The Monty Hall problem is one of the most consistently counter-intuitive examples presented in game theory. It has stumped doctors, scientists, readers of Marilyn Vos-Savant, and countless students over the years.

The problem hinges on completeness of information.

The confusion happens because we are asked to arrive at the probability of something, and then offered a chance to revise our choice, with better information – but that information is presented in a counter-intuitive way.