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#monte-carlo

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01 ·Probability & Statistics·★ MEMBER·10 min read Monte Carlo Methods from Scratch — Solving Integrals with Dice An integral you cannot solve can still be estimated: scatter random points and take the average. This piece builds up why the law of large numbers buys you only 1/√N, what importance sampling rescues, and how MCMC samples from a distribution whose normalizing constant nobody can compute. 02 ·Complexity·★ MEMBER·12 min read Randomized Algorithms — Why Rolling Dice Makes Things Faster Why does adding randomness make an algorithm faster? We build up quicksort with a random pivot, the one-sided error of Bloom filters, and the Monte Carlo / Las Vegas split from zero background — ending with the ways mishandled randomness actually breaks systems in production.