3 ms·

Exactly. If Monty doesn't know what's behind the doors, then sometimes he'll reveal the winning door, and of course you'll choose to switch to that door. The b

by baddox 7y ago

Exactly. If Monty doesn't know what's behind the doors, then sometimes he'll reveal the winning door, and of course you'll choose to switch to that door. The bizarre scenario some people try to propose is that Monty doesn't know what's behind the doors, but if he happens to reveal the winning door, then we...ignore that entire Universe, or...rewind the simulation and try again, until he "by chance" reveals a non-winning door.

bonoboTP 7y ago
No need to talk about ignoring Universes or rewinding simulations, that just sounds confusing to most people. Enough to say that if Monty opens the winning door then he apologizes, closes it, and his helpers place the car to a new random place and they try again from the start. Or say, ignorant Monty may open the winning door accidentally, but here I have a stack of DVDs of all lucky episodes where Monty got a goat. When binge watching these videos, would you expect to see switchers win at a higher rate? Answer to both: it becomes 50-50 if Monty was ignorant, even if we post hoc filter out those cases where he got it right. Bonus philosophical question: you don't know whether Monty knew the car's location. He may say he does, or he may say he doesn't but you don't trust him. Or maybe he says "phew, how lucky to be a goat, I actually had a short amnesia an bluffed it". How can such a murky thing whether a human knows something or not impact the very, financially real world, even when all outward appearances are equal: I saw with my eyes that Monty opened a goat door with his hands. Yes it might have been an accident/luck but what is the precise definition of luck anyway? How can it have an influence whether his brain contained this information, given that he ended up opening this goat door anyway. How can counterfactual Universes influence ours? I have my own answers but it's an interesting thing to ponder.
- baddox 7y ago
  > No need to talk about ignoring Universes or rewinding simulations, that just sounds confusing to most people. It should sound confusing. People who justify their claim that switching doors doesn’t change your odds in this way are proposing a very bizarre and confusing revision of the problem. The original statement of the problem is a very straightforward description of a simple and realistic game show, that happens to have a solution that is counterintuitive to many people.
- henrikschroder 7y ago
  > Answer to both: it becomes 50-50 if Monty was ignorant, even if we post hoc filter out those cases where he got it right. It's not 50/50 because he is ignorant, it's 50/50 because you've discarded 1/3 of the outcomes, and all the outcomes you've discarded were ones where the contestant initially picked a goat.
  - bonoboTP 7y ago
    That's true, but I discarded it based on what I think Monty knew and counterfactual reasoning. The question is why "knowledge" or "luck" or "just accidentally" have an effect on what I should discard. Another "more serious" related "paradox" is in scientific hypothesis testing. You can have different p values even if you observed the exact same experimental outcome but your stepping criterion was different. The only difference is the speculation of what you would have done if the experimental outcome had been different. [0] These things are quite unexpected unless you've already worked through such examples. [0] https://en.m.wikipedia.org/wiki/Likelihood_principle https://en.m.wikipedia.org/wiki/Likelihood_principle
henrikschroder 7y ago
It doesn't matter. If Monty knows what's behind the doors, we arrive at the scenario immediately where the door that's left has 2/3 chance of hiding the car, because the door you picked has 1/3 chance of hiding the car. If Monty doesn't know what's behind the doors, and goes into a cycle of opening doors and shuffling the prizes if it was the car, or rewinding the universe, or whatever, at the end of that sequence, you will still hold on to the same door you initially picked that has 1/3 chance of hiding the car. And the door that you get the offer to switch to therefore has a 2/3 chance of hiding the car.

by baddox 7y ago

bonoboTP 7y ago

No need to talk about ignoring Universes or rewinding simulations, that just sounds confusing to most people. Enough to say that if Monty opens the winning door then he apologizes, closes it, and his helpers place the car to a new random place and they try again from the start. Or say, ignorant Monty may open the winning door accidentally, but here I have a stack of DVDs of all lucky episodes where Monty got a goat. When binge watching these videos, would you expect to see switchers win at a higher rate? Answer to both: it becomes 50-50 if Monty was ignorant, even if we post hoc filter out those cases where he got it right. Bonus philosophical question: you don't know whether Monty knew the car's location. He may say he does, or he may say he doesn't but you don't trust him. Or maybe he says "phew, how lucky to be a goat, I actually had a short amnesia an bluffed it". How can such a murky thing whether a human knows something or not impact the very, financially real world, even when all outward appearances are equal: I saw with my eyes that Monty opened a goat door with his hands. Yes it might have been an accident/luck but what is the precise definition of luck anyway? How can it have an influence whether his brain contained this information, given that he ended up opening this goat door anyway. How can counterfactual Universes influence ours? I have my own answers but it's an interesting thing to ponder.

baddox 7y ago
> No need to talk about ignoring Universes or rewinding simulations, that just sounds confusing to most people. It should sound confusing. People who justify their claim that switching doors doesn’t change your odds in this way are proposing a very bizarre and confusing revision of the problem. The original statement of the problem is a very straightforward description of a simple and realistic game show, that happens to have a solution that is counterintuitive to many people.
henrikschroder 7y ago
> Answer to both: it becomes 50-50 if Monty was ignorant, even if we post hoc filter out those cases where he got it right. It's not 50/50 because he is ignorant, it's 50/50 because you've discarded 1/3 of the outcomes, and all the outcomes you've discarded were ones where the contestant initially picked a goat.
- bonoboTP 7y ago
  That's true, but I discarded it based on what I think Monty knew and counterfactual reasoning. The question is why "knowledge" or "luck" or "just accidentally" have an effect on what I should discard. Another "more serious" related "paradox" is in scientific hypothesis testing. You can have different p values even if you observed the exact same experimental outcome but your stepping criterion was different. The only difference is the speculation of what you would have done if the experimental outcome had been different. [0] These things are quite unexpected unless you've already worked through such examples. [0] https://en.m.wikipedia.org/wiki/Likelihood_principle https://en.m.wikipedia.org/wiki/Likelihood_principle

henrikschroder 7y ago

It doesn't matter. If Monty knows what's behind the doors, we arrive at the scenario immediately where the door that's left has 2/3 chance of hiding the car, because the door you picked has 1/3 chance of hiding the car. If Monty doesn't know what's behind the doors, and goes into a cycle of opening doors and shuffling the prizes if it was the car, or rewinding the universe, or whatever, at the end of that sequence, you will still hold on to the same door you initially picked that has 1/3 chance of hiding the car. And the door that you get the offer to switch to therefore has a 2/3 chance of hiding the car.