Every poker player eventually asks the same question: is this downswing normal, or am I just bad? The answer almost always involves variance — the mathematical reality that separates short-term results from long-term expectation.
This article explains what variance is, how to estimate your expected swings, how cash game and tournament variance differ, and how many hands you need before your results mean anything. For interactive analysis using your own numbers, use our Poker Variance Calculator.
What Variance Actually Means
Variance measures how much your results fluctuate around your expected value (EV). In poker, it is quantified by standard deviation (SD), measured in big blinds per 100 hands (bb/100). Your winrate tells you where you’re heading; your standard deviation tells you how bumpy the ride will be.
Consider two players, both winning at 5 bb/100. Player A plays tight Full Ring with an SD of 70. Player B plays aggressive 6-max with an SD of 110. Over 50,000 hands, Player A’s 95% confidence interval is roughly +0.5 to +9.5 bb/100. Player B’s is -1.9 to +11.9 bb/100. Same edge, but Player B has a meaningful chance of being a losing player over that sample — while Player A is almost certainly in profit.
This is not theoretical. It is the mathematics of poker that Bill Chen and Jerrod Ankenman formalized in The Mathematics of Poker (2006), and it applies to every hand you play. The practical consequence: you cannot evaluate your results without knowing both your winrate and your standard deviation.
The Confidence Interval Formula
The 95% confidence interval tells you the range where your observed winrate will fall 95% of the time:
The key variable is the denominator: √(hands / 100). As your sample size increases, the denominator grows (slowly), and the confidence interval narrows. But it narrows by a square root — meaning you need four times the hands to cut the interval in half.
| Hands Played | 95% CI Width (±) | Range for 5 bb/100 | What You Know |
|---|---|---|---|
| 10,000 | ±17.6 bb/100 | -12.6 to +22.6 | Almost nothing |
| 50,000 | ±7.9 bb/100 | -2.9 to +12.9 | Direction, roughly |
| 100,000 | ±5.6 bb/100 | -0.6 to +10.6 | Reasonable confidence |
| 250,000 | ±3.5 bb/100 | +1.5 to +8.5 | Good estimate |
| 500,000 | ±2.5 bb/100 | +2.5 to +7.5 | High confidence |
All calculations assume 90 bb/100 standard deviation (typical for NL Hold’em 6-max). At 10,000 hands, a 5 bb/100 winner could appear to be a 12 bb/100 crusher or a 12 bb/100 loser — the range is that wide. To simulate your own numbers, enter them into the Variance Calculator.
Cash Game Variance vs Tournament Variance
Cash games and tournaments are fundamentally different variance environments, and players who move between formats without adjusting their expectations are asking for trouble.
Cash Games
Cash game variance is relatively well-behaved. Results follow a roughly normal distribution, standard deviation is consistent across sessions, and the confidence interval formula gives reliable estimates. Typical standard deviations range from 70 bb/100 (tight Full Ring) to 160 bb/100 (aggressive PLO 6-max). A solid 5 bb/100 NL 6-max winner with proper bankroll management (40-50 buy-ins) can ride out most downswings without existential dread.
Tournaments
Tournament variance is a different beast entirely. The distribution is heavily right-skewed: you lose your buy-in more than 80% of the time, with occasional massive scores when you final table. This means:
- A winning MTT player with 20% ROI can go 200+ tournaments without a significant cash
- Standard bankroll guidelines are 100-300 buy-ins for tournaments vs 40-50 for cash
- The confidence interval formula for cash games doesn’t apply directly to tournaments because the distribution is not normal
- You need 1,000+ tournaments before ROI becomes statistically meaningful
The Primedope Tournament Variance Simulator is the industry standard for modeling MTT-specific variance. For cash game analysis, use our Poker Variance Calculator.
What Downswings to Expect
The most common mistake in interpreting poker results is assuming downswings are a sign of playing badly. They are a mathematical certainty. The only question is how deep and how long.
For a solid 5 bb/100 winner playing NL Hold’em 6-max (SD: 90), roughly 1 in 4 players will experience a 20+ buy-in downswing over any 500,000-hand stretch. For a marginal 2 bb/100 winner, that probability rises to nearly 1 in 2. And for breakeven players, the math guarantees regular 20+ buy-in drawdowns with near-certainty.
The relationship between winrate and downswing severity is nonlinear. Doubling your winrate from 2 to 4 bb/100 doesn’t just halve your expected downswings — it reduces them by roughly 75% in both depth and duration. This is why the most effective way to “reduce variance” is not to play tighter (which lowers SD but often lowers winrate too), but to improve your edge through study, coaching, and game selection.
For concrete downswing probabilities based on your specific winrate and SD, run the numbers in the Variance Calculator. For bankroll sizing that accounts for these downswings, use the Scientific Risk of Ruin Calculator.
How to Use Variance Information Practically
Understanding variance is not an academic exercise. It directly affects three decisions every serious player faces:
1. Bankroll Management
Your required bankroll is a function of both winrate and variance. A 5 bb/100 winner with 90 SD needs roughly 35 buy-ins for a 5% risk of ruin. The same winrate with 140 SD (PLO) requires 80+ buy-ins. Plug your numbers into the Risk of Ruin Calculator for exact figures.
2. Game Selection
A game with soft competition and high variance (PLO, short-handed, live) may have a higher EV hourly than a tighter game with less variance — but it demands more bankroll. You cannot evaluate a game’s attractiveness without considering both the winrate opportunity and the variance cost.
3. Mental Game
Knowing that a 20 buy-in downswing has a 25% probability for a 5 bb/100 winner transforms how you experience bad runs. The downswing becomes a data point, not a crisis. Players who understand variance don’t tilt from results; they tilt (if at all) from genuine mistakes — which is a much more useful feedback signal.