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See also: Monte Carlo simulation introduction, Random sampling from distributions
There are many algorithms that have been developed to generate a series of random numbers between zero and one with equal probability density for all possible values. ModelRisk uses the Mersenne Twister. All good random number generating algorithms will start with a seed value and all subsequent random numbers that are generated will rely on this initial seed value.
Most risk analysis packages now offer the option to select a seed value. We personally do this as a matter of course, setting the seed to one (because one can remember it!). Providing the model is not changed, and that includes the position of the distributions in a spreadsheet model and therefore the order in which they are sampled, the same simulation results can be exactly repeated. More importantly, one or more distributions can be changed within the model and by running a second simulation one can look at the effect these changes have on the model's outputs. It is then certain that any observed change in the result is due to changes in the model and not a result of the randomness of the sampling.