Poker Variance Calculator
Free Monte Carlo poker simulator — enter your win rate and standard deviation to visualize downswings, confidence bands, and risk of ruin over up to 1,000,000 hands.
Enter your stats and tap Simulate
Expected
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Worst 5%
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Risk of Ruin
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What Is Poker Variance?
Variance measures how far your actual results can stray from your expected value. If you're new to EV, start with our EV calculator guide — variance is the volatility around your long-run average; EV is that average. In poker, even a strong winner with a 5 bb/100 win rate will experience massive swings due to the inherent randomness of the cards. A player might run 50,000 hands below expectation despite playing perfectly — and that's completely normal.
This calculator uses Monte Carlo simulation to model 1,000 independent bankroll trajectories based on your win rate and standard deviation. Each simulation batch uses normally distributed random variables (Box-Muller transform) to generate realistic results, then aggregates them into percentile bands and summary statistics.
Understanding Standard Deviation
Standard deviation (SD) quantifies how spread out your results are around your average. It's measured in bb/100 just like win rate. A typical NL Hold'em cash game player has an SD of 60-100 bb/100. PLO players typically see 100-150 bb/100 because pots run bigger relative to stack sizes and equities run closer.
Why does SD matter? Consider two players, both winning at 5 bb/100. Player A has an SD of 60 bb/100 (tight style) and Player B has 100 bb/100 (aggressive style). After 100,000 hands, Player A's worst 5% outcome might be around breakeven, while Player B's worst 5% could be a significant loss. Same win rate, very different experiences — that's the impact of standard deviation.
How to Read the Chart
Green line (mean): Your expected profit over time. This is what you'd earn on average if you played the same number of hands thousands of times. It's a straight line determined entirely by your win rate.
Inner shaded band (70th percentile): 70% of all simulations fall within this band. Think of it as the "likely" range of outcomes.
Outer shaded band (95th percentile): 95% of all simulations fall within this wider band. Only 5% of outcomes are more extreme in either direction.
Thin white lines (sample paths): Three individual simulated trajectories showing what a single run could actually look like. These illustrate the choppy, non-linear reality of poker results versus the smooth theoretical expectation.
Typical Standard Deviations by Game Type
| Game Type | Typical SD | Notes |
|---|---|---|
| NLH Full Ring (9-max) | 60–80 bb/100 | Tighter play, smaller pots |
| NLH 6-max | 75–120 bb/100 | Most common online format |
| PLO Full Ring | 100–140 bb/100 | Bigger pots, closer equities |
| PLO 6-max | 120–160 bb/100 | Highest variance cash format |
| NLH Heads-Up | 100–130 bb/100 | Wide ranges, aggressive play |
Find your exact standard deviation in tracking software like PokerTracker or Hold'em Manager.
Sample Size Requirements
One of the most counterintuitive aspects of poker is how many hands you need before results become meaningful. With a win rate of 5 bb/100 and an SD of 75 bb/100, after 10,000 hands your 95% confidence interval spans roughly -100 bb to +200 bb — an enormous range. Even after 100,000 hands, the interval is still wide.
The rule of thumb: you need at least (SD / WinRate)^2 x 100 hands to have reasonable confidence in your results. For a 5 bb/100 winner with 75 bb/100 SD, that's (75/5)^2 x 100 = 22,500 hands just to achieve a 1-standard-deviation signal. For 2-sigma confidence, quadruple that number.
Bankroll Implications
Variance directly determines how large your bankroll needs to be. The standard recommendation is 20-30 buy-ins for cash games, but this depends on your win rate and standard deviation. A player with a high win rate and low SD might be fine with 15 buy-ins, while a marginal winner with high SD could need 50+.
Use the Risk of Ruin stat to gauge whether your bankroll can withstand the swings. If risk of ruin exceeds 5%, consider moving down in stakes or building a larger bankroll before taking shots at higher levels. The simulator's "Worst 5%" figure shows the bottom of the realistic range — make sure your bankroll can absorb that number.
What the simulation tells you
The chart shows possible outcomes, not predictions. Each line represents one of thousands of trajectories your bankroll could have followed given your inputs — none of them are "what will happen." The bands show the full distribution of plausible outcomes; the green mean line is what you'd average across infinite parallel universes, not what any single run looks like. Read the chart to understand the range of possibilities, not to forecast a specific outcome.
Variance is a feature, not a bug. Without variance, weaker players would lose every session and quickly stop playing — and no profitable game would exist. Variance is what gives losing players occasional wins and keeps them depositing, which sustains the rake-paying ecosystem winners depend on. Embrace the swings: they're the price (and the reason) for your edge.
Standard deviation is the volatility dial. Doubling your SD from 75 to 150 bb/100 doubles your typical swings even at the same win rate. PLO players see SD of 100-150+ bb/100 because preflop equities run closer (typical matchups are 55-45 vs 70-30 in NLH) and pots are larger relative to stacks — that's why PLO bankrolls need to be 50-100% larger. Tracking your SD via your tracker is as important as tracking your win rate.
5 sample win-rate scenarios
Below are five typical win-rate profiles modeled over 100,000 hands at SD = 75 bb/100 (the reference for 6-max NL Hold'em). The 95% confidence interval shows where 95% of all 100k-hand trajectories end. Notice how a 1 bb/100 "high-stakes pro" has a much wider relative CI than the +5 bb/100 microstakes winner — same SD, much smaller edge.
| Player profile | Win rate | Expected ending | 95% CI | 95th-pct max downswing |
|---|---|---|---|---|
| Microstakes winner | +5 bb/100 | +5,000 bb | +350 to +9,650 | ~850 bb (8.5 BI) |
| Low-stakes winner | +3 bb/100 | +3,000 bb | −1,650 to +7,650 | ~1,500 bb (15 BI) |
| Mid-stakes winner | +2 bb/100 | +2,000 bb | −2,650 to +6,650 | ~2,200 bb (22 BI) |
| High-stakes pro | +1 bb/100 | +1,000 bb | −3,650 to +5,650 | ~3,500 bb (35 BI) |
| Losing player | −1 bb/100 | −1,000 bb | −5,650 to +3,650 | unbounded |
CI width is identical across all rows (±4,649 bb at SD 75 over 100k hands) — what changes is the centering. Read the CI lower bound carefully: even a +3 bb/100 winner can be 16 buy-ins down at the 2.5th percentile.
Downswing probability table
For a cash-game random walk with drift μ (win rate in bb/100) and volatility σ (SD in bb/100), variance grows linearly in hands but the probability of hitting any specific drawdown threshold is well-approximated by Monte Carlo simulation. The table below shows the probability of experiencing a peak-to-trough downswing of at least 100, 300, or 500 big blinds at any point during a 100,000-hand stretch, by win rate. SD = 75 bb/100 throughout (typical NL Hold'em 6-max; see Mason Malmuth's Gambling Theory and Other Topics for the underlying random-walk math).
| Win rate | P(>100 bb) | P(>300 bb) | P(>500 bb) |
|---|---|---|---|
| +5 bb/100 | ~95% | ~50% | ~25% |
| +3 bb/100 | ~99% | ~80% | ~55% |
| +2 bb/100 | ~99% | ~90% | ~75% |
| +1 bb/100 | ~99% | ~95% | ~85% |
| −1 bb/100 | ~100% | ~99% | ~99% |
Even a strong +5 bb/100 winner has a 1-in-4 chance of hitting a 500bb (5 buy-in) downswing inside any 100k-hand window. For mid-stakes 1-2 bb/100 pros, large downswings are the rule, not the exception — a 5-buy-in or larger downswing happens in 75-85% of 100k-hand stretches. This is why bankroll sizing matters: your roll has to absorb downswings that are nearly inevitable, not just the average swing.
How to use this calculator
Step-by-step:
- Enter your win rate in bb/100. Pull the exact number from your tracking results software (PokerTracker, Hold'em Manager, or PokerLog). If you don't have a tracker, use 5 bb/100 for microstakes winners, 2-3 for low-mid stakes, 1-2 for high stakes.
- Enter your standard deviation in bb/100. If unknown, use 75 bb/100 (typical 6-max NL Hold'em). PLO runs 100-150; full-ring 9-max is closer to 60-80.
- Choose sample size. 10k-50k hands shows short-term volatility (what a "bad month" looks like). 100k-1M hands shows convergence toward your true win rate.
- Read the chart and the stat panel below it for expected profit, worst 5% outcome, and risk of ruin.
Interpreting the line chart: the green mean line is your expected profit (a straight line proportional to your win rate). The shaded bands show 70th and 95th percentile outcomes — 95% of all simulated runs fall inside the outer band, 70% inside the inner band. The thin sample paths show three individual trajectories, illustrating the choppy non-linear reality of any single run versus the smooth theoretical expectation.
When to trust your win rate: below 20,000 hands, don't trust your tracker results — sample is too small. From 20k to 100k hands, your tracker hints at direction but the confidence interval is wider than your win rate. From 100k to 500k hands, your results are directionally trustworthy. Above 500k hands of consistent play in similar games, your results are authoritative. Cross-reference with this simulator: if your actual results fall outside the 95% band, your true win rate likely differs from what you entered.
Frequently Asked Questions
›What is variance in poker?
Variance is the statistical measure of how much your actual results deviate from your expected results (win rate). Even a winning player will experience significant downswings and upswings due to the inherent randomness of the cards. Variance is proportional to the square of the standard deviation — a higher standard deviation means wider swings. In poker, variance is unavoidable; the key is having a large enough bankroll and sample size to let your true win rate emerge.
›What is a good standard deviation in poker?
For No-Limit Hold'em cash games, a typical standard deviation is 60-100 bb/100 hands, depending on play style. Tight-aggressive players tend to have lower standard deviations (60-75 bb/100), while loose-aggressive players run higher (80-100+ bb/100). Tournament players experience even higher variance. For Pot-Limit Omaha, standard deviations of 100-150 bb/100 are common due to the closer equities and bigger pots. You can find your exact standard deviation in your tracking software.
›How many hands do I need to know my true win rate?
At a typical standard deviation of 75 bb/100 and a win rate of 5 bb/100, you need roughly 100,000 hands before your results are statistically meaningful — and even then, your confidence interval is still wide. At 500,000 hands, you can be more confident but still not certain. The rule of thumb is: the lower your win rate relative to your standard deviation, the more hands you need. This simulator helps you visualize exactly how wide the range of outcomes is at any sample size.
›Why am I losing even though I'm a winning player?
Downswings are a mathematical certainty in poker, even for strong winners. With a win rate of 5 bb/100 and a standard deviation of 75 bb/100, a 50,000-hand breakeven or losing stretch is completely normal. The simulator's sample paths show how individual trajectories can look dramatically different from the expected value line. If your fundamentals are sound, the solution is to keep playing through the variance — your edge will manifest over a large enough sample.
›What is risk of ruin in poker?
Risk of ruin is the probability that your bankroll drops below zero (goes bust) at any point during the simulation. It depends on your win rate, standard deviation, and bankroll size. A higher win rate reduces risk of ruin, while a higher standard deviation increases it. Professional players typically aim for a risk of ruin below 5%. This calculator estimates risk of ruin by checking how many simulated paths dip below zero at any point.
›How should I handle downswings?
First, verify your edge still exists by reviewing your play away from the table. If your fundamentals are solid, trust the math — downswings are temporary. Practical steps: (1) ensure your bankroll is large enough (20-30 buy-ins for cash, 100+ for tournaments), (2) move down in stakes if the downswing threatens your bankroll, (3) take breaks to avoid tilt, and (4) focus on decision quality rather than short-term results. Use this simulator to see that your current downswing is likely within the normal range of variance.
›Is PLO more swingy than No-Limit Hold'em?
Yes, significantly. PLO (Pot-Limit Omaha) has standard deviations of 100-160 bb/100 compared to 60-100 bb/100 for NLH. This happens because equities run closer in PLO (typical preflop matchups are 55-45 rather than 70-30), pots are larger relative to stacks, and more money goes in with thin edges. A winning PLO player needs a substantially larger bankroll — often 50+ buy-ins — to withstand the variance. Use this calculator to compare how different standard deviations affect your swings.
›What does the 95th percentile band mean?
The 95th percentile band (outer shaded area on the chart) shows the range where 95% of all simulated outcomes fall. Only 2.5% of results are above the upper edge and 2.5% below the lower edge. If your actual results fall outside this band, it's a strong signal that your true win rate may differ from what you entered — either your edge is bigger than you thought (if above) or you may be overestimating your win rate (if below). The narrower 70th percentile band shows the 'likely' range of outcomes.
›What counts as a normal downswing?
For typical NL Hold'em cash games (5 bb/100 winner, 75 bb/100 SD), downswings of 200-400 big blinds (2-4 buy-ins) happen frequently — multiple times per 100k hands. Downswings of 500-1,000 bb (5-10 buy-ins) happen in roughly 30-50% of 100k-hand stretches even for solid winners. Downswings exceeding 1,500 bb (15 buy-ins) are unusual but not abnormal for marginal winners (1-2 bb/100). The lower your win rate relative to SD, the larger the 'normal' downswing range. PLO and short-handed games run 50-100% wider swings than full-ring NL Hold'em.
›How does my standard deviation affect my expected swings?
Standard deviation scales linearly with swing magnitude. Doubling your SD from 75 to 150 bb/100 doubles the width of your variance bands and roughly doubles your typical downswings, even at the same win rate. This is why PLO players need much bigger bankrolls than NLH players despite similar win rates — closer-equity preflop matchups and bigger relative pots produce SD of 100-150+ bb/100 vs 60-100 for NLH. To bring your effective swings down, you can either play a tighter style (lowers SD), play a softer game (raises win rate), or both. The variance-to-bankroll relationship is roughly: required buy-ins ∝ SD² / win rate.
›Should I trust the simulator's results more than my own actual results?
For sample sizes under ~100,000 hands, yes — the simulator's expected value (based on your win rate and SD inputs) is more reliable than your specific run. Your actual results below 100k hands are dominated by noise; one good or bad month can shift your apparent win rate by 4-5 bb/100 even if your true win rate is unchanged. Above 500,000 hands of consistent play in similar games, your actual results become more authoritative than any simulator estimate. In between, trust them roughly equally and triangulate. If your actual results land outside the simulator's 95% band, that's a strong signal your true win rate differs from your assumed value.
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