<< In August 2001, I argued stridently on the fledgling Wikipedia that switching was irrelevant, and wrote code to prove it, only to be proven wrong by my own code. I posted the code as an "empirical example" subpage off the main article. Unfortunately, the current article no longer includes an executable demonstration.
The key point in the explanation of why switching is better is that the showing of a goat does not affect the probability of 1/3 that the original door is correct. If you agree to that, the other steps are pretty routine and easy to accept. So a good explanation should address this issue. The reasoning is simple: After the initial guess, the two remaining doors play identical roles with respect to what the player knows. The player knows that at least one of them hides a goat. So when a goat is shown, that gives the player no new information about the original guess. This is true regardless of what algorithm may be used to choose the goat door, as long as the player doesn't know the algorithm. And so the probability of 1/3 cannot change. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele