# Monte Carlo Simulations

Monte Carlo techniques emerged out of World War II and the efforts to create the first atomic bomb. The scientists working on the Manhattan Project named their models after the famous European casino in Monaco, and used them to estimate the probabilities of the random behaviors of subatomic particles in the weapons they were building. Monte Carlo techniques took advantage of statistical analyses and the availability of electronic computers capable of doing more sophisticated calculations more quickly than the existing manual methods.

Put simply, Monte Carlo models function by allowing people to repeatedly simulate events about which they know certain things, such as a set of possible outcomes and the likelihood of each of those outcomes. A good example is the outcomes from rolling two six-sided dice. Assuming the dice are fair, the probability of rolling a 7 is known (1/6 or about 17 percent). But how could we test whether 7 really comes up once out of every six rolls?

One way would be to roll two dice 100 or 1000 or 10,000 times and record the result of each scenario (the rolling of two dice). After all those repeated scenarios, we would expect the number of 7s we rolled to approach 17 percent of our total rolls. Rolling dice thousands of times, however, is not something most people have time to do outside of Las Vegas. But, those parameters can be plugged into a computer to have it randomly simulate rolling dice, which would be much faster and achieve the same result. That's a Monte Carlo simulation.

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