Stick or switch? Probability and the Monty Hall problem

It is a puzzle which has had mathematicians and the public scratching their heads for decades.

The Monty Hall problem, first posed in 1975, imagines a game show in which you choose one of three closed doors and win whatever is behind it.

One door conceals a Cadillac, behind the other two doors are goats. The game show host, Monty Hall, knows where the Cadillac is and opens one of the doors that you did not choose.

You are duly greeted by a goat, and then offered the chance to switch your choice to the other remaining door.

Most people believe that with two choices remaining and one Cadillac, the chances are 50-50, yet the evidence shows that switching doubles your chances of winning. But why?

Marcus du Sautoy demonstrates the rule to Alan Davies.

Video courtesy of Horizon