[jonathanstrange]

Oh man, I'm always glad to hear I'm not the only one who got the Monty Hall problem wrong. Here is my embarrassing MH story.

Like Paul Erdős, I resorted to experimentation. Very much unlike Paul Erdős the computer program I wrote contained a one-off error in its PRNG that coincidentally confirmed the wrong result. I then spent a day or so on Usenet insisting stubbornly on the wrong solution until some very kind person on sci.crypt made a complete truth table as a proof. That exhaustive proof immediately convinced me of my idiocy.

Lesson: If a bunch of smart and educated people tell you that you're wrong, then you're probably wrong.

[dhimes]

I embarrassed myself on usenet. Still remember it. Still can...feel it.

It was that problem that made me realize that although physicists deal with probabilities all the time, we don't really understand them.

[WilliamEdward]

The thing is that the person who got it right was not a researcher while all those that got it wrong were.

Either way, you should never feel bad about getting the monty hall problem wrong because it was never set up as a fair question. Marilyn Savant made some incredible assumptions about the premise of the question that were never clear and thus almost completely made up the question herself.

[umvi]

> Lesson: If a bunch of smart and educated people tell you that you're wrong, then you're probably wrong.

Not always the case. As they say, science advances one funeral (of smart and educated people) at a time...

[EForEndeavour]

There will always be exceptions, hence the "probably" in their lesson. There's paradigm shifts, and then there's an unnoticed bug in code hacked together to prove something to oneself.

[Skrillex]

I will probably continue to get the Monty Hall problem wrong for the foreseeable future despite understanding the logic. I think the issue with it for me is the difference between probability and calculated probability (which I do not think is a proper mathematical term).

Like...when someone makes reference to a given probability X "changing" from ~33% to ~67%, they are referring to the updated model that we use to calculate the probability. Nothing in reality has changed, but rather the model has.

[delinka]

“If a bunch of smart and educated people...”

Well, you do have to first recognize that the particular bunch is composed of smart and educated people...

[arayh]

As Richard Feynman says, "Some people say, How can you live without knowing? I do not know what they mean. I always live without knowing. That is easy. How you get to know is what I want to know."

I always try to weave some skepticism into my thought process, because you never know when some of your fundamental assumptions can be wrong.