Free poker tool
Poker Variance Calculator
The swings a win rate really produces, and what a sample of that size can and cannot prove.
Variance calculator
How wide your results can swing over a sample, and what that sample can actually prove.
From your own tracker
Expected result
3,000 bb
95% range
-3,198 to 9,198 bb
Chance of being down
17.1%
After the full sample
Result range over 100,000 hands
Over 100,000 hands, 95% of the time you finish between -3,198 and 9,198 big blinds — a spread of 12,396 bb around an expectation of 3,000. That same sample is consistent with a true win rate anywhere from -3.20 to 9.20 bb/100, which is why a sample this size cannot settle whether you are a winning player.
Win rate this sample is consistent with
-3.20 to 9.20 bb/100
The sample cannot distinguish between any two rates inside this range
What this model assumes
- Results per 100 hands are treated as independent and normally distributed. Real sessions are neither, so the tails are thicker than this model shows.
- Your win rate is treated as a known, fixed number. In reality it is itself an estimate, and games change.
- Standard deviation is your input. StackedPoker publishes no SD figures because it has no reviewed source for them — take yours from your own tracking software.
- Results are in big blinds, not currency, and ignore rake changes, table selection and tilt.
Why a winning player still loses for months
A win rate is an average, and averages say nothing about any particular stretch. Over any sample short enough to actually play, the spread around that average is wider than most players expect — often wider than the average itself.
This calculator puts a number on the spread so a downswing can be recognised as normal instead of as evidence that something is broken.
How the calculation works
Results per 100 hands are treated as independent draws with your win rate as the mean and your standard deviation as the spread. Over N hands the expectation grows linearly while the spread grows with the square root, which is exactly why more hands narrows the estimate of your win rate without narrowing the swings themselves.
The confidence interval then comes from the normal approximation. Four times the hands means twice the standard deviation, never four times.
expected = winrate x hands/100 spread = SD x sqrt(hands/100)
Common mistakes
- Treating a sample as proof of a win rate
- 100,000 hands at a 100 bb/100 standard deviation still leaves a confidence interval several big blinds wide. Most players who 'know' their win rate have a sample that cannot distinguish winning from breaking even.
- Guessing at standard deviation
- The spread depends entirely on this number, and it varies by game, format and stake. Take it from your own tracking software — StackedPoker publishes no SD figures because it has no reviewed source for them.
- Reading the interval as a limit on how bad things can get
- A 95% interval is breached one time in twenty, and real results have thicker tails than the normal model. The interval describes the ordinary case, not the worst one.
Practical examples
- 10,000 hands at 3 bb/100
- 95% of the time you finish between -1,660 and 2,260 big blinds, against an expectation of 300. Chance of being down after the whole sample: 38.2%. The same results are consistent with a true win rate anywhere from -16.6 to 22.6 bb/100.
- 100,000 hands at 3 bb/100
- 95% of the time you finish between -3,198 and 9,198 big blinds, against an expectation of 3,000. Chance of being down after the whole sample: 17.1%. The same results are consistent with a true win rate anywhere from -3.2 to 9.2 bb/100.
- 500,000 hands at 3 bb/100
- 95% of the time you finish between 1,141 and 28,859 big blinds, against an expectation of 15,000. Chance of being down after the whole sample: 1.7%. The same results are consistent with a true win rate anywhere from 0.2 to 5.8 bb/100.
- 1,000,000 hands at 3 bb/100
- 95% of the time you finish between 10,400 and 49,600 big blinds, against an expectation of 30,000. Chance of being down after the whole sample: 0.1%. The same results are consistent with a true win rate anywhere from 1.0 to 5.0 bb/100.
Key takeaway
Variance decides what your results look like; your win rate decides where they end up. Sizing the first is what stops the second from being abandoned halfway through.
Frequently asked questions
How many hands do I need to know my win rate?
More than most players think. Enter your own numbers above — at a 100 bb/100 standard deviation, even 100,000 hands leaves a confidence interval several big blinds wide.
What standard deviation should I use?
Your own, taken from your tracking software. It varies enough between games and formats that a borrowed number produces a misleading interval.
Is a long losing stretch normal?
For a small edge and a normal standard deviation, yes — the calculator will show you the probability of being down after any sample size you enter.
Related
Concepts, lessons and tools that build on this page.
- Free toolPoker Bankroll CalculatorHow many buy-ins your roll covers, what your own rule asks for, and when to move up or down.
- Free toolPoker Equity CalculatorExact hand-versus-hand equity: every remaining runout dealt and counted, not simulated.
- Free toolPoker EV CalculatorPut a number on a decision: expected value weighs every outcome by how often it happens.
- ConceptEquity Realization (EqR)How much of your theoretical equity you capture in practice.
- LessonDecision LabThree real hands. Every tool from this module, working together.
- LessonThink in Expected ValueJudge decisions by what they earn over time, not by what happened this one time.
Source: Confidence intervals use the normal approximation to a sum of per-100-hand results — textbook statistics, computed in lib/tools/variance.ts. The model's assumptions are listed on the page. StackedPoker publishes no win-rate or standard-deviation figures.