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Comment by EvanKelly | Hacker News Reader

That was a great read. It reminds me of the Monty Hall problem fiasco that arose from the "Ask Marilyn" column about it. I appreciate the author of Polymath actually refuting all of the arguments against his post (to a reasonable degree).

Coding Horror describes it here: http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fa...

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Wow, that expert mathematicians refused to accept the solution is quite amazing to me...

When I was originally asked the Monty Hall problem, I asked "Does the host know where the prize is?" to which they replied "it doesn't matter". I also used simulations to show it does.

The host has to know where the prize is, otherwise how could he open one of the two other doors after the player's first choice?

I've seen it worded poorly where it is stated that contestant picks door 2 and then the host opens door 1 revealing an empty stage.

The problem becomes to 50/50 if you change the rules that the host always opens the left most door not picked by the contestant.

If the host always opens the left-most door not picked by the contestant, the host would open the door on the prize one out of every three times.

Indeed, and these cases are the ones we don't examine.

Because it may be that the host opened a random door, which happened not to have the prize in it.

If that's the case then you're only examining a subset of the probability distribution, which means you're getting skewed results.

Yes, and being asked about the nature of these skewed results.

Reasonable people get in arguments over Monty Hall because the problem is usually stated incompletely. The odds depend on what the show's host is doing.

Reasonable people do usually get in arguments (and are wrong) over the Monty Hall problem even when the problem is correctly stated (as the Vos Savant or Erdős' stories show).

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