Marilyn vos Savant solved a problem that defied the mathematical intuition of thousands of scholars

When Marilyn vos Savant published her response to the famous Monty Hall problem in the Ask Marilyn column of Parade Magazine in September 1990, she couldn’t have known that her simple explanation would spark a storm of criticism worldwide. A woman recognized for having the highest recorded IQ on the planet faced an unprecedented wave of skepticism—including dismissive letters from PhDs. Her story is not just about mathematics but about the courage to stand up to public opinion, even under immense pressure.

The Puzzle That Confused Generations

It all begins with a seemingly simple scenario. A contestant is on a game show and must choose one of three doors. Behind one door is a car; behind the other two are goats. After the contestant makes their choice, the host—who knows exactly what’s behind each door—opens one of the remaining doors to reveal a goat.

At this moment, the contestant faces a decision: stay with their original choice or switch to the other unopened door. Which strategy maximizes the chance of winning?

Marilyn’s Controversial Answer

Marilyn vos Savant’s answer was clear and uncompromising: switch. According to her explanation, switching to the other door increases your chances of winning from one-third to two-thirds. A simple tip that should be obvious—but wasn’t.

The Avalanche of Doubt and Disbelief

The reaction was, in many ways, brutal. Marilyn received over ten thousand letters from all over the world. Nearly a thousand of them came from people with doctorates, and about nine out of ten insisted Marilyn was wrong. Her answer became the target of ridicule and criticism, openly voiced by many mathematicians and scientists.

She was accused of “completely misunderstanding the basics of probability” or “making the worst mistake I’ve ever seen in print.” Some letters even carried sexist tones—many critics implied that women simply don’t master mathematics as men do.

Mathematics Doesn’t Lie

But Marilyn vos Savant was undeterred. And she was entirely correct. The mathematical explanation is cold and infallible:

Initial probabilities:
When you first choose a door, you have a one-in-three chance of picking the car. A two-in-three chance that you picked a goat.

The pivotal moment—what the host does:
Here lies the key to understanding. If you initially chose a goat (which happens two-thirds of the time), the host is forced to open the other goat. If you switch in this situation, you win the car. Yes. Conversely, if you initially chose the car (one-third chance), switching means you lose.

The final outcome:
By switching, you win in all scenarios where you initially picked a goat—that’s two-thirds of the time. Therefore, your chances increase to two-thirds.

Scientific Verification Changed Minds

Over time, Marilyn’s answer underwent rigorous testing. Mathematicians and programmers at MIT ran computer simulations—thousands and thousands of trials—that continually confirmed: switching directly leads to a success rate of two-thirds. The popular American show MythBusters, which tests legends and scientific mysteries, decided to physically test this puzzle and unequivocally confirmed Marilyn’s explanation.

Gradually, the situation reversed. Many academics who initially condemned her returned with apologies and admissions. Science was not subjective—it was objective and infallible.

Why Our Brains Deceive Us

Although the mathematics is clear, the human brain initially resists. Several psychological reasons explain why the correct answer seems inaccessible:

Illusion of symmetry:
After the host reveals a goat, it seems to us that the remaining two doors have an equal 50-50 chance. We ignore the fundamental truth—that your original choice had a one-third chance, which remains unchanged.

Cognitive reset:
The human brain tends to perceive the second choice as a new, independent event. In reality, the original probabilities persist and are simply reorchestrated.

Intuitive failure:
When there are few doors and options, the problem appears simpler than it actually is. This leads us to underestimate its true complexity.

Marilyn vos Savant: A Genius Ahead of Her Time

Marilyn vos Savant’s story itself is fascinating. With an IQ of 228—recognized by Guinness World Records as unparalleled—she has been extraordinary since childhood. At ten years old, she read all twenty-four volumes of Encyclopaedia Britannica and memorized much of it.

Yet her path was not without obstacles. Growing up, she faced financial difficulties that eventually forced her to leave university and support her family. Later, she gained fame through her column Ask Marilyn, where she solved complex puzzles and questions, earning radio acclaim.

But she also faced much criticism—foreshadowing what she would encounter with the Monty Hall problem.

The Legacy of One Woman and a Lesson for All

Marilyn vos Savant’s story and the Monty Hall problem are not just about mathematics. They reveal how public opinion and academic consensus can sometimes lead us astray. It’s about how logic wins when you defend it long enough. Most importantly, it’s about the courage of one woman who refused to succumb to pressure and debunked thousands of misconceptions to stay true to mathematical truth.

Marilyn vos Savant reminds us that sometimes we see what we want to see—not what is there. Her answer to the Monty Hall problem has become a classic lesson in how intuition and reality often diverge—and why it’s always wise to trust evidence, even when it’s uncomfortable.