How Many Iterations Should I Use?
Many @RISK users ask, “How many iterations should I use for my Monte Carlo simulation run?” It’s a good question and here’s a quick tip to help you decide.
In general, the number of iterations are affected by two opposing pressures:
- Too few iterations will give you inaccurate outputs and graphs (particularly histogram plots) that look ‘scruffy’
- Too many iterations will take a longer time to simulate, and may take even longer to plot graphs or export and analyze data afterwards
The Minimum Number of Iterations
for a Monte Carlo simulation
The short answer for general risk models, burdened with many caveats, is ‘use no less than 300’. At 300 iterations you start to get a reasonably well defined cumulative distribution, so you can approximate the 50th and 85th percentiles and the mean is pretty well determined for most output distributions. At the same time, if you export the generated values from two or more random variables in your model to produce scatter plots, 300 is the minimum you need to get some sense of the patterns that they produce (i.e. their joint distribution).
Vose Consulting usually sets its models to run 3,000 iterations as a default (that figure should be increased if a particularly high level of accuracy is warranted), because they plot a great deal of scatter plots from @RISK generated data, and 3000 is about the right number of points before the scatter plot gets clogged up, and certainly enough for all the percentiles and statistics to be well-specified.
See the Results
The figures below show what type of variation you’d typically get for a cumulative distribution between runs of 300 iterations and of 3,000 iterations. Since most models include an element of guess work in the choice of model, distributions or parameter values to use, one should not usually be too concerned about exact precision in the Monte Carlo results but you’ll see that 300 iterations is probably the least level of accuracy you would find acceptable.
Now the figures below show the same input and output plotted together as a scatter plot for 300 and 3,000 iterations. We find scatter plots to be a great, intuitive presentation of how, among others, the input variability influences the output value. You’ll see that the pattern is just about visible for 300 iterations, and just starting to get clogged up at 3,000 iterations (if you run more than 3,000 iterations, you can plot a sample of just 3,000 to keep the scatter plot clear). If the pattern were simpler, the left panel of 300 iterations would be more clear.
