Consider a square on the plane with a side length of 1 and an irregularly shaped "figure" inside it. How to find the area of ??this "figure"? The Monte Carlo method is a "randomization" method: N points are "randomly" thrown into the square and fall within the "graph", then the area of ??the "graph" is approximately M/N.

A loose analogy can be made with opinion polls. Rather than consulting every registered voter, pollsters conduct small samples of voters to identify possible winners. The basic idea is the same.

The problems in scientific computing are much more complex than this. For example, in the pricing and transaction risk estimation of financial derivatives (options, futures, swaps, etc.), the dimensionality of the problem (that is, the number of variables) may be as high as hundreds or even thousands. For this type of problem, the difficulty increases exponentially as the number of dimensions increases. This is the so-called "Curse Dimensionality" and is difficult to deal with with traditional numerical methods (even with the fastest computers). The Monte Carlo method is well used to deal with the curse of dimensionality because the computational complexity of the method no longer depends on the dimensionality. Problems that were previously impossible to calculate can now be calculated. To improve the efficiency of their methods, scientists have proposed a number of so-called "variance reduction" techniques.