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Comment by saeranv | Hacker News Reader

I guess Monte Carlo simulations weren't well-known or easily accessible back then? It would have been the perfect way to shut up her critics.

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i was about 15 when this went down and immediately wrote one that confirmed she was right. formative experience in my life.

You don't need Monte Carlo, you just need a table with three rows. GGC, GCG, CGG. Pick the first door, cross out the other goat, and switch. you will lose once and win twice. if for some reason you think the door you pick at first matter somehow, make nine rows, and you will lose three times in win 6. Easy peasy.

You can't fight fire with fire, but you can fight Monty with Monte. :-)

You often can and should fight fire with fire. For a literal instance, https://en.wikipedia.org/wiki/Controlled_burn

This particular one isn’t that hard to just do by hand. Which I did at the time, was surprised at the result, and stared at the column long enough to convince myself why she was right.

Using Bayes theorem? But if you know to use Bayes theorem, then you're already formulating the problem correctly, which is the problem all the critics are running into.

Edit: Someone mentioned you could manually "simulate" it with a pen and paper, which I think is what you meant. If so, very good point.

You can brute force this without knowing Bayes’ theorem (see the grids in the article as an example of iterating through every possible solution then counting to arrive at the right probability).

Ah! I see, I thought the commentator was saying to solve it mathematically. Manually "simulating" it makes sense.

I was unable to convince my father of this, so he and I just put together a little model with paper plates and coins and carried out the simulation manually until we had twenty or thirty trials and he became convinced by seeing it in action.

A simple probability table works just as well

Not really because you can create a valid Monte Carlo model that does "prove" the odds are 50-50 if you don't incorporate the essential rule that throws most people off - that the host's choice of which door to reveal is not random.

they were. the critics didn't use them. she told them to "try it" in one or two columns before she had to explain it very slowly and methodically in a third, as I recall. I'm old. I read each of these as they arrived in the paper.

> I'm old. I read each of these as they arrived in the paper.

So back in the day, Parade magazine was a thing that people actually read, and not just ignored or recycled immediately? The past really is a foreign country.

You could do it in Excel in probably 20 minutes.

You could do it with a pen and paper in less than 5.

The point of doing it in Excel would be to convince someone who won't be convinced by the pen and paper demonstration.

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