What is a Monte Carlo simulation?

A Monte Carlo simulation is a method that estimates the behavior of an uncertain system by running it many times, each time with values drawn at random from the probability distributions of its input variables. Instead of computing a single result from the most likely values, you obtain thousands of possible results, and their distribution is the answer: not "the project will cost €400,000", but "in 90% of the simulations it costs between €380,000 and €620,000, and in one run in twenty it exceeds €700,000". The method was born at Los Alamos in the 1940s out of Stanislaw Ulam and John von Neumann's work on neutron diffusion problems, and the name comes from the Monte Carlo casino. It is needed exactly when a problem has too many interdependent variables for a closed formula to be practical, which is the normal condition of any real project.

Why it replaces the worst case

The usual alternative to simulation is three-scenario analysis: optimistic, expected, pessimistic. It is reassuring and statistically wrong, because the pessimistic scenario built by combining the worst case of every single variable describes an event of negligible probability, while the expected scenario, built from the most likely value of each, almost never coincides with the most likely outcome of the whole. Simulation solves this because it makes the variables work together, correlations included, and returns the shape of the distribution instead of three hand-picked points. That is how the tail becomes visible, the part that actually matters in risk decisions, and how you can answer the right question, which is not what it will cost but how high it can go and with what probability.

An enterprise example

A company has to decide whether to accept a fixed-price contract. The traditional calculation adds up the expected costs of the eight phases and concludes the margin is fifteen percent. The simulation assigns each phase a duration and cost distribution derived from previous projects, accounts for the fact that a delay in phase two causes one in phase five, and runs ten thousand iterations. The typical result of this exercise is not that the margin disappears, but that in a non-trivial fraction of the iterations it turns negative. That is information the expected-value calculation could not have contained, and it changes the decision or at least the price.

Why it matters for decision makers

The value for a decision maker is that it moves the conversation from a number to a distribution, and so makes risk arguable rather than just the average. There is a constraint to understand properly though, because it is where this tool is most often misused: a simulation does not create information, it propagates it. If the input distributions are invented in a meeting, the result is an invented confidence interval, with the aggravating factor of looking rigorous because ten thousand iterations produced it. The distributions therefore have to be derived from the history of finished projects, which is exactly the discipline of reference class forecasting, and the simulation should be seen as the step after it rather than an alternative to it. A second warning belongs here: almost every widespread tool treats variables as independent unless told otherwise, and in real projects things go wrong together. Ignoring correlations systematically produces tails that are too thin, which is the opposite of the error the simulation was run to avoid.