[n3ur0n]

> just means trying out

this statement trivializes a very hard problem.

> literally just means trying out, or simulating

Simulating is an incredibly hard problem and MC methods and theory is an incredibly rich area of study. Some tools I use for my work in probabilistic machine learning models are MCMC techniques like HMC (Hamiltonian Monte Carlo), variance reduction techniques (Rao Blackwellization). If you would like to learn more, here is a great course: https://statweb.stanford.edu/~owen/mc/ -- you can take a look at the syllabus. Also, Casella Berger is a standard MC method book.