Poker Variance Calculator — Swings, Downswings & Bankroll
Enter your win rate, standard deviation, and sample size to see your 95% confidence interval, the odds you are still stuck after the sample, how deep a normal downswing runs, and the bankroll your edge actually requires.
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Calculate Your Variance
Buy-ins are treated as 100bb. Pull your real standard deviation from PokerTracker or Hold'em Manager for accurate output.
After 100,000 hands, an observed 3 bb/100 is consistent with a true win rate anywhere in that range. The lower bound is still below zero, so this sample does not yet prove you are a winner.
Hands needed to prove your win rate: 345,744. That is the sample at which the lower bound of a 95% interval finally clears zero at 3 bb/100 with 90 bb/100 standard deviation.
Bankroll for a 5% risk of ruin: 40 buy-ins ( $4,044 at your stake). Players who reload from outside income can run leaner; full-time grinders should sit above this line.
Downswing Odds at Your Win Rate
Probability of ever experiencing a downswing of at least this depth over an unlimited career.
| Downswing Depth | In Big Blinds | In Dollars | Chance You See It |
|---|---|---|---|
| 10 buy-ins | 1,000 bb | $1,000 | 47.7% |
| 20 buy-ins | 2,000 bb | $2,000 | 22.7% |
| 30 buy-ins | 3,000 bb | $3,000 | 10.8% |
| 40 buy-ins | 4,000 bb | $4,000 | 5.2% |
| 60 buy-ins | 6,000 bb | $6,000 | 1.2% |
| 100 buy-ins | 10,000 bb | $10,000 | <0.1% |
Typical Standard Deviation by Format
Use your own tracker figure where possible. These are the ranges most online samples land in.
| Format | Typical SD | Roll at 3bb/100 | Notes |
|---|---|---|---|
| Full-ring NLHE (9-max) | 75 bb/100 | 28 buy-ins | Tightest ranges, fewest multiway pots |
| 6-max NLHE (regular tables) | 90 bb/100 | 40 buy-ins | The default assumption for most trackers |
| 6-max NLHE fast-fold (Blitz / Zoom) | 100 bb/100 | 50 buy-ins | Wider ranges, more 3-bet pots per 100 |
| Heads-up NLHE | 130 bb/100 | 84 buy-ins | Every hand is contested, huge swings |
| 6-max PLO (Pot-Limit Omaha) | 150 bb/100 | 112 buy-ins | Equities run close, stacks go in often |
| 5-card PLO / Short Deck | 190 bb/100 | 180 buy-ins | Extreme variance, needs 2-3x the bankroll |
How Poker Variance Actually Works
Over a large sample, cash game results behave like a random walk with an upward drift. The drift is your win rate; the noise is your standard deviation. Both are measured per 100 hands, but they scale differently as your sample grows: profit grows in a straight line with hands played, while the spread of outcomes grows only with the square root of hands played. That asymmetry is the whole reason volume works. Quadruple your hands and your expected profit quadruples, but your uncertainty only doubles.
Why the Confidence Interval Is So Wide
At 90 bb/100 standard deviation, a 100,000-hand sample carries a margin of error of roughly plus or minus 5.6 bb/100 at 95% confidence. A player showing 3 bb/100 over that sample could truly be an 8.6 bb/100 crusher or a 2.6 bb/100 loser, and the data cannot tell them apart. This is not a flaw in the measurement; it is the reality of a high-noise game. Treat every win rate under a few hundred thousand hands as an estimate with a wide band around it, and make bankroll decisions from the pessimistic end of that band rather than the middle.
Risk of Ruin and Bankroll Sizing
Risk of ruin collapses exponentially as your bankroll grows, which is why the jump from 20 to 40 buy-ins matters enormously while the jump from 80 to 100 barely moves the needle. Plug your own numbers in above and watch the figure fall. The practical rule that emerges is that a modest winner in a high-variance format needs a bankroll that looks absurd to a recreational player, while a strong winner in full-ring can operate on far less. Rakeback and rewards effectively raise your win rate, which shrinks both your ruin risk and your required roll.
What This Calculator Cannot Tell You
The model assumes your win rate is stable, that games do not get tougher, and that you keep playing the same format at the same stake. In reality, table selection, rake changes, and your own form all shift the drift term over time. It also assumes a normal distribution, which fits cash games well but fits tournaments poorly. For MTT bankroll and ROI work, use the tournament ROI calculator instead, and treat any cash-game projection beyond a few hundred thousand hands as directional rather than precise.
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