Variance is the tax you pay to be a winning poker player
Here is the uncomfortable truth nobody tells beginners: a genuinely winning player can lose money over 100,000 hands and never know why. Not because they played badly. Because variance is enormous, and 100k hands is a small sample. This tool shows you the size of that swing before it happens, so a downswing feels like math instead of a personal failure.
I built this after watching a friend quit 2NL convinced he was a loser. He was up 4 bb/100 over 60k hands, which his tracker drew as a flat, scary graph. We ran the numbers: at his standard deviation, a 60k-hand stretch that flat was completely normal for a 4 bb/100 winner. He kept going. The variance simulator is that conversation, automated.
The formulas behind every poker variance calculator
Every tool on this page, ours included, rests on one fact: in poker your result over N hands is approximately normal. Variance grows with the number of hands; standard deviation grows with the square root of it. From that, everything else follows.
Expected result
Multiply your win-rate by the number of 100-hand blocks. A 5 bb/100 winner over 100,000 hands expects 5 × 1000 = 5,000 bb, which is 50 buy-ins.
Standard deviation over the sample
Total SD equals your bb/100 standard deviation times the square root of the number of blocks. With SD 100 over 100k hands: 100 × √1000 ≈ 3,162 bb. That single number is why two players with identical skill can finish 100k hands thousands of big blinds apart.
Confidence interval
Your true result sits inside expected ± z × total SD. For 95% confidence z is about 1.96. Over 100k hands at 5 bb/100 and SD 100, the 95% range runs from roughly a 1,200 bb loss to an 11,000 bb win. Yes, a 5 bb/100 crusher can lose over 100k hands.
Probability of a losing stretch
It equals the normal CDF of minus your expected result divided by the total SD. A 5 bb/100 winner still finishes 100k hands at a loss about 6% of the time. One in sixteen samples lies to you.
Risk of ruin
The Brownian approximation is e^(-2 × win-rate × bankroll / SD²), with bankroll in big blinds. A break-even player has a 100% risk of ruin given enough time, which is the whole reason an edge matters.
How many hands before you can trust your win-rate?
This is the question the math actually answers best, and the one most calculators bury. The standard error of your win-rate is your standard deviation divided by the square root of the number of blocks. Quadruple your hands and the error only halves, which is why the sample size you need is brutal.
To prove a 5 bb/100 win-rate is genuinely above zero at 95% one-sided confidence, you need roughly 108,000 hands. To shrink the uncertainty to a standard error of just ±1 bb/100 at that standard deviation, you need about a million. Most players who think they have a read on their win-rate have nowhere near enough hands. The tool flags this for your exact numbers.
Downswings are deeper than your gut expects
The worst peak-to-trough drop inside a run is almost always larger than the final result would suggest, because variance compounds. A solid 5 bb/100 reg over 100k hands routinely sees a 20 to 30 buy-in downswing somewhere along the way. At lower win-rates and higher variance games like 6-max PLO, 40 to 60 buy-in downswings are not rare events, they are scheduled.
Simulate your own numbers above. The downswing table shows the probability of a drop of at least 10, 20, 30 and 50 buy-ins, in big blinds and in real dollars at your stake. Set your stop-loss and your move-down rules around those numbers, not around how you feel after a bad session.
What the swings cost in real money
Big blinds are abstract until they are your rent. Enter your big blind size and the calculator translates every figure, the confidence band, the worst-5% downswing, the expected result, into dollars at your stake. A 25 buy-in downswing is a shrug at NL10 and a crisis at NL200. Same variance, very different life.
Common variance mistakes
Treating a downswing as proof you got worse
Skill changes slowly. Variance changes everything in a week. Before you tear apart your game after a losing month, check whether that month is even unusual for your win-rate. Usually it isn't.
Trusting a win-rate from too few hands
A great-looking graph over 30k hands tells you almost nothing. The confidence interval at that sample is enormous. Keep playing and keep studying, but don't bet your stake selection on a number the sample can't support.
Bankrolling for the average instead of the swing
You don't go broke on the expected line, you go broke in the downswing. Size your bankroll against the worst-5% drop the simulator shows, not against your average month.
Free poker tools on toolsgambling.com
The variance simulator pairs with the rest of the free poker math suite on toolsgambling.com. Use the bankroll calculator to turn these swings into a safe number of buy-ins, the staking calculator to price a backing deal around the variance, and the equity calculator to make sure your edge is real in the first place.
Variance terms, in plain English
- Variance
- How spread out your results are around the average. High variance means bigger swings in both directions, not a worse expectation.
- Standard deviation (bb/100)
- The everyday measure of swinginess. Roughly the size of a typical 100-hand result's distance from your average. NLHE sits around 75-120, PLO higher.
- Downswing
- A stretch where your bankroll falls from a previous peak. The depth that matters is peak-to-trough, measured in big blinds or buy-ins.
- Risk of ruin
- The probability of losing your entire bankroll before variance turns around, given your edge, your standard deviation and your bankroll size.
- Confidence interval
- The range your true result or win-rate is likely to fall in. A wider interval means more uncertainty, which is what a small sample gives you.
- Win-rate (bb/100)
- Your expected profit in big blinds per 100 hands. The single most argued-about number in cash poker, and the hardest to actually measure.
