What is variance in poker?

Variance in poker is the statistical noise around your true win rate. Even a skilled player who wins 5 big blinds per 100 hands long-term will see massive short-term swings — winning 20bb/100 over a thousand hands or losing 10bb/100 over the same span, purely due to chance. Variance is measured as the standard deviation of your bb/100 results, typically 80-120 bb/100 for cash games and 150+ for tournaments.

How many hands do I need to know my true win rate?

To be 95% confident in your win rate within a 1bb/100 margin, you need about 38,000 hands at a standard deviation of 100bb/100. To be 99% confident within the same margin, you need about 66,000 hands. Most online cash players need 50,000-100,000 hands before their observed win rate is a reliable estimate of their true win rate.

Why am I losing for 10,000 hands if I'm a winning player?

A 5bb/100 winning player has roughly a 15% chance of being down after 10,000 hands due to variance alone. With a standard deviation of 100bb/100, your expected result over 10,000 hands is +500bb plus or minus a 95% confidence band of ±196bb. Losing for 10,000 hands is well within normal variance for any reasonable win rate.

What is a standard deviation in poker?

Standard deviation in poker is the square root of variance — measured in bb/100. For 6-max no-limit cash games, typical standard deviation is 90-110 bb/100. For full-ring games it's lower, around 70-85bb/100. For tournaments measured as ROI, standard deviation is much higher because of the top-heavy payout structure — often 150-200 bb/100 effective.

How is poker variance calculated?

Over N hands at win rate W (in bb/100) and standard deviation S (also bb/100), your expected total profit is N × W / 100 big blinds, with a 95% confidence interval of plus or minus 1.96 × S × sqrt(N/100). The square-root scaling is why variance feels overwhelming in the short run and shrinks in the long run.

Does playing more hands reduce variance?

Not the variance per hand — that's fixed by the game. But the variance of your observed win rate shrinks with the square root of sample size. After 4,000 hands your bb/100 estimate has half the noise of after 1,000 hands. After 100,000 hands you have one-tenth the noise of after 1,000. This is why long-term sample sizes are everything in poker.

Poker Math· 10 min read · live simulator· By Dexas· Published 2026-06-01

Poker variance — how many hands until you're actually winning?

Variance is the single most under-appreciated number in poker. A skilled 5bb/100 winner has a 15% chance of being down after 10,000 hands of cash. A losing 1bb/100 player has a 25% chance of being up after the same span. The math doesn't care that you "feel" you're a winner — it cares about sample size. Drag the sliders below to see 20 sample lifetime paths at your stated win rate, and find out how many hands it actually takes to know.

The headline number To be 95% confident in your win rate within ±1bb/100, you need roughly 38,000 hands at a standard deviation of 100 bb/100. Most players have far fewer hands than they think — and far more variance than they admit.

The live simulator

Each path below is one possible 1× lifetime at your stated win rate and standard deviation. The shaded gold band is the 95% confidence interval — 19 out of 20 lifetimes will land somewhere inside it. The dashed gold line is the expected (mean) result. Sessions that finished above water are green; below water are red. Click "Re-roll" to see new sample paths at the same settings.

Variance Simulator

Live · 20 sample paths

Win rate 5 bb/100

Std deviation 100 bb/100

Sample size 100,000 hands

Winning lifetimes

Losing lifetimes

Expected (mean)

95% confidence band

Expected total

+5,000 bb

95% CI (±)

±620 bb

P(losing)

0.0%

Hands for ±1bb/100

38,400

Why the math is brutal in the short term

The standard deviation of total profit over N hands scales as the square root of N. Your expected profit scales linearly with N. That difference — square-root vs. linear — is the entire reason poker is variance-heavy in the short term and skill-dominant in the long term.

Total expected = N × winrate / 100 (grows linearly). Total std dev = stddev × √(N / 100) (grows by the square root).

Plug in some numbers. A 5bb/100 winner over 10,000 hands has +500bb expected, with a standard deviation of 100 × √100 = 1000bb. The 95% confidence band is roughly ±1.96 × 1000 = ±1960bb. That means anywhere from -1,460bb to +2,460bb is a "normal" 10,000-hand result. A 60-buy-in stretch underwater is well inside one standard deviation.

Now run 100,000 hands at the same rate. Expected is +5,000bb. Std dev grows to 100 × √1000 = 3162bb. 95% band is ±6200bb. The band is wider in absolute terms — but the band as a fraction of expected has shrunk from 1960/500 = 4× to 6200/5000 = 1.24×. That's why long-term sample sizes are everything.

How many hands until your win rate is real?

The 95% confidence interval around your observed win rate is ±1.96 × stddev / √(N/100) in bb/100 units. Solving for the sample size required to nail down your win rate to within ±X bb/100:

Sample-size formula Hands required for ±X bb/100 confidence = (1.96 × stddev / X)² × 100. At stddev 100 and X = 1: about 38,000 hands. At X = 2: about 9,600 hands. At X = 0.5: about 153,000 hands.

These are the numbers that determine whether you can trust your own win rate:

Confidence interval	Hands needed (std dev 100)	Hands needed (std dev 150 — tournaments)
±5 bb/100 (very loose)	1,540	3,460
±3 bb/100 (loose)	4,270	9,610
±2 bb/100 (moderate)	9,610	21,620
±1 bb/100 (tight)	38,420	86,440
±0.5 bb/100 (publishing-grade)	153,660	345,750

The takeaway: if you've played 5,000 hands and your "win rate" is +8 bb/100, the truth is "your win rate is somewhere between -2 and +18 with 95% confidence." That includes "you're a losing player" inside the confidence band. Most "I'm crushing this stake" claims at the home game level are statistical noise.

The downswing math everyone should know

A downswing is the gap between your peak bankroll and a later trough. Over a long enough sample, every winning player will hit downswings. Here's what's normal for a 5bb/100 winner at stddev 100:

Worst expected drawdown over 10,000 hands: about 150 big blinds (1.5 buy-ins).
Worst expected drawdown over 100,000 hands: about 480 big blinds (~5 buy-ins).
Worst expected drawdown over 1,000,000 hands: about 1,500 big blinds (15 buy-ins).

The wider your sample, the deeper the worst drawdown — even for the same player. This is why "30-buy-in" bankrolls are conservative-but-honest for cash play, not paranoia. The math says you will, statistically, see a 15+ buy-in downswing if you play long enough.

Variance differs by format — a lot

Format	Typical std dev (bb/100)	Hands to ±1bb/100
Full-ring NL cash (9-handed)	75	21,600
6-max NL cash	100	38,400
Heads-up NL cash	130	64,900
Sit-and-go tournaments	125	60,000
Multi-table tournaments	175+	~117,500
PLO (cash)	160	98,300

PLO has roughly 2.5× the variance of full-ring NL. Tournaments have 4-5×. Heads-up sits in between. If your "study group" includes someone whose PLO win rate "stabilized" at 8bb/100 over 30,000 hands, they're statistically a coin-flip away from being a 0bb/100 player. The variance is that big.

What this means for your bankroll

The standard guidance — keep 30 buy-ins for NL cash, 100 buy-ins for MTTs — comes directly from this variance math. The number isn't arbitrary; it's the bankroll size below which the risk of ruin (going broke at this stake) exceeds about 5% for a player at typical win rates.

For exact numbers given your specific win rate and stake, use the bankroll calculator. It computes the bankroll required to keep your risk of ruin below your stated tolerance.

Compute your exact bankroll requirements

The dedicated bankroll calculator computes minimum bankroll given your win rate, standard deviation, and risk-of-ruin tolerance. For pre-game equity reads, use the equity calculator.

Bankroll calculator → Equity calculator → Rule of 2 and 4

Where to go from here

Pot odds explained — the math that pays for variance
The Rule of 2 and 4 — interactive equity estimation
Bankroll calculator — minimum bankroll for your stake
MTT simulator — explore tournament variance

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