You've watched a TV game-show many times, and have become familiar with the format. You appear on the show and become that week's winner. Three boxes are put in front of you. In one, is the star prize. You must pick which box to open, and you will claim the contents of the one you pick.

You pick one, and the host says "Are you sure that's the one you want? There's still time to change your mind." He always does this, so this doesn't surprise you. He only does that to raise the tension for the purpose of entertainment. You stick to your guns.

"Okay," says the host, "I'll just open one of the other two boxes, and then we'll see if you want to change your mind." He opens one of the two boxes which you did not pick, and it is empty. Again, this is nothing unfamiliar. "There are two boxes left," he says. "Do you want to change now, or stick with the one you picked?"

Should you stick, or swap? Does it make no difference?