# What are Monte Carlo simulations?

Is Monte Carlo Simulation the same as just conducting experiment several times and then averaging results? Why is it then called like that?

• conducting experiment several times and then averaging results indeed relates to Monte Carlo Simulation such as for Monte Carlo Integration but it is only small part of the method I think Commented Sep 25, 2015 at 12:47
• You might find this question interesting. Also, here is an MC answer I gave to a very basic probability question. Commented Sep 25, 2015 at 16:45
• How is such a basic question not a duplicate many years after this site was launched? Commented Sep 25, 2015 at 17:00
• If you can find a duplicate, suggest it, @PeterMortensen. But there are many basic questions that are still not covered on the site, & many issues that have been covered multiple times but indirectly or partially only. Commented Sep 25, 2015 at 17:37
• @PeterMortensen Interesting question. There have been related posts such as "Are all simulation methods some form of Monte Carlo?" but this seems to be the first post of its type, so I don't think it's a duplicate. There have been rather more questions about "What is MCMC?" but that something quite distinct Commented Sep 25, 2015 at 17:37

Monte Carlo method (there is also Monte Carlo algorithm) is a general name for a broad class of algorithms that use random sampling to obtain numerical results. It is used to solve statistical problems by simulation. It was one of the first methods of computer simulation that was described (see here for broader introduction and references). In plain English, Monte Carlo is drawing random numbers to simulate something and afterwards some kind of aggregation is often used to make conclusions about the simulated phenomenon.

The name, as Metropolis himself recalls (see also here), is inspired by the name of casino,

It was that time I suggested an obvious name for statistical method - a suggestion not unrelated to the fact that Stan [Ulam] had an uncle who would borrow money from the relatives because he "just had to go to Monte Carlo".

Metropolis, N. (1987). The Beginning of Monte Carlo Method. Los Alamos Science, 125-130.

Anderson, H.L. (1986). Metropolis, Monte Carlo, and MANIAC. Los Alamos Science, 96-108.

A repeated experiment is a good start .

In finance, for example, we try to plan for a 30 year retirement, with investment returns that are not guaranteed. One model states that each year has a 10% return with 14% standard deviation. Monte Carlo can help us understand the expected return by treating this return as a random event and running the 30 year return some 1000+ times.