Monte Carlo
Last Updated: July 29, 2026 | By Mihail Sebastian | AI Dictionary
A method that estimates hard-to-compute quantities by running many random samples, used in ML for uncertainty estimates, dropout, and game-tree search.
What is Monte Carlo?
Monte Carlo is a family of methods that estimate hard-to-compute quantities by running many random samples and averaging the results. Named after the Monaco casino district, the approach trades exact calculation for repetition and chance.
Its value shows where direct math fails: problems with too many variables, no closed-form solution, or genuine uncertainty. Rather than solve such a problem, a Monte Carlo simulation plays it out thousands of times and reads the answer off the outcomes.
How Monte Carlo Works
The recipe has three steps. Define the possible inputs and their probabilities; draw random samples from them; run each sample through the system and aggregate the results into an estimate.
The law of large numbers does the heavy lifting: as the number of samples grows, the average of the outcomes converges on the true value. Accuracy is bought with computation – quadrupling the samples roughly halves the error.
Applications of Monte Carlo
- Risk assessment: Financial analysts simulate thousands of market scenarios to price options and estimate the probability of portfolio losses, and engineers use the same technique to model complex systems under uncertainty.
- Machine learning: Monte Carlo dropout runs a network multiple times with dropout active at prediction time; the spread of the outputs estimates the model’s uncertainty. Monte Carlo methods also power probabilistic inference when exact computation is intractable.
- Game-playing AI: Monte Carlo Tree Search evaluates moves by simulating random playouts from each candidate position. DeepMind’s AlphaGo combined it with neural networks to defeat Go champion Lee Sedol in 2016.
Example of Monte Carlo
A classic demonstration is estimating Pi. Inscribe a quarter circle inside a unit square, then throw random points at the square.
Each point either lands inside the quarter circle or outside it. Since the quarter circle covers \(\pi/4\) of the square’s area, the fraction of points landing inside approaches \(\pi/4\) as the points accumulate. Multiply that fraction by 4 and you have an estimate of Pi.
With 100 points the estimate is rough. With a million, it is accurate to a few decimal places – no geometry solved, just sampling repeated until the answer emerges.
Related AI terms: Normal Distribution · Joint Probability Distribution · Dropout · Reinforcement Learning
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