Monte Carlo Algorithm
Warning
The Monte Carlo algorithm uses random sampling to get approximate answers to hard problems. The name comes from the randomness of the Monte Carlo Casino. You run a ton of random simulations and estimate the outcome from them. Say you want π. Throw darts at random at a square with a circle inside it. The share of darts that land in the circle, out of all the darts you threw, gets you an estimate of π. People use it in finance, physics, game theory, and graphics, mostly for messy systems and high-dimensional spaces where the usual methods give up. The catch is that accuracy improves slowly, so every bit of extra precision takes a lot more samples.
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.