bemusedthrow75

I'm sorry what now? Stop second guessing the puzzle which is clearly stated.

I'm so, so done with this now that I am actually going to render inoperable my only HN account so I cannot possibly come back to this, or any other thread.

Nope.

But I am going to leave this to someone else to explain. I'm tired out now.

It doesn't make a difference what causes Monty to reveal a goat.

A goat behind a door the contestant did not choose is eliminated. That is all that matters. It could have been done by a Heath-Robinson machine, or a passing lonely shrubber, or elves.

Monty isn't a floating variable in the puzzle who makes choices. His choice is fixed. Which I imagine is why vos Savant adds the actually extraneous information that Monty is fully aware what is going on behind the scenes -- to underscore the concept that Monty isn't a variable.

The fact that a goat behind an unchosen door was revealed is what is crucial to the setup of the entire puzzle.

And that -- despite jncfhnb's protestations -- is information that makes the puzzle determinate.

I am suddenly reminded of the clever, morally educational joke about the dead horse raffle.

> You do not know if he would have shown door 3 had you picked door 2! This is NOT in the prompt. You cannot assume that.

Monty isn't a contestant. Monty's action and outcome is part of the fixed description of the problem. He opens one of the doors and reveals a goat. Full stop.

If you think revealing one of the two goats (the other of which might or might not be behind your current selection) isn't information of value in assessing whether your chances in that scenario are improved by switching, I'd encourage you to consider why.

And now I really must leave it to someone else to help you, if they will. But I very much appreciate your politeness.

> You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt.

Yes. It is. It is a fixed part of the scenario. Monty opens a door and shows you a goat. He knows it is going to be a goat (he is "well-aware of what is going on behind the scenes"). He's showing you a goat as part of the problem which is: should you switch?

Again: think through what the problem actually SAYS:

> Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

> “Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”

No matter what: the goat Monty shows you is not a matter of chance. It is a fixed part of the problem. It's there in writing: he shows you a goat. Full stop.

You've restated the problem (incorrectly) -- changed it.

There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat.

I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem.

Which is that one can quite clearly fairly argue the point, as you are doing, without resorting to misogynistic or patronising rudeness as so many did at the time!

But you're still wrong. :-)

And I'm going to leave it here.

This is an even better learning experience than coding it right the first time, and I am so happy you had it!

> You have no way to know if he would only show you a goat if you picked the car.

What do you mean?

It's specified in the scenario. He shows you a goat. It's right there. This isn't a variable. It's a fact.

Your only job is to work out whether, given the scenario described, it makes sense to switch. Given all your possible choices.

"If all you know is that he opened a goat door you have learned nothing."

This is precisely where you are wrong.

It doesn't matter what he only does, or always does.

It matters what he did in the problem as it is described. Because that is what you're solving.

> His purposeful behavior could also be random.

It doesn't matter. Because the problem explains what happens: he opens a door and reveals a goat.

That is crucial information. There's now only one goat and one car left. But the choices have not been shuffled: you're definitely still pointing at your original choice.

What were the odds that your original choice is a goat? Two in three.

If you picked a goat, what is guaranteed to be behind the other door? A car.

So what are the odds that behind the other door is a car? Two in three.

You should switch.