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Monte Carlo Algorithm

The Monte Carlo algorithm is a stochastic method that uses random sampling to approximate solutions to complex problems. Inspired by the concept of randomness, as in the Monte Carlo Casino, the technique performs numerous random simulations to estimate the desired outcome. For instance, to estimate the value of π, you could imagine randomly throwing darts at a square with a circle inside it. Compared to the total number thrown, the proportion of darts landing in the circle can help estimate π. Used in varied fields like finance, physics, game theory, and graphics, Monte Carlo can tackle intricate systems and high-dimensional spaces where traditional methods falter. However, its accuracy typically improves slowly, requiring many more samples to achieve finer precision.

An interesting observation is that Monte Carlo always gives fast results but sometimes gives a very wrong answer. You bet (risk) accuracy on the promise of quick results—exciting property in Computational Theory.