I have always been fascinated by this story. In September 1990, a woman with extraordinary intelligence published an answer to a seemingly simple puzzle that caused a storm. It concerns the Monty Hall problem — a famous paradox inspired by the game show Let's Make a Deal. Marilyn vos Savant, widely regarded as the person with the highest IQ in history, wrote something that seemed absurd to all of America.

The scenario is simple: a participant sees three doors. Behind one is a car, behind the other two are goats. They choose a door. Then the host, who knows where the car is, opens one of the remaining doors to reveal a goat. Now the question: should the participant switch their initial choice or stick with it?

Marilyn vos Savant did not hesitate. Her answer was categorical: always switch. According to her, changing doors increases the chance of winning from one-third to two-thirds. Sounds strange? To most people — yes.

The reaction was explosive. Marilyn received over ten thousand letters, nearly a thousand of which were from people with a doctorate. Ninety percent of them claimed she was wrong. She read comments like: this is the biggest blunder I’ve ever seen, or suggestions that women simply don’t understand math the way men do. She was ridiculed, questioned, attacked.

But Marilyn vos Savant was not right just because she had a high IQ. She was right because mathematics supported her. The explanation is elegant. Initially, the chance of choosing the car is one-third. The chance of choosing a goat is two-thirds. That’s the key. When the host opens a door with a goat, he changes the probability distribution. If the player initially chose a goat, which had a two-thirds chance, the host will always reveal the other goat. Switching guarantees a win. If the player initially chose the car, which had a one-third chance, switching would cause a loss. Therefore, switching leads to a win in two out of three scenarios.

It turns out that the logical mistake is something simple. People think that after revealing the goat, the odds are equal — fifty-fifty. They ignore the original probability. They treat the second choice as a completely new event, but in fact, it’s a continuation of the initial probabilities. This illusory simplicity of three doors masks the deep logic of the problem.

Marilyn vos Savant was not alone in her confidence. MIT conducted thousands of computer simulations. The result was always the same: the effectiveness of switching is exactly two-thirds. The popular show MythBusters tackled the problem and verified her explanation. Many academic circles, which initially criticized her, later admitted their mistake.

It’s worth knowing a bit more about Marilyn vos Savant herself. She was listed in the Guinness Book of World Records for unparalleled intelligence. As a child, she read all twenty-four volumes of the Encyclopaedia Britannica and memorized entire books. But despite her genius, she struggled with financial difficulties, dropping out of college to support her family. Her column Ask Marilyn became a platform where she solved complex puzzles, earning both admiration and hatred.

The story of Marilyn vos Savant and the Monty Hall problem is a lesson in how far intuition can be from mathematics. It’s a reminder that logic doesn’t always win on the first try. Despite widespread ridicule, Marilyn stood by her answer, ultimately proving that millions of people were wrong. Her determination to challenge public opinion, even when doubts overwhelmed her, left a lasting mark on probability theory.