Poker Variance Calculator

Professional poker is not merely about playing cards but managing risk capital against statistical noise. Variance represents the dispersion of results around the expected value (EV) of a player. In games like No-Limit Hold'em or Pot-Limit Omaha, standard deviation values often exceed win rates by a factor of 10 or more. This discrepancy creates extended periods where results diverge significantly from skill levels. A winning player with a high win rate can still face downswings lasting tens of thousands of hands purely due to variance.

This tool separates the signal from the noise. It calculates the theoretical spread of outcomes over a defined sample size using the Law of Large Numbers and the Central Limit Theorem. By simulating potential bankroll trajectories, players can visualize the probability of downswings and determine if their current bankroll is sufficient to withstand the inherent volatility of their specific game format. Accurate bankroll management prevents the mathematical certainty of ruin, regardless of skill edge.

The confidence interval for a poker win rate over a given sample is derived from the standard error. We assume a normal distribution for large sample sizes.

Where W is the observed win rate, σ is the standard deviation per 100 hands, and N is the number of hands. The Risk of Ruin (RoR) approximates the probability of losing the entire bankroll B before doubling it or reaching the long run.