The World's Highest IQ: Marilyn vos Savant and the Controversial Monty Hall Problem

In September 1990, Marilyn vos Savant, recognized as the person with the highest recorded IQ, ignited a heated debate that continues to captivate mathematicians and the general public alike. Her response to the Monty Hall problem, a probability puzzle inspired by the famous TV show Let's Make a Deal, challenged conventional wisdom and sparked an uproar among readers, including academics.

The Puzzle: The Monty Hall Problem

Picture this scenario:

• A contestant faces three doors. Behind one lies a car, while goats lurk behind the other two.
• After the player selects a door, the host (privy to the car's location) reveals a goat behind one of the remaining doors.
• The contestant then faces a choice: stick with their original door or switch to the other unopened door.

The question at hand: To maximize the chances of driving away with the car, should the contestant hold firm or make the switch?

Marilyn's Bold Answer: "Always Switch"

In her Parade magazine column, Marilyn's stance was unequivocal: "Yes, you should switch."

Her reasoning? Switching doors boosts the winning odds from 1/3 to 2/3.

The Backlash: A Storm of Criticism

The public reaction was explosive. Marilyn's inbox flooded with over 10,000 letters, including nearly 1,000 from Ph.D. holders, with 90% insisting she was mistaken. Critics scoffed at her response, declaring:

• "You've completely misunderstood the concept of probability."
• "This is the biggest blunder I've ever witnessed!"
• "Perhaps women don't grasp mathematics as well as men do."

Was she off the mark? Not in the slightest.

The Mathematical Explanation:

1. Initial Choice Probability:

   • The chance of selecting the car on the first try is 1/3.
   • The likelihood of choosing a goat is 2/3.

2. Impact of Host's Knowledge:

   • If the contestant initially picked a goat (2/3 probability), the host will always reveal the other goat. In this case, switching guarantees victory.
   • If the initial choice was the car (1/3 probability), switching leads to a loss.

3. Conclusion: By switching, the contestant wins in 2 out of 3 scenarios, thus increasing the success probability to 2/3.

Proof and Validation

Marilyn's answer was later confirmed by:

• Computer simulations: MIT and others conducted thousands of trials, consistently showing a 2/3 success rate for switching.
• MythBusters: The popular show tested the problem and verified its explanation.
• Academic apologies: Many who initially criticized her later admitted their error.

Why It Seems Counterintuitive

1. Misassessment of probabilities: People assume that once a goat is revealed, the remaining doors each have a 50% chance, disregarding the original 1/3 and 2/3 probabilities.
2. Reset bias: Many view the second choice as a new, unrelated event, when in fact, it's a continuation of the initial probabilities.
3. Deceptive simplicity: The small number of doors gives the impression that the problem is simpler than it actually is, thus masking the underlying complexity.

Marilyn vos Savant: A Genius Ahead of Her Time

The woman behind the 228 IQ:

• Recognized by Guinness World Records for her unparalleled intelligence.
• By age 10, she had read all 24 volumes of the Encyclopaedia Britannica and memorized entire books.

Despite her intellect, Marilyn faced financial hardships growing up, abandoning her university studies to support her family. Her talent later shone in her Ask Marilyn column, where she tackled complex puzzles, garnering both admiration and criticism.

The Monty Hall Problem: A Lesson in Logic and Resilience

Marilyn's experience with the Monty Hall problem serves as a powerful reminder of the gap between intuition and mathematics. Despite widespread mockery, she stood by her answer, ultimately proving millions wrong and leaving a lasting legacy in probability theory.

Her story exemplifies the power of logic, perseverance, and the courage to challenge popular opinion, even in the face of overwhelming doubt.