In the classic brain teaser ''Monty Hall Problem''( http://en.wikipedia.org/wiki/Monty_Hall_problem) the higher chances of you winning the car after switching your door choice is explained by the fact that the host does not increase the probability of a car being behind the door you chose because of opening one door with a goat.
I find this explanation unconvincing.IF your had chosen the door with a car and the host opened the next door should you still be worried because there is only 1/3 chance you are correct? Reductio ad absurdum