Even a winning poker player can lose money over 50,000 hands. This is called Variance — the mathematical reality that separates short-term results from long-term expectation.
Our Poker Variance Calculator helps you distinguish between “running bad” and “playing bad.” It simulates thousands of possible outcomes based on your winrate and standard deviation, showing you the realistic range of results you should expect — including those soul-crushing downswings that are completely normal.
🃏 Poker Variance Calculator
Cash Game Downswing Simulator & Confidence Interval Analysis
Enter your expected winrate and actual results to see if you're running within normal variance.
📊 Standard Deviation by Game Type
| Game Type | Typical SD | Tight Style | LAG Style |
|---|---|---|---|
| 🃏 NL Hold'em Full Ring | 60-80 bb/100 | 55-65 | 75-90 |
| 🃏 NL Hold'em 6-max | 85-110 bb/100 | 75-90 | 100-120 |
| 🎴 PLO Full Ring | 100-140 bb/100 | 100-120 | 130-150 |
| 🎴 PLO 6-max | 120-160 bb/100 | 120-140 | 150-200 |
| 🎯 Heads-Up NL | 100-150 bb/100 | — | — |
📉 Downswing Probability (5 bb/100, 90 SD)
| Downswing Size | Probability | Avg Duration | How It Feels |
|---|---|---|---|
| 10+ buy-ins | ~60% | 15K-30K hands | Normal bad stretch |
| 20+ buy-ins | ~25% | 30K-60K hands | "Am I still good?" |
| 30+ buy-ins | ~10% | 50K-100K hands | Soul-crushing but possible |
| 50+ buy-ins | ~2% | 100K+ hands | Rare but mathematically real |
🎲 Probability of Loss After X Hands
| Winrate | 10K hands | 50K hands | 100K hands | 500K hands |
|---|---|---|---|---|
| 2 bb/100 | 42% | 35% | 28% | 11% |
| 5 bb/100 | 30% | 18% | 11% | ~1% |
| 8 bb/100 | 21% | 8% | 3% | |
| 10 bb/100 | 15% | 4% | 1% |
CI = Winrate ± (2 × SD / √(hands / 100))
Standard Deviation after X hands:
SD_total = SD × √(hands / 100)
Probability of Loss:
P = Φ(-Winrate × √(hands/100) / SD)
What is Poker Variance?
Variance in poker refers to the natural fluctuation in results caused by luck and probability. Even with a significant skill edge, your short-term results can deviate wildly from your expected value (EV).
📈 Skill (Long-Term)
Your winrate (bb/100) represents your edge over the competition. Over hundreds of thousands of hands, results converge toward this expected value.
🎲 Variance (Short-Term)
Standard Deviation (SD) measures how much your results swing around that expectation. Higher SD = wilder swings, regardless of skill level.
The uncomfortable truth: A solid 5 bb/100 winner can easily lose money over 50,000 hands — not because they’re playing poorly, but because variance is that powerful. Understanding this concept is crucial for your mental game and bankroll management.
For a rigorous mathematical treatment, see the GTO Wizard variance analysis, which includes Kelly Criterion applications for optimal bankroll strategy.
Standard Deviation by Game Type
Standard Deviation (SD) varies significantly based on game format and playing style. Here are typical values you can use if you don’t know your exact SD from tracking software:
| Game Type | Typical SD | Tight Style | LAG Style |
|---|---|---|---|
| 🃏 NL Hold’em Full Ring (9-max) | 60-80 bb/100 | 55-65 | 75-90 |
| 🃏 NL Hold’em 6-max | 85-110 bb/100 | 75-90 | 100-120 |
| 🎴 PLO Full Ring (9-max) | 100-140 bb/100 | 100-120 | 130-150 |
| 🎴 PLO 6-max | 120-160 bb/100 | 120-140 | 150-200 |
| 🎯 Heads-Up NL | 100-150 bb/100 | — | — |
These ranges are based on aggregate data from PokerTracker and Hold’em Manager user populations across online cash games.
Playing Style & Standard Deviation
Tight Passive
VPIP 12-16%
SD: 60-75
TAG
VPIP 18-24%
SD: 80-95
LAG
VPIP 26-32%
SD: 100-120
Maniac
VPIP 35%+
SD: 130+
Note: Higher SD isn’t necessarily bad — aggressive winners often have higher SD but also higher winrates. Focus on maximizing EV, not minimizing variance.
How to Use the Variance Simulator
- Winrate (bb/100): Your expected edge. Find this in your tracking software, or estimate:
- Breakeven: 0 bb/100
- Small winner: 2-3 bb/100
- Solid winner: 4-6 bb/100
- Crusher: 8+ bb/100
- Standard Deviation (bb/100): Your volatility. Use the table above if you don’t know yours.
- Number of Hands: The sample size to simulate (e.g., 50,000 or 100,000).
- Analyze the Results:
- Expected Value: Your theoretical profit over this sample.
- 95% Confidence Interval: 19 out of 20 times, your results will fall within this range.
- Probability of Loss: The chance you’ll be down despite being a winner.
- Downswing Data: Expected depth and duration of downswings.
The Variance Formula & Confidence Intervals
The 95% Confidence Interval tells you the range where your results will fall 95% of the time. Here’s the formula:
This confidence interval formula is the standard approach described in Bill Chen and Jerrod Ankenman’s The Mathematics of Poker (2006), adapted for poker-specific standard deviation units.
Example Calculation
Player Profile: 5 bb/100 winrate, 90 bb/100 SD, 100,000 hands
95% CI = 5 ± (180 / 31.62)
95% CI = 5 ± 5.69
95% CI = −0.69 to +10.69 bb/100
What this means: After 100K hands, this 5 bb/100 winner could be showing anywhere from -0.69 bb/100 (small loser) to +10.69 bb/100 (crusher) — and both outcomes are statistically normal!
Typical Downswing Statistics
Downswings aren’t bad luck — they’re mathematical certainty. Here’s what to expect based on your winrate:
For Solid Winner (5 bb/100, 90 SD)
| Downswing Size | Probability | Avg Duration | How It Feels |
|---|---|---|---|
| 10+ buy-ins | ~60% | 15K-30K hands | Normal bad stretch |
| 20+ buy-ins | ~25% | 30K-60K hands | “Am I still good?” |
| 30+ buy-ins | ~10% | 50K-100K hands | Soul-crushing but possible |
| 50+ buy-ins | ~2% | 100K+ hands | Rare but mathematically real |
For Marginal Winner (2 bb/100, 90 SD)
| Downswing Size | Probability | Avg Duration | Reality Check |
|---|---|---|---|
| 20+ buy-ins | ~45% | 50K-100K hands | Almost coin flip |
| 30+ buy-ins | ~25% | 80K-150K hands | 1 in 4 players experience this |
| 50+ buy-ins | ~10% | 150K+ hands | Bankroll-destroying if underfunded |
Real-World Downswings: NL50 and NL100 in Dollar Terms
Downswing tables in big blinds are useful for analysis, but players feel the pain in dollars. Here is what typical downswings translate to at two of the most common online stakes, assuming a 5 bb/100 winrate with 90 bb/100 standard deviation.
| Downswing | NL50 ($0.25/$0.50) | NL100 ($0.50/$1.00) | Probability | Typical Duration |
|---|---|---|---|---|
| 10 buy-ins | -$500 | -$1,000 | ~60% | 2-4 weeks |
| 20 buy-ins | -$1,000 | -$2,000 | ~25% | 1-2 months |
| 30 buy-ins | -$1,500 | -$3,000 | ~10% | 2-4 months |
| 50 buy-ins | -$2,500 | -$5,000 | ~2% | 4+ months |
Duration assumes ~25,000 hands per month (roughly 12-15 hours per week of 4-tabling online 6-max). A 20 buy-in downswing at NL100 means watching $2,000 evaporate over 30,000-60,000 hands — which takes a regular grinder one to two months to play through. This is why bankroll sizing is not optional at these stakes.
For a rigorous calculation of exactly how many buy-ins you need to survive the worst-case variance at your stakes and winrate, use our Scientific Risk of Ruin Calculator.
Probability of Loss Over Sample Size
Even winning players can show losses over significant samples. Here’s the probability of being down after X hands (assuming 90 bb/100 SD):
| Winrate | 10K hands | 50K hands | 100K hands | 500K hands |
|---|---|---|---|---|
| 2 bb/100 | 42% | 35% | 28% | 11% |
| 5 bb/100 | 30% | 18% | 11% | ~1% |
| 8 bb/100 | 21% | 8% | 3% | <0.1% |
| 10 bb/100 | 15% | 4% | 1% | <0.01% |
Reading this table: A 5 bb/100 winner still has an 11% chance of being down after 100,000 hands. That’s more than 1 in 10 solid winning players who will question their entire existence after 100K hands — purely due to variance.
Bankroll Requirements Based on Variance
Your required bankroll depends on both your winrate AND your standard deviation. Higher variance = more buy-ins needed:
| Winrate | SD | 5% RoR | 2% RoR | 1% RoR |
|---|---|---|---|---|
| 2 bb/100 | 90 (NL 6-max) | 80 BI | 100 BI | 120 BI |
| 5 bb/100 | 90 (NL 6-max) | 35 BI | 45 BI | 55 BI |
| 8 bb/100 | 90 (NL 6-max) | 22 BI | 28 BI | 35 BI |
| 5 bb/100 | 140 (PLO 6-max) | 80 BI | 100 BI | 120 BI |
RoR = Risk of Ruin: The probability of losing your entire bankroll before your edge plays out. Professional players typically target 1-2% RoR.
How Many Hands for Statistical Significance?
One of the most common questions in poker: “How many hands until I know my true winrate?” The uncomfortable answer: more than you think.
| Sample Size | Confidence Level | What You’re Really Measuring |
|---|---|---|
| 10,000 hands | Very rough estimate | Mostly luck (±8-10 bb/100 swing) |
| 50,000 hands | Moderate confidence | Mix of skill and luck (±4-5 bb/100) |
| 100,000 hands | Reasonable confidence | Skill emerging (±3 bb/100) |
| 250,000 hands | Good confidence | Mostly skill (±2 bb/100) |
| 500,000+ hands | High confidence | True winrate showing (±1-1.5 bb/100) |
The poker “long run” is genuinely long. Most recreational players will never reach statistical significance in their lifetime. Even regular grinders need months or years to accumulate enough hands.
Hourly Rate: Where Variance Meets Volume
The formula for converting winrate to an hourly rate is straightforward: Hourly Rate = (Winrate × Big Blind × Hands per Hour) / 100. But variance means your actual hourly rate fluctuates wildly over small samples.
| Scenario | Stakes | Hands/hr | EV Hourly | SD Hourly | Worst Hour (95%) |
|---|---|---|---|---|---|
| Online 6-max, 4 tables | NL100 | 400 | $20/hr | ±$180/hr | -$340/hr |
| Online 6-max, 4 tables | NL50 | 400 | $10/hr | ±$90/hr | -$170/hr |
| Live $1/$2, single table | NL200 | 25 | $2.50/hr | ±$28/hr | -$54/hr |
| Live $2/$5, single table | NL500 | 25 | $6.25/hr | ±$71/hr | -$135/hr |
All examples assume 5 bb/100 winrate and 90 bb/100 SD. The “Worst Hour” column shows the bottom 2.5th percentile — meaning 1 in 40 hours will be at least this bad. The hourly standard deviation dwarfs the expected hourly rate at every stake, which is why single-session results tell you almost nothing about your skill. Only cumulative results over hundreds of hours matter. For a complete analysis of how rake affects your effective winrate and hourly, try the Rake & Rakeback Calculator.
“Am I Running Bad?” — How to Analyze Your Results
If your observed winrate is below your expected winrate, the variance calculator can tell you whether this is normal variance or a sign you should review your game.
Example Analysis
Scenario:
- Expected winrate (your estimate): 5 bb/100
- Observed winrate (from HUD): 2 bb/100
- Sample size: 80,000 hands
- Standard Deviation: 90 bb/100
Question: What’s the probability a true 5 bb/100 winner runs at only 2 bb/100 or worse over 80K hands?
Answer: ~18% — This is within normal variance. About 1 in 5 players with your edge would experience this run.
✅ Verdict: Likely variance, not a leak.
However, if your results are outside the 95% confidence interval (less than 5% probability), it’s worth reviewing your game for leaks. The calculator helps you make this determination objectively.
Related Poker Calculators
For complete poker bankroll and variance analysis, use these complementary tools:
- Bankroll Requirements Calculator — Calculate exact buy-ins needed for your risk tolerance
- Scientific Risk of Ruin Calculator — Precise probability of going broke at your stakes
- General Risk of Ruin Calculator — Universal risk of ruin model for any gambling format
- Rake & Rakeback Calculator — Factor rakeback into your effective winrate
- MTT Bankroll Calculator — Variance analysis for tournament players
- Spin & Go Variance Calculator — The highest variance format in poker