Poker Variance Calculator

How this simulation works

Winrate and standard deviation are both expressed per 100 hands (bb/100), the standard units poker tracking software already reports. 80bb/100 is a typical standard deviation reference figure for 6-max no-limit cash. Rather than a closed-form formula, this tool runs a Monte Carlo simulation: it draws 2,000 independent random paths of results (using a normal distribution around your winrate, scaled by your standard deviation) and reports statistics across all of them. This captures the shape of real variance (including the fact that risk of ruin depends on the whole path, not just the final result) better than a single formula can. Risk of ruin is the fraction of simulated paths whose running total ever fell to or below your full starting bankroll before the hands ran out.

Worked examples

1. Example 1

   A winning player, thin bankroll

   A 5bb/100 winner with 80bb/100 standard deviation, over 100,000 hands, still shows a meaningful risk of ruin with only a 2,000bb bankroll (100 buy-ins at 20bb, thin for this much variance). The mean result is comfortably positive, but downswings large enough to bust a thin roll happen often enough to matter.

2. Example 2

   The same winrate, a comfortable bankroll

   Keep the same 5bb/100 winrate and 80bb/100 standard deviation but raise the bankroll to 10,000bb. Risk of ruin drops close to zero. The winrate hasn’t changed, only the cushion against the swings has.

3. Example 3

   A losing player looks fine in the short run

   A −5bb/100 losing player over just a few thousand hands can easily show a positive mean result in the 90% confidence interval. Variance this large swamps a small sample. Simulating far more hands is what reveals the true expected losing trend.

Related pages

• EV Calculator →
• Pot Odds Calculator →
• Every ranked puzzle type →

Frequently asked questions

What is risk of ruin?

The probability that your bankroll drops to zero (or your full starting bankroll in losses) at some point during the simulated hands, even if your overall winrate is positive. A thin bankroll can carry meaningful risk of ruin even for a winning player.

Why simulate instead of using a formula?

A closed-form risk-of-ruin formula exists for simple cases, but a Monte Carlo simulation captures the actual shape of the swings (including drawdowns that happen mid-way through a session rather than only at the end) across thousands of possible paths.