Variance and Standard Deviation in Poker Explained

Standard deviation tells you how far your results scatter around your true win rate. A typical online 6-max cash game runs near 90 bb/100, which means that across any 100 hands, a result 90 big blinds either side of expectation is entirely ordinary. That one number explains nearly every downswing you have had, and it is why 10,000 hands tells you almost nothing about how well you play.

What standard deviation actually measures

Variance and standard deviation describe the same thing in different units. Variance is the average squared distance between your results and your expectation. Standard deviation is its square root, which puts the figure back into big blinds so you can hold it next to your win rate.

Your win rate is the drift — the long-run average that expected value calculations pin down hand by hand. Standard deviation is the noise stacked on top of the drift.

Poker is unusual in how lopsided that ratio is. A 5 bb/100 winner in a 90 bb/100 game is trying to read a signal buried under eighteen times as much static. Every other question in this article — sample size, bankroll, how long a bad run can last — follows from that single comparison.

Put it in money. In a $1/$2 game, 90 bb/100 means a 100-hand session finishing $180 either side of expectation is a thoroughly average result. Around two thirds of your sessions land inside that band, and one in twenty finishes more than $360 away from where it should have.

How the noise grows with sample size

Standard deviation is quoted per 100 hands, so you scale it up with the square root of the number of hands.

Standard deviation over N hands = your bb/100 figure × √(N ÷ 100)

Your winnings grow linearly with hands played. The noise only grows with the square root. That gap is what eventually lets skill show through, and it is also why it takes so long.

Run the numbers for a 5 bb/100 winner in a 90 bb/100 game:

• 1,000 hands: expectation 50 bb, standard deviation about 285 bb. The noise is nearly six times the signal.
• 10,000 hands: expectation 500 bb, standard deviation 900 bb. Still almost double.
• 100,000 hands: expectation 5,000 bb, standard deviation about 2,850 bb. The signal finally leads.

The square root is why patience is not optional. Quadrupling your hands only doubles the noise, so every extra month of volume buys you a slightly clearer picture rather than a sudden one.

A losing month is not evidence of anything at 10,000 hands. Roughly one winning player in three is still down after a stretch that long, purely from the arithmetic above.

Standard deviation by format

The 90 bb/100 baseline moves with the game you sit in. Multiway pots, deeper stacks, and more three-bet and four-bet action all push it up.

Format	Typical standard deviation
Live full ring	60-80 bb/100
Online 9-max	75-85 bb/100
Online 6-max	85-100 bb/100
Fast-fold 6-max	90-105 bb/100
Online heads-up	110-140 bb/100

What a sample can actually prove

Take your measured win rate, and the 95% confidence band around it is roughly two standard errors wide in each direction. Assuming 90 bb/100:

Hands played	95% margin on your win rate
10,000	±17.6 bb/100
25,000	±11.2 bb/100
50,000	±7.9 bb/100
100,000	±5.6 bb/100
250,000	±3.5 bb/100
1,000,000	±1.8 bb/100

Read the 100,000-hand row carefully. A player showing 5 bb/100 over 100,000 hands could genuinely be a 10 bb/100 crusher or a break-even grinder. That is after months of full-time volume.

Two things follow. First, stop treating your graph as a report card — at anything under six figures of hands it is mostly weather. Second, judge your play by decisions rather than outcomes, because decisions give you feedback immediately and results give you feedback in a year.

Why downswings run deeper than they feel

Drawdowns behave worse than most players expect, because the depth you can reach depends on the ratio between noise and drift rather than on either one alone.

For a 5 bb/100 winner at 90 bb/100, a 10 buy-in fall below a previous peak carries close to a one in three chance of happening at some point. Halve the win rate to 2.5 bb/100 and that same 10 buy-in drop becomes near enough a coin flip, with 20 buy-in holes a live possibility.

Nothing about that is punishment for playing badly. A weaker win rate simply gives the drift less pull against the same noise, so the random walk wanders further before it recovers.

• Marginal winners swing hardest. At 1 bb/100 the drift barely exists, and downswings that would be freak events for a strong regular become routine.
• Shot-taking multiplies the effect. Moving up cuts your win rate and raises the stakes at the same time, which is exactly the combination that produces deep holes.
• The recovery is slower than the fall. A 20 buy-in hole at 5 bb/100 takes 40,000 hands of expectation to climb out of, and that is before any further noise.

The mirror image is just as misleading. The same noise that digs holes also produces months where you appear to be beating the game for double your real rate, and those months feel like progress rather than luck.

If your graph has been ugly for a month, the useful question is not how you feel about it but whether a downswing is normal given your win rate and the hands you have played. Most are. The practical side — game selection, stakes, and staying sane through it — is covered in surviving a long downswing.

What it means for your bankroll

Bankroll requirements exist to survive the drawdown distribution above, not to cover a bad night.

• 20-30 buy-ins is the floor for a confident winner in a soft 6-max game with no rent riding on it.
• 50 buy-ins is the standard for a full-time cash player at 90 bb/100 who cannot easily reload.
• 100 buy-ins or more belongs to tougher games, higher standard deviation formats, and anyone whose win rate is under 3 bb/100.

Standard deviation also governs how fast you may move up. Taking a shot with 20 buy-ins in a game running 100 bb/100, at a stake where your win rate is untested, is not a shot — it is a wager on whether you get to keep playing that stake at all.

Withdrawals matter as much as the starting figure. Pulling money out at every peak turns a healthy roll into a permanently thin one, because you keep resetting to the level where the next ordinary downswing is dangerous.

Lowering your own standard deviation

You have less control here than over your win rate, but some of it is real.

Table selection. Games with several loose callers create bigger multiway pots and push standard deviation up. Tighter, more predictable tables reduce it, usually along with your win rate.

Line selection. Three-bet and four-bet heavy strategies, big river overbets, and thin value shoves all add noise. They are frequently correct anyway — never trade away expected value to smooth a graph.

Volume. The only reliable route to a calmer graph is more hands, because the noise grows with the square root while the drift grows in a straight line.

Plug your own numbers into a poker variance calculator before your next session. Enter your win rate, your standard deviation, and the hands you plan to play, and the range of outcomes it returns will look far wider than you expect. That, rather than any single result, is the honest picture of what poker does to a bankroll.