Cash Game Variance Calculator

What the Bands Mean

The green bands on the simulation chart are confidence intervals. They tell you the range of outcomes you should expect given the win rate and standard deviation you entered. A 95% confidence interval means that 95 out of every 100 simulated runs ended within that band at any given hand count. The remaining 5 runs landed outside it, either above or below.

The narrower 70% band shows where the majority of outcomes cluster. If you run your session 100 times, 70 of them finish inside this band. The gap between the 70% and 95% band is where the unlucky and lucky runs live. Anything outside the 95% band is a statistical outlier at your entered win rate.

Higher Confidence Levels Widen the Range

A confidence interval is a net. The more certain you want to be that the true outcome lands inside it, the wider you have to cast. A 70% interval accepts a 30% chance the result falls outside. A 95% interval accepts only 5%. To shrink that miss rate, you have to extend the boundaries to cover more of the distribution's tails.

In concrete terms: if your win rate is 5 BB/100 and you play 100,000 hands, the 70% interval might span +200 BB to +800 BB. The 95% interval for the same inputs might span -100 BB to +1,100 BB. The expected value does not move. What moves is how much of the distribution you are choosing to capture. Demand more certainty and you necessarily include more extreme outcomes.

Reading Your Own Results Against the Bands

When your actual results fall inside the 95% band, the simulation is saying: this outcome is consistent with your entered win rate. It shows only that variance alone can explain where you landed. When your results fall outside the 95% band, the model is flagging a mismatch. Either you ran exceptionally hot or cold, or the win rate you entered does not reflect your actual edge.

Confidence intervals widen as standard deviation increases and narrow as hand count increases. A player with 100 BB/100 standard deviation at NL50 6-max needs roughly four times the sample to achieve the same interval width as a player with 50 BB/100 standard deviation at NL10 full ring. This is why high-variance formats require larger samples before you can draw meaningful conclusions about your win rate, and why the bankroll simulator and this tool should be used together.

Standard Deviation Sets the Spread

Win rate determines where the center of the distribution sits. Standard deviation determines how wide the bands spread. Two players with identical win rates but different standard deviations will produce confidence intervals of very different widths. The aggressive player who 3-bets wide and runs big bluffs will have a standard deviation of 90 to 120 BB/100 and correspondingly wide confidence bands. The tight grinder who plays a low-variance style might sit at 50 to 70 BB/100 with much narrower bands.

If you do not know your standard deviation, most tracking software reports it. In 6-max NLHE, 75 to 100 BB/100 is a reasonable default. For full ring, 55 to 75 BB/100. For PLO, 120 to 160 BB/100. Entering the wrong standard deviation will distort the confidence intervals more than entering the wrong win rate.

Methodology

1,000 Monte Carlo simulations per calculation. The simulation walks a random path in 100-hand increments using normally distributed steps centered on your entered win rate with variance scaled to your entered standard deviation. Confidence bands are empirical percentiles (2.5th/15th/85th/97.5th) across all 1,000 runs at each step. The normal distribution assumption holds well for cash games where each hand is an independent trial with bounded outcomes.