The Biggest "Collective Face-Slap" in History: The Monty Hall Problem

This is the most sensational "collective face-slap" event in history—the Monty Hall problem—that caused top intellectuals worldwide to collectively stumble, with the spotlight on Marilyn vos Savant, the woman with the "highest IQ in the world."
In 1985, Marilyn was listed in the Guinness World Records as the person with the highest IQ globally. In 1986, "Travel" magazine launched a Sunday column called "ASK Marilyn" (which ran until 2022), and a nationwide debate in the United States began from this column.
A reader posed the Monty Hall problem: In a game show, behind three doors are 1 car and 2 goats. After choosing door number 1, the host opens door number 3 (revealing a goat). At this point, you have the chance to change your choice—should you switch to door number 2?
Everyone believed that the probability of winning was 50% whether you switch or not, since the remaining two doors seemed equally likely. But Marilyn confidently answered: "You must switch"—insisting that sticking with door 1 gives a 1/3 chance, while switching to door 2 doubles the chance to 2/3.
Once her answer was announced, all of America exploded. Tens of thousands of mocking and insulting letters flooded her inbox, not from keyboard warriors but from top university math professors and PhDs in the U.S. A PhD from the University of Florida criticized her as "misleading the public," and a professor from George Mason University demanded she publicly admit her mistake, accusing her of being "completely wrong."
Faced with the intellectual backlash, Marilyn did not argue back but used simpler logic to clarify: Suppose there are 100 doors, with 1 hiding a car. You pick door number 1 (1% chance), the host opens 98 goat doors, leaving one door unopened. That remaining door now carries a 99% chance of winning—switching is a sure win. Returning to the three-door problem, door 1 has a 1/3 chance, while doors 2 and 3 together have a 2/3 chance. After the host eliminates door 3, door 2 alone holds a 2/3 chance.
This explanation silenced even the most vociferous critics. MIT's simulation confirmed her reasoning was correct, and the professor who demanded she admit her mistake publicly apologized, admitting it was the most embarrassing "car crash" of his career.
If it were you, would you insist on not switching doors, or decisively switch?