Poker Variance Calculator

Variance is the headline; win rate is the footnote

Your true win rate sits underneath a mountain of noise. A genuinely strong 5bb/100 cash-game player with a standard deviation of 100bb/100 will spend roughly 30% of any 20,000-hand stretch in the red. That is not a leak. That is the math doing its job.

The model

The calculator uses a normal approximation to the sum of independent hand outcomes. Over N hands, your result in big blinds is approximately normally distributed with mean mu = (wr / 100) * N and standard deviation sigma = (sd / 100) * sqrt(N). Those two parameters completely describe every confidence interval and downswing probability the tool outputs.

So: wr = 5, sd = 100, N = 10,000. Expected profit: 500 bb. Standard deviation of that result: 1,000 bb. The 95% confidence interval runs from roughly 500 - 1.96 * 1000 = -1,460 bb to 500 + 1.96 * 1000 = +2,460 bb. A winning player can post a four-figure loss over ten thousand hands and still be performing exactly as the math predicts.

Worked example

Say you're a 5bb/100 winner with sd = 100bb/100, playing a 30,000-hand sample. The numbers:

• Expected result: (5/100) * 30,000 = 1,500 bb
• Standard deviation: (100/100) * sqrt(30,000) = 173 bb * sqrt(100) ... = 100 * sqrt(300) = 1,732 bb
• 70% confidence interval: roughly -232 bb to +3,232 bb
• Probability of being in the red: P(Z < -1,500 / 1,732) = P(Z < -0.866) = about 19%

One in five 30k-hand samples ends negative for this player. If you've ever been results-oriented about a losing month, that number is the antidote.

What each output means

Expected winnings is simply your win rate times the hand count, in big blinds. It's what a frictionless long run looks like. Confidence bands (70%, 95%, 99.7%) show the range your actual result is statistically likely to land within. Probability of loss is the most psychologically useful number on the page: the chance you finish the sample below zero, regardless of your edge. Downswing depth table answers "how bad can it get?" by reporting how often a player of your profile will be stuck in 200bb, 500bb, or 1,000bb downswings over the target sample.

Where the model breaks

The normal approximation assumes hand outcomes are independent and identically distributed. They are neither in reality. Win rates and standard deviations shift with game selection, opponent pool changes, and your own skill development. A player moving between NL50 and NL200 mid-sample invalidates the single-sd assumption immediately.

PLO players get this wrong constantly. A typical PLO6max standard deviation is 120-160bb/100, not the 70-90bb/100 you see in NL presets. Running a PLO simulation with an NL sd understates your true downswing risk by a factor that can reach 2x or more at normal sample sizes.

The model also has no memory. It doesn't know you're tilting, that the game broke, or that you moved down a stake after a bad session. Monte Carlo simulations can produce results that look nothing like your actual experience because actual poker sessions are correlated in ways that random walks are not.

Finally, the tool outputs variance around a fixed win rate. Your win rate is not fixed. It is itself an estimate with confidence intervals, and those intervals are wide at typical sample sizes. For guidance on how many hands you actually need to establish a win rate, see the bankroll calculator and read through our guide to poker variance and sample size.

Advanced: downswing duration vs. downswing depth

Most players conflate these. Depth is the maximum you drop from peak to trough. Duration is how many hands you spend below a prior high-water mark. A 5bb/100 player will experience 500bb downswings with some regularity, but those downswings can last 15,000-30,000 hands even when the depth is moderate. Duration is psychologically harder to survive than depth, because you start questioning whether the model is even valid. It is. See also the risk of ruin calculator for bankroll sizing that lets you outlast the duration.