Poker Variance Calculator: How Swings Work

A poker variance calculator takes your win rate and standard deviation over a number of hands and returns the realistic range of results you can expect — how far luck alone can push you above or below your expected win. It matters because your standard deviation dwarfs your win rate: a strong online grinder might win 3 bb/100 while swinging with a standard deviation near 90 bb/100. Understanding that gap is the difference between panicking over a normal downswing and knowing it’s just math.

The core formula

Variance over a sample scales with the square root of hands, not linearly. To get one standard deviation of swing over N hands:

SD over sample = SD(per 100) × √(hands ÷ 100)

Your expected result is simply win rate × (hands ÷ 100). The likely range is the expected result plus or minus one or two of these swing figures. Roughly:

• ±1 SD covers about 68% of outcomes.
• ±2 SD covers about 95% of outcomes.

So a “2-SD downswing” is unlucky but entirely normal — you’ll hit one every so often just by playing enough.

Worked example

You win 3 bb/100 with an SD of 90 bb/100 over 40,000 hands.

• Expected win = 3 × (40,000 ÷ 100) = 3 × 400 = 1,200 bb.
• Swing (1 SD) = 90 × √(40,000 ÷ 100) = 90 × √400 = 90 × 20 = 1,800 bb.
• 68% range: 1,200 ± 1,800 → from −600 bb to +3,000 bb.
• 95% range: 1,200 ± 3,600 → from −2,400 bb to +4,800 bb.

Read that again: a genuine 3 bb/100 winner can be down 600 big blinds after 40,000 hands and still be entirely on track. That’s six full buy-ins in the red over a huge sample — pure variance, no leak required.

Why the sample size fixes it

Because the swing grows with the square root of hands while the expected win grows linearly, skill eventually overtakes luck. Watch the ratio:

Hands	Expected (bb)	1-SD swing (bb)	Swing ÷ expected
10,000	300	900	3.0×
40,000	1,200	1,800	1.5×
100,000	3,000	2,846	0.95×
500,000	15,000	6,364	0.42×

At 10,000 hands the swing is triple your expected win — the result is almost meaningless. By 500,000 hands the swing is under half of it, and your true win rate finally shows through.

Turning variance into a bankroll

The whole point of measuring variance is sizing your cushion. A game with an SD of 90 and a thin win rate needs far more buy-ins than a low-variance full-ring grind. This feeds directly into your risk of ruin — the probability your roll ever hits zero — which combines win rate, SD, and bankroll into a single safety number.

Common misreadings

• Treating a normal downswing as a leak. A 2-SD dip is a coin-flip-level rare event that still happens routinely across a career. Check your sample before rebuilding your strategy.
• Judging tiny samples. Under ~30,000 hands, variance dominates so completely that the number tells you almost nothing.
• Ignoring SD entirely. Two players with the same win rate but different SDs need different bankrolls. The spread, not just the average, sets your risk.

The deeper mechanics of why these swings feel so brutal are in understanding poker downswings.

Estimating your standard deviation

If your tracker doesn’t report SD directly, you can estimate it from your game type using typical benchmarks:

Game	Typical SD (bb/100)
Full-ring NLHE	60–75
6-max NLHE	80–100
Heads-up NLHE	100–120
Pot-Limit Omaha	110–130+

Higher SD isn’t “worse” — it just means the same win rate takes more hands to prove and demands a deeper bankroll to survive. A loose, aggressive style raises your SD; a tight, positional one lowers it. Neither is automatically more profitable, but they carry very different bankroll requirements.

Using the range to stay sane

The practical payoff of running these numbers is emotional as much as financial. Before a session, know your realistic swing so a bad run doesn’t read as a broken game:

• Set expectations, not predictions. The calculator gives a range, never a forecast. Being down within your 1-SD band is completely normal.
• Check the sample before you panic. A losing stretch over 10,000 hands is noise; the same result over 200,000 hands is a signal.
• Let the range size your cushion. A wide range means more buy-ins — match the roll to the variance and downswings become survivable, not emergencies.

Put it together

Variance scales with the square root of your hands, and your standard deviation is far larger than your win rate — so short-run results are dominated by luck. Use the formula to map your realistic range, size your roll off your true SD, and connect it to risk of ruin. Ground the whole thing in the expected-value thinking behind the math, and see the full system in the bankroll management hub.