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Comment by jncfhnb | Hacker News Reader

I have not restated the problem.

You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. All you know is that you were shown a goat on one play. This is possible in the setup I’ve listed. You landed in that 33% case where you chose a car.

There is nothing in the prompt that says we are not playing my variant of the game.

Being told that you SAW a goat does not mean you would ALWAYS SEE a goat if the previous conditions had gone differently. And that is why you’re wrong :)

Again > all you know is that he opened a goat door

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> 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.

No! Read the prompt very carefully.

You know nothing except you picked door 1 and then he decided to show door 3.

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.

The experience of this contestant is fully and equally possible within my version of the game too!

> 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.

> 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.

Incorrect and I invite you to cite the line of the prompt that says otherwise. This is the critical missing piece of information that makes it the commonly understood “Monty hall problem” and not the improperly stated prompt that we actually have.

“Monty did this” != “Monty would have done this regardless of your previous choices”.

Unless this is stated, you just have an incomplete problem. If you don’t know the mechanics by which Monty decides to share information, it does not give you probabilistic info.

Probability questions frankly often require you to make judgements about the probable starting conditions based on information given so far. You frequently need to recognize that your current situation is the result of prior processes that are or are not defined.

No, you're solving the wrong thing. This is a thought experiment, not a real life scenario with ambiguity.

In this thought experiment, MH will always open a door to a goat on purpose and always ask if you want to switch, because the entire point of the thought experiment is that people find the 2/3 odds if you switch unintuitive and baffling, leading to extremely long thread chains.

You're doing the equivalent of saying "why can't we wait and see if the cat meows" when talking about the Schrödinger's thought experiment. It can't because that's not the point of the exercise.

With all due respect, no. Please don’t jump in at the end of a long thread and bring it back to the beginning. We are not discussing “The Monty Hall Problem”. We are discussing the specifics of the actual original prompt with its failure to document all assumptions.

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