Monty Hall Problem - Vos Savant and The Media Furor

Vos Savant and The Media Furor

"You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! Scott Smith, Ph.D. University of Florida"

Vos Savant responded in her column (vos Savant 1991a) that the player should switch and correctly said that the first door has a 1/3 chance of winning, hence the second door offered to switch to has a 2/3 chance as the host always opens a losing door on purpose. She went on to explain her answer by asking the reader to visualize the case where there are a million doors and the player picks #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens all remaining doors except door #777,777.

In response to her answer, vos Savant received thousands of letters from her readers, many with PhDs, telling her that she was wrong. Of the letters from the general public, 92% were against her answer, and of the letters from universities, 65% were against her answer. Overall, nine out of ten readers completely disagreed with her answer (vos Savant 1990-1991).

Vos Savant replied with further explanation, "The winning odds of 1/3 on the first choice can’t go up to 1/2 just because the host opens a losing door," and she proposed a shell game to illustrate her thinking: "You look away, and I put a pea under one of three shells. Then I ask you to put your finger on a shell. The odds that your choice contains a pea are 1/3, agreed? Then I simply lift up an empty shell from the remaining other two. As I can (and will) do this regardless of what you’ve chosen, we’ve learned nothing to allow us to revise the odds on the shell under your finger." She also proposed a similar simulation of the game with three playing cards.

Even after her further explanations, readers continued to write in telling her that she was wrong. Nevertheless, people did begin to change their minds about the solution. Of those that actually carried out vos Savant's shell simulation, nearly 100% wrote to say that they agreed with her. Of the general public, about 56% came to believe that switching was best; and of academic institutions, 71%. Vos Savant commented that some confusion was caused by people not realizing that the host must always reveal a goat but that most people did understand the question this way.