Monte Carlo-simulations depend on random numbers.
It's easy to see why GOOD random number-generators are crucial.
Example 1: Monte Carlo-integration
Draw some shape on a piece of paper. Want to know the area? Draw a square around the shape. Now toss a pinch of salt on the drawing (-> random numbers).
You know the area of the square and the number of grains of salt inside it (supposedly).
Count the grains of salt inside the shape and you get the ratio of the shape's area vs the square's area. (Providing you have a good random number-generator which delivers an even distribution and not the whole pinch ending up in a heap in the middle of the square.)
No calculations. Just generating a shit-load of random numbers and counting where they end up. The more complicated the shape, the better fares this method compared to others, especially in higher dimensions.
Example 2: Monte Carlo-simulation
You have a set of laws or a theory (e.g. the laws of physics how particles interact or how a single human interacts with other commuters/passengers/neighbors). Now you want to know how these behave in the big picture:
What will you see in the detector of your particle accelerator? How will people move if they suddenly want to leave the room at the same time and there is only one door?
You create a template-object and fill it with random attributes: speed, direction, angle of impact... Once you overlay thousands or millions of possible scenarios, you will see which outcomes are most likely.
For example, thats how physicists calculated what the signal of a Higgs-boson at the LHC should look like.
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