The Monte Carlo method uses randomness for computer simulations.

Core idea

• It relies on random sampling to model and solve problems that might be deterministic in principle. By generating many random inputs and observing the resulting outcomes, proportions or averages converge to the desired quantities as the number of simulations grows.

Common uses

• Numerical integration and solving high-dimensional integrals.

• Optimization and risk assessment under uncertainty.

• Generating samples from probability distributions (including via Markov chain methods).

How it works in practice

• Define a probabilistic model or a random process that reflects the problem.

• Use random number generators to produce samples of the uncertain inputs.

• Run the model many times (simulations) and aggregate results (e.g., compute averages, variances, confidence intervals).

If you’d like, I can tailor this explanation to a specific field (finance, physics, engineering) or provide a short worked example.