Monty Hall Problem

Application of the Stochastic Workflow Technology

You are probably familiar with the famous “Monty Hall” problem, but if not, here it is:

Problem

You’re on a game show hosted by Monty Hall, the handsome Canadian fellow pictured above. Before you, there are three closed doors. Behind a uniformly randomly selected door, there is a new car; behind the other two, there is nothing. You get to choose a door, and you get what is behind it as a prize: either a car or nothing. You randomly choose a door, again by some uniform process.

Monty — who knows where the car is — now always opens a door that meets two criteria: it does not have the car behind it, and it is not the door you chose.

To clarify: if you chose the door with the car, Monty chooses one of the remaining two doors by a uniform random choice. If you chose a door without the car, Monty only has one door he can open, and he opens that one. Monty gives you the opportunity to switch your choice to the other still-closed door. Assuming you wish to maximize your probability of winning the car, should you switch doors or stay with your ...