Marilyn vos Savant and the Monty Hall Problem (2015)
A famous probability puzzle from the TV game show “Let’s Make a Deal” — the Monty Hall problem — is revisited through the lens of Marilyn vos Savant’s controversial but correct claim that switching doors doubles your chance of winning. Commenters explore why so many people, including mathematicians, initially rejected her answer: ambiguous wording about the host’s behavior, intuitive but wrong “50/50” reasoning, and confusion over variants where the host might act randomly or maliciously. The thread also reflects on the social dynamics around the episode, including hostile reactions to vos Savant and how simulations, larger-door variants, and clearer assumptions help people finally accept the counterintuitive result.
Name, persona, and “smartest person” branding
- Commenters note the coincidence of the surname “Savant” with her public image, linking it to nominative determinism and marketing.
- Thread explains the surname came via her mother’s maiden name; the “world’s smartest” label is seen as largely a media construct.
Core Monty Hall reasoning
- Under the standard assumptions: one car, two goats, host always opens a goat door and always offers a switch, switching wins 2/3 of the time.
- Intuitive framings:
- Treat switching as “take both of the other doors” vs “keep just your 1/3 door.”
- Extend to 100 or 1,000 doors; switching to the sole unopened non-chosen door is then obviously better.
- Key asymmetry: if your first pick is a goat (2/3 chance), the host is forced to reveal the other goat, so switching guarantees the car in those cases.
Ambiguity and host-variant debates
- Large subthread disputes whether the original wording clearly states that the host must always open a goat door and always do so regardless of your initial choice.
- Several variants are discussed:
- “Informed/Fair” host (canonical): 2/3 win by switching.
- “Ignorant” or random host: if he just happens to reveal a goat, odds become 50/50.
- “Malicious” or strategic host: if he only offers a switch when you initially picked the car, switching always loses.
- Some argue the problem is ill-posed without explicit rules on host behavior; others say the intended reading is obvious and determinate.
Simulations, teaching, and intuition-building
- Many describe writing small programs (from BASIC to Python) to empirically verify the 2/3 result, sometimes after initially getting the math wrong.
- Educators report using classroom simulations to resolve confusion and highlight the importance of modeling the host’s rule precisely.
Meta-discussion, psychology, and discourse
- Commenters reflect on how this puzzle exposes overconfidence, nitpicking, and reluctance to revise beliefs.
- Some emphasize gendered and hostile tone in historical criticism; others focus on how ambiguity versus misreading drove the backlash.
- The thread itself is used as an example of how much heat ambiguous probability puzzles can generate.
Real game show vs thought experiment
- Multiple comments note the actual TV show’s rules differed: the host didn’t always offer a switch and sometimes played psychologically, so the real-life optimal strategy is not the clean 2/3 solution of the idealized puzzle.