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The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows wh

The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. Imagine a universe with many simultaneous Monty Hall clones playing at once in many studios, where Monty doesn't know and opens another door at random. If that door has the car behind it, Monty and contestant are both shot in the head and the studio burned down and erased from all records. This bloody culling of branches of the probabilities is the same as effected by giving Monty the knowledge and telling him to act on it.

GloucesterBoy 4y ago
wow... what a grim approach!
- pfdietz 4y ago
  That Escalated Quickly would be a great name for a game show.
- adhesive_wombat 4y ago
  Next on 4: Brian Cox presents Quantum Squid Game, in partnership with Academi.
TarasBob 4y ago
In the scenario where they are shot that you described, it is still better to switch!
- masklinn 4y ago
  You can’t switch if your universe has been pruned Morty.
darkerside 4y ago
This explained it better to me than the article
Linosaurus 4y ago
> If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. And perhaps also, “remember: Monty will always open a door, and the contestant knows it”. Makes me wonder if there were similar shows where the host can choose not to open a door.
- adhesive_wombat 4y ago
  That presumably quickly gets into a game-theoretic double-triple-etc-bluff affair where you have to assume the host is using his knowledge against you. If you choose the door with the car, the host will open another door to tempt you, so then you don't switch, unlike in traditional Monty Hall. And if he didn't open a door, well, that means you choose a goat, so you should switch for a 50% chance. Except the host knows you're thinking this. And you know he knows. And he knows you know he knows. And... Perhaps, iterated infinitely, this eventually resolves into a limiting expected value for switching and not, but I have no idea how to compute such a scenario.
  - em500 4y ago
    See: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...
- em500 4y ago
  The puzzle is is commonly stated is not how any TV show ever worked. In a real (repeated) TV show the host behavior will be non-deterministic, and will sometimes be benign, sometimes adverse, to increase the suspense and ratings. If the host follows a deterministic set of rules (as is usually implicitly assumed in the puzzle version), the optimal strategy is pretty easy to work out.
  - mcphage 4y ago
    > If the host follows a deterministic set of rules (as is usually implicitly assumed in the puzzle version), the optimal strategy is pretty easy to work out. And yet it is the subject of endless discussions. The optimum strategy is pretty easy to work out, yet not widely believed.
Metus 4y ago
> The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. The associated line of reasoning resolved the paradox for me. If I stick with my original choice, it is as if I ignored the new information. If I switch the choice, I react to the new information. The extreme of this is to pick among countably infinite doors, having the presenter open countably infinite doors and leaving just yours and another closed. Who could reasonable suggest that the chance is still 50/50, assuming you don't flip a coin and base your choice on that?
- Jensson 4y ago
  > If I switch the choice, I react to the new information This assumes that him opening a door is new information. It isn't unless you make an assumption about the game masters intentions. If the host doesn't want you to win then you will lose 100% of the time if you switch, if the host wants you to win then you could win 100% of the time by switching etc. But people think that these assumptions are "obvious" so of course you must make them, but that makes the riddle bad. If the riddle doesn't say that the host always opens an empty door after you pick a door, then the typical solution isn't correct. People does the typical "X happened once" and assumes it means "X always happens", that is a typical naive assumption but no, just because it happened once doesn't mean it always happens, you can't make that assumption here unless stated in the riddle.
  - basch 4y ago
    >if the host wants you to win then you could win 100% of the time by switching etc. 66% of the time. 33% of the time you picked right first time and lost it by switching. The host never conveys "dont switch."
mountainlks 4y ago
The problem I always struggle with is the premise that presenter not only knows which box is the prize, but also does not want you to win. In other words, there should never be a scenario where the show host gives you an opportunity to switch boxes unless you have already chosen the prize box, in which your choice should be to not change boxes. I guess I just naturally assumed that game shows don't want contestants to win and the odds are against you.
- mcphage 4y ago
  > there should never be a scenario where the show host gives you an opportunity to switch boxes unless you have already chosen the prize box The host always gives you an opportunity to switch boxes.
  - Jensson 4y ago
    That is an assumption though, the problem usually doesn't say that.
    - mcphage 4y ago
      What would the problem even be asking if you don't get that choice? The problem (as given) requires you to make a choice about keeping or switching—if the host doesn't offer you that option, then what is the problem even about?
igetspam 4y ago
I'm giving you an up vote for creative writing and nothing else. I'm not claiming anything about your data, just your creative writing skills. Thank you.
pjdemers 4y ago
I agree that this additional information is necessary to understand the problem. I've seen that show maybe twice in my lifetime, both times when I was a little kid. I did not know that Monty never opens the door with the prize behind it. Not one time in the history of the show did he ever open the prize door. Knowing that is additional information, and can be used to figure out the problem. But you need to watch the show more than twice to know that.

GloucesterBoy 4y ago

wow... what a grim approach!

pfdietz 4y ago
That Escalated Quickly would be a great name for a game show.
adhesive_wombat 4y ago
Next on 4: Brian Cox presents Quantum Squid Game, in partnership with Academi.

TarasBob 4y ago

In the scenario where they are shot that you described, it is still better to switch!

masklinn 4y ago
You can’t switch if your universe has been pruned Morty.

darkerside 4y ago

This explained it better to me than the article

Linosaurus 4y ago

> If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. And perhaps also, “remember: Monty will always open a door, and the contestant knows it”. Makes me wonder if there were similar shows where the host can choose not to open a door.

adhesive_wombat 4y ago
That presumably quickly gets into a game-theoretic double-triple-etc-bluff affair where you have to assume the host is using his knowledge against you. If you choose the door with the car, the host will open another door to tempt you, so then you don't switch, unlike in traditional Monty Hall. And if he didn't open a door, well, that means you choose a goat, so you should switch for a 50% chance. Except the host knows you're thinking this. And you know he knows. And he knows you know he knows. And... Perhaps, iterated infinitely, this eventually resolves into a limiting expected value for switching and not, but I have no idea how to compute such a scenario.
- em500 4y ago
  See: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...
em500 4y ago
The puzzle is is commonly stated is not how any TV show ever worked. In a real (repeated) TV show the host behavior will be non-deterministic, and will sometimes be benign, sometimes adverse, to increase the suspense and ratings. If the host follows a deterministic set of rules (as is usually implicitly assumed in the puzzle version), the optimal strategy is pretty easy to work out.
- mcphage 4y ago
  > If the host follows a deterministic set of rules (as is usually implicitly assumed in the puzzle version), the optimal strategy is pretty easy to work out. And yet it is the subject of endless discussions. The optimum strategy is pretty easy to work out, yet not widely believed.

Metus 4y ago

> The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. The associated line of reasoning resolved the paradox for me. If I stick with my original choice, it is as if I ignored the new information. If I switch the choice, I react to the new information. The extreme of this is to pick among countably infinite doors, having the presenter open countably infinite doors and leaving just yours and another closed. Who could reasonable suggest that the chance is still 50/50, assuming you don't flip a coin and base your choice on that?

Jensson 4y ago
> If I switch the choice, I react to the new information This assumes that him opening a door is new information. It isn't unless you make an assumption about the game masters intentions. If the host doesn't want you to win then you will lose 100% of the time if you switch, if the host wants you to win then you could win 100% of the time by switching etc. But people think that these assumptions are "obvious" so of course you must make them, but that makes the riddle bad. If the riddle doesn't say that the host always opens an empty door after you pick a door, then the typical solution isn't correct. People does the typical "X happened once" and assumes it means "X always happens", that is a typical naive assumption but no, just because it happened once doesn't mean it always happens, you can't make that assumption here unless stated in the riddle.
- basch 4y ago
  >if the host wants you to win then you could win 100% of the time by switching etc. 66% of the time. 33% of the time you picked right first time and lost it by switching. The host never conveys "dont switch."

mountainlks 4y ago

The problem I always struggle with is the premise that presenter not only knows which box is the prize, but also does not want you to win. In other words, there should never be a scenario where the show host gives you an opportunity to switch boxes unless you have already chosen the prize box, in which your choice should be to not change boxes. I guess I just naturally assumed that game shows don't want contestants to win and the odds are against you.

mcphage 4y ago
> there should never be a scenario where the show host gives you an opportunity to switch boxes unless you have already chosen the prize box The host always gives you an opportunity to switch boxes.
- Jensson 4y ago
  That is an assumption though, the problem usually doesn't say that.
  - mcphage 4y ago
    What would the problem even be asking if you don't get that choice? The problem (as given) requires you to make a choice about keeping or switching—if the host doesn't offer you that option, then what is the problem even about?

igetspam 4y ago

I'm giving you an up vote for creative writing and nothing else. I'm not claiming anything about your data, just your creative writing skills. Thank you.

pjdemers 4y ago

I agree that this additional information is necessary to understand the problem. I've seen that show maybe twice in my lifetime, both times when I was a little kid. I did not know that Monty never opens the door with the prize behind it. Not one time in the history of the show did he ever open the prize door. Knowing that is additional information, and can be used to figure out the problem. But you need to watch the show more than twice to know that.