Monte Carlo method

The Monte Carlo method is a technique that estimates a quantity by repeating a large number of random draws and observing the average results. Rather than seeking an exact formula, sometimes too difficult to establish, you let the experiment speak by replaying it thousands of times.

An image illuminates the approach: to estimate the share of a target occupied by a complicated shape, you could throw darts at it at random, without aiming, then count what proportion falls within the shape. The more darts you throw, the closer this proportion comes to the true area. You thus replace a hard calculation with patient counting.

The method rests on observed frequency. You simulate the experiment a very large number of times, count how many times the sought event occurs, and divide by the total number of trials. This frequency approaches the real probability as the trials accumulate, in accordance with the law of large numbers.

A pitfall deserves mention: the method gives only an estimate, never an exact value. With few draws, the result can deviate noticeably from the truth. Increasing the number of trials tightens the estimate, but precision progresses slowly: to gain one notch of reliability, you often have to multiply the draws considerably. Numerical patience has a cost.

On the site, this logic offers a concrete way to test a game or a draw through experimentation. By rerunning a simulated coin, die, or wheel a large number of times, you can verify that the results are distributed as expected and that the tool behaves fairly, without having to work through the theoretical calculation.