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For anybody interested in robotics out there, Monte Carlo methods are used in what's called a particle filter. The scenario where a particle filter is used is when a robot has a map of a landscape and takes sensor measurements of the landscape, but it doesn't specifically know where in the map it is. The robot keeps predicting where it is and resampling based on how good it's guesses are. What's cool is that this eventually converges to the robot's actual position.

Don't let me drone on about it though. Check out this better video!