Why does the Monte-Carlo Method Work? I've been reading about the Monte-Carlo Method and how it is much simpler for computers to use the Monte-Carlo Method to guesstimate solutions to complex problems like the Standard Model. It is supposed to use random values. But what I don't understand is how the Monte-Carlo Method can calculate solutions with random numbers. If the guess is wrong, how can the answer possibly be right? Thanks for your help.

Monte Carlo method solves a parameter estimation problem, in fact, it works as follows: Let $\mu$ be the parameter to be estimated, we think $\mu$ as the expected value of some observable of a certain phenomenon (for example, $\mu$ can be the average weight of a population). We repeat the experiment many times, each times, we have a observable value. Monte Carlo method takes the average of these values as an estimate value of $\mu$

In mathematical language: Let $\mu=\mathbb{E} X$ with $X$ random variable. Then $$ \frac{X_1+\cdots +X_n}{n}\to \mu$$ (when $n\to \infty$) where $X_1,X_2,\dots$ are independent copies of $X$.

Now, the problem of simulating (making) a copy of $X$ is solved by Markov Chain Monte Carlo algorithm.