software.

1. Open the simulator and select Cash game.
2. Select NLHE 6-max—six-player no-limit Texas hold'em—and the Standard preset.
3. After selecting the preset, manually check Win-rate at 5 bb/100, Standard deviation at 100 bb/100 and Number of hands at 100,000.
4. Set Big blind size to $1 and Bankroll to 30 buy-ins. Leave Observed win-rate blank.
5. Set Confidence level to 95% and Simulated runs to 10,000.

English simulator inputs showing cash game, a win rate of 5 bb/100, standard deviation of 100 bb/100 and 100,000 hands

Local localhost capture of the example inputs. The preset was selected before manually checking standard deviation.

The analytical calculation appears immediately: expected result +5000 bb, standard deviation 3162 bb, a 95% outcome range of −1198 to +11,198 bb and a 5.7% probability of final loss.

Analytical results showing an expected result of plus 5000 bb and a 5.7 percent probability of final loss

Local localhost capture. The analytical values are conditional on the entered win rate and rounded for display.

Next, click Run simulation. This generates repeated random paths using Monte Carlo simulation: here, normally distributed changes in results in 100-hand steps, not actual hand histories.

Simulated drawdown results showing a median maximum drawdown of 22.1 buy-ins and a 95th percentile of 41.4 buy-ins

Local localhost capture of 10,000 paths over 100,000 hands each. Drawdown is measured from a peak to a subsequent trough.

The example run used the fixed random seed 0x2f6b1d3c. If you change the inputs, run the simulation again: the previous output belongs to the previous parameters. The Observed win-rate field does not replace the assumed true win rate used in this simulation.

How is a drawdown different from a final loss?

A drawdown measures a decline within a path, so even a profitable sample can include a substantial downswing. A final loss asks a different question: did the ending result fall below zero?

For example, the cumulative-result sequence [0, 600, 200, -300, 1000, 100] ends with a net profit of +100 bb. Its maximum drawdown is nevertheless 900 bb, or 9 buy-ins: results fall from +1000 to +100 bb. The earlier decline from +600 to −300 bb is also 900 bb.

In the example simulation, the proportion of paths whose maximum drawdown reaches at least each threshold is:

These results come from 10,000 paths with an assumed win rate of 5 bb/100, standard deviation of 100 bb/100 and a 100 bb buy-in. Percentages are rounded to one decimal place; the model advances in 100-hand steps. These steps can miss peaks and troughs within each block, so the drawdown estimates apply to the discretised model rather than precisely capturing real hand-by-hand risk.

The median maximum drawdown is 2211 bb, or 22.1 buy-ins. Its 95th percentile is 4136 bb, or 41.4 buy-ins. The 95th percentile is not the worst possible drawdown: some paths experience deeper declines.

The paths do not stop when the specified bankroll is exhausted and can cross that boundary. These percentages therefore must not be described as risk of ruin. Likewise, a percentile band at an individual point in the sample does not mean the entire path has the same probability of staying inside it.

How accurately does a sample estimate your win rate?

A confidence interval describes uncertainty in the estimated mean win rate, not a range of future profits. When estimating an unknown mean from your own results, its centre must be your observed win rate.

The standard error is standard deviation divided by the square root of the number of 100-hand blocks. In this normal model, a two-sided 95% confidence interval uses a multiplier of 1.96. This calculation assumes known, constant SD; if SD is estimated from the sample, the interval is only approximate, and a Student's t framework may be needed.

If your measured win rate is 5 bb/100, SD is 100 bb/100 and the sample contains 100,000 hands, the interval is −1.20 to +11.20 bb/100. If your measured win rate is −2 bb/100 with the other inputs unchanged, it is −8.20 to +4.20 bb/100.

The table and chart assume a hypothetical measured win rate of 5 bb/100 at every sample size and constant SD of 100 bb/100. They do not predict how your results will develop. Interval bounds are rounded to two decimal places.

In the main example, Observed win-rate is blank. A range centred on the entered 5 bb/100 therefore cannot be presented as an independent assessment of skill: its centre is an assumption.

The meaning of a 95% confidence interval concerns the method's coverage when the procedure is repeated on new samples. It does not mean there is a 95% probability that your unknown personal win rate lies inside a particular interval already calculated. The method and its assumptions are explained in the NIST handbook.

What does an observed win rate of −2 bb/100 mean?

It is compatible with several explanations, not just random variation. Assuming a true win rate of 5 bb/100, the probability of observing a result no higher than −2 bb/100 over 100,000 hands is approximately 1.3%.

That is a conditional probability of a result under the specified model. It is not the probability that you are a winning player, and it does not prove the absence of mistakes.

Do not treat categorical verdicts in the interface as an assessment of decision quality. The calculator does not analyse hands or establish whether losses were caused by tilt, leaks or random variation.

How many hands do you need for a narrower interval?

The answer depends on the desired precision and standard deviation; there is no universal threshold. With known, constant SD of 100 bb/100, a two-sided 95% interval with a half-width of 2 bb/100 requires approximately 960,400 hands.

The tool's one-sided 95% calculation uses a multiplier of 1.6449, while the two-sided calculation uses 1.96. With a centre of 5 bb/100 and SD of 100 bb/100, the corresponding thresholds are approximately 108,228 and 153,664 hands. These are conditional on those parameters; they do not promise that a future sample will establish a positive win rate.

Can all-in equity adjusted winnings help?

All-in equity adjusted winnings help examine some randomness after an all-in, but they do not measure the full expected value of your decisions or confirm your true win rate.

In PokerTracker 4, this statistic uses the expected pot share at the all-in point when the actual hands are known and the calculation's conditions are met. Hands without an applicable all-in retain their actual result. Exceptions include unknown cards and some multiway pots with unequal stacks. See the official PokerTracker 4 documentation for details.

Equity here means the expected share of the pot under specified hands and runout assumptions. It is not an evaluation of a decision against an opponent's unknown range. The adjustment neither removes all randomness nor turns a results graph into a graph of true skill.

Review winning and losing hands from the same positions, similar pots and recurring decision types. Compare rake, opponents, the number of tables played simultaneously and signs of tilt. Random variation and a leak—a recurring weakness in your decisions—can coexist. A single bad beat or cooler does not explain the entire sample.

Can you use the same calculation for cash games, PLO and tournaments?

No: the units and model limitations must match the format. A cash-game calculation in bb/100 cannot be transferred directly to tournament results.

For no-limit Texas hold'em (NLHE) and pot-limit Omaha (PLO), you can use the cash model, but the win rate and SD must come from the relevant sample. One format's presets are not verified standards for another. There is also no universal number of buy-ins that is safe for every format.

For multi-table tournaments (MTT), the tool uses ROI—average net return relative to the entry cost—and standard deviation in buy-ins per tournament. Define the entry cost consistently and account for fees.

Payout structure, field size, bounties and re-entries affect the distribution of tournament results. Tournament mode approximates each entry with an independent normal result. This can produce impossible individual outcomes and distort rare large wins. It is therefore not an exact tournament-payout simulator, and its output should not be used to draw cash-game conclusions about risk of ruin.

What does risk of ruin show?

Risk of ruin estimates the probability of exhausting a bankroll over an infinite horizon at fixed stakes with an unchanged edge. It is a different model from drawdown frequency over 100,000 hands.

The diffusion approximation used is:

P ≈ exp(−2 × WR × B / SD²)

Here, WR is the assumed win rate in bb/100, SD is standard deviation under the same 100-hand convention, and B is bankroll in bb. With 30 buy-ins of 100 bb each, the bankroll is 3000 bb. The calculation assumes fixed parameters; the displayed percentages are rounded.

This comparison shows how sensitive the conclusion is to your unknown true win rate. You cannot call 30 buy-ins safe simply because the input field contains 5 bb/100.

At a win rate of 5 bb/100 and SD of 100 bb/100, the model gives approximately 30 buy-ins for a 5% risk and 46.1 buy-ins for a 1% risk. These are calculated values, not personal budget recommendations. With a zero or negative win rate, risk equals 1 in this infinite-horizon model—not as a claim that you will inevitably lose your bankroll in the next session.

For further analysis, use the bankroll calculator and the risk of ruin guide.

What should you do during a downswing?

Separate financial limits from a review of your play: first decide how much you can afford to lose without affecting essential expenses, then examine your data and decisions. The calculation does not require you to keep playing until a supposed recovery.

Use this practical sequence:

1. Check the sample conditions. Confirm format, stakes, rake, period and the basis used for net winnings. Recalculate the inputs if conditions have changed.
2. Review recurring decisions. Compare winning and losing hands from the same positions and similar pots. Do not focus only on the most painful losses.
3. Assess your state of mind and table load. If you notice tilt or poorer decisions while playing many tables, take a break and reconsider your workload.
4. Apply financial limits chosen in advance. Keep your bankroll separate from money for everyday needs. Move down in stakes or stop playing if necessary.
5. Update the calculation using comparable data only. Do not change the assumed win rate or SD merely to obtain a reassuring result.

The poker bankroll management guide explains budgeting principles in more detail. Do not replenish your bankroll with money needed for essential expenses, raise stakes or increase playing volume solely to recover losses.

The useful takeaway is not a promise of a turnaround. It is a clearer understanding of the losses your chosen model allows, the uncertainty in your win rate estimate and the decisions you can control now.