[daveFNbuck]

This roundabout, hand-wavy, vague way to deal with things is how mathematicians solve problems. You have to have an intuitive understanding of what's going on before you can formalize the solution into a proof.

I majored in math in undergrad, and one of the required courses was about communicating mathematical ideas. One of my bigger projects in that course was to explain the Monty Hall problem so it could be understood by the general public, and I got a good grade by putting together a lesson plan that included this type of simulation.