Applies to: @RISK 7.x and Up

Why Standard Deviation Convergence Always Occurs at 2200 Iterations

When you select Auto iterations and test convergence on standard deviation, @RISK consistently converges at 2200 iterations due to its method of testing convergence.

How Convergence Is Tested:

• Every 100 iterations, @RISK checks if the current statistic (mean, SD, or percentile) is within a confidence interval: ±3% by default, at 95% confidence.

• For standard deviation, @RISK actually tests the variance using the χ² distribution.

• This leads to a formula independent of the underlying distribution:

  cum. prob. of χ² with df=n−1 between (n−1)/1.0609 and (n−1)/0.9409 ≥ 95%
  

• Solving gives n ≈ 2140 iterations. Since convergence is tested in 100-iteration steps, the first multiple ≥2140 is 2200.

Multiple CPUs:

• The master CPU tests convergence using results from workers. If workers process 1000-iteration blocks, convergence may require more iterations (e.g., 3330).

Why Means and Percentiles Differ:

• Their confidence intervals don’t use χ²; convergence depends on the progressive estimates. Only SD/variance convergence is purely iteration-based.