On Wed, Oct 28, 2009 at 3:17 PM, James Propp <jpropp@cs.uml.edu> wrote:
Did Martin Gardner ever try his hand at explaining the paradox?
Yes, but not in the form of the Monty Hall game. One of his columns, anthologized in one of his books, has the puzzle in the form of 3 prisoners, one of whom is to be pardoned, but by order of the governor, they're not to be told whether they are the one to be pardoned or not. A gets told that B is to be executed, and then tells this to C. The question is what A and C should now consider their chances to be. Same problem, except without the possibility of "switching". Part of his explanation is the thing I always find most effective in convincing people; play the game with them with 52 doors. I shuffle a deck of cards, and give you one (don't look yet!). The winning card is the Ace of spades. I then say I'm going to turn up 50 non-Ace-of-Spades cards. I look at my 51 cards, and say "Let's see, I think I'll turn up all but....*this* one!". Now all the people who insisted the answer is 1/2 in the original problem want to switch their card for *that* one. Andy