In response to Tom's riddle: Switch. This very problem was the subject of one of my Artificial Intelligence lectures this past term. I could give you a simple explanation of why you should switch but then you wouldn't be in awe of my intelligence any more. Well maybe a little glimpse. Think of it this way. You have a third of a chance of winning with the original door, by switching you increase that to two thirds.



Did you ever wonder how much it would be worth you while to pay for the doorman to open a door is? Exactly one third of the prize in question.