This page provides an empirical proof of the Monty Hall Problem.
Monty Hall hosted an American TV show, Let's Make a Deal, which culminated in a contestant having to pick one of three doors. Behind two of those doors was a goat, behind a third, a car.
Having chosen a door, Monty hall then opened one of the other doors to reveal one of the goats. He then gave the contestant the chance to change their mind an choose the other closed door.
Intuitively, it seems there is little point in changing the original selection. However, Monty Hall's intervention means that the probability of selecting the door with the car has changed and that by selecting the other door the contestant has twice the probability of winning the car.
This page lets you prove the odds are better if you switch - either by playing the game yourself of letting the browser do all the work for you.