Numerical estimation of mathbbE[f(X)] ≈ dfrac1Nsum_i=1^N f(X^(i)) by sample averaging, with O(1/√(N)) convergence regardless of dimension — the property that makes MC the only practical pricer for high-dimensional path-dependent claims. Variance reduction (antithetic variates, control variates, importance sampling, stratified sampling) cuts the constant in front of 1/√(N) — often by an order of magnitude. Quasi-Monte Carlo (Sobol, Halton sequences) replaces pseudo-random with low-discrepancy points for O((log N)^d / N) convergence in smooth settings.