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Can you elaborate on why you feel this proves that the host's knowledge is important in deciding on whether to switch after a goat is revealed from one of the t

Can you elaborate on why you feel this proves that the host's knowledge is important in deciding on whether to switch after a goat is revealed from one of the two doors you haven't chosen? As far as I'm aware (but it's been a while), the host's knowledge is only important up to the point where the first door to be revealed contains a goat. All scenarios where the host reveals a prize on the first door to be opened are discarded for the sake of the problem statement (when dealing with the host being ignorant).

colinmhayes 4y ago
So if the host can reveal a prized door your odds are 1/3 prize, 1/3 goat, 1/3 redo. So each door has a 50% chance of having the prize after Monty reveals a goat door. Basically the game is just reduced to having 2 doors instead of your choice vs. all other doors.
- deleted 4y ago
  [deleted]
jdminhbg 4y ago
Sure. This simulation shows the scenario OP described in his misunderstanding of the MHP, which is that he didn't realize the host was picking with foreknowledge of which doors were which. So if the host doesn't know that and is himself simply picking a random door (and 1/3 of the time, revealing the prize), then switching does not improve your odds.
- ALittleLight 4y ago
  Foreknowledge has absolutely no effect. Again, go back to the problem I posed where Monty reveals a random door and has revealed a goat. Should you switch or not? The correct answer is that you should. Monty's knowledge has no effect on the problem or the player's choices. What has an effect is the information the player learns from seeing the revealed door. If the player sees a goat behind the revealed door - that is the relevant information. Whether Monty was surprised or not by the revealed goat is irrelevant.
  - jdminhbg 4y ago
    This is just asserting the same thing over and over again. You can go upthread to the simulation to see that when you are in the "Monty showed you a goat" scenario, the results for staying and switching are equal. If you rewrite the simulation such that Monty always shows you a goat and look at the scenarios where "Monty showed you a goat" (i.e., all of them), you will see that switching wins.
    - ALittleLight 4y ago
      I'm not familiar with Clojure, so I can't point out the error in your simulation, but there undoubtedly is one. Here is a simulation in javascript that supports my point - https://pastebin.com/y5G4PE75 https://pastebin.com/y5G4PE75 And yes, your simulation should include that Monty always shows a goat. That is given in the problem statement.
      - jdminhbg 4y ago
        > And yes, your simulation should include that Monty always shows a goat. I feel like I've said this thirty times now, I'm specifically discussing a misinterpretation of the problem where Monty does not know what he's opening, so he sometimes opens a prize door. A game where Monty always opens a goat door is the original, correct Monty Hall Problem, and switching is the correct strategy.
        ALittleLight 4y ago
        The parent comment that starts this thread[1] is antris writing "The fact that the show host knows what's behind the doors and never chooses a door with the prize behind it is crucial." (Emphasis added). Then, I reply[2], saying "I don't think the host's knowledge is important." I include an example where the host has no knowledge, but has coincidentally revealed a goat, and the best strategy remains switching. In other words, antris says the host's knowledge is crucial and I'm saying the host's knowledge is irrelevant, what matters is what was revealed. If you are talking about some other scenario - then why? I've just explained what this thread is about. Why would you invent an alternate scenario, not tell anyone about your alternate scenario, and argue that correct interpretations of the scenario I laid out in [2] are wrong because they don't fit with your interpretation of your private variation? 1 - https://news.ycombinator.com/item?id=31684653 https://news.ycombinator.com/item?id=31684653 2 - https://news.ycombinator.com/item?id=31683850#31684801 https://news.ycombinator.com/item?id=31683850#31684801

colinmhayes 4y ago

So if the host can reveal a prized door your odds are 1/3 prize, 1/3 goat, 1/3 redo. So each door has a 50% chance of having the prize after Monty reveals a goat door. Basically the game is just reduced to having 2 doors instead of your choice vs. all other doors.

deleted 4y ago
[deleted]

jdminhbg 4y ago

Sure. This simulation shows the scenario OP described in his misunderstanding of the MHP, which is that he didn't realize the host was picking with foreknowledge of which doors were which. So if the host doesn't know that and is himself simply picking a random door (and 1/3 of the time, revealing the prize), then switching does not improve your odds.

ALittleLight 4y ago
Foreknowledge has absolutely no effect. Again, go back to the problem I posed where Monty reveals a random door and has revealed a goat. Should you switch or not? The correct answer is that you should. Monty's knowledge has no effect on the problem or the player's choices. What has an effect is the information the player learns from seeing the revealed door. If the player sees a goat behind the revealed door - that is the relevant information. Whether Monty was surprised or not by the revealed goat is irrelevant.
- jdminhbg 4y ago
  This is just asserting the same thing over and over again. You can go upthread to the simulation to see that when you are in the "Monty showed you a goat" scenario, the results for staying and switching are equal. If you rewrite the simulation such that Monty always shows you a goat and look at the scenarios where "Monty showed you a goat" (i.e., all of them), you will see that switching wins.
  - ALittleLight 4y ago
    I'm not familiar with Clojure, so I can't point out the error in your simulation, but there undoubtedly is one. Here is a simulation in javascript that supports my point - https://pastebin.com/y5G4PE75 https://pastebin.com/y5G4PE75 And yes, your simulation should include that Monty always shows a goat. That is given in the problem statement.
    - jdminhbg 4y ago
      > And yes, your simulation should include that Monty always shows a goat. I feel like I've said this thirty times now, I'm specifically discussing a misinterpretation of the problem where Monty does not know what he's opening, so he sometimes opens a prize door. A game where Monty always opens a goat door is the original, correct Monty Hall Problem, and switching is the correct strategy.
      - ALittleLight 4y ago
        The parent comment that starts this thread[1] is antris writing "The fact that the show host knows what's behind the doors and never chooses a door with the prize behind it is crucial." (Emphasis added). Then, I reply[2], saying "I don't think the host's knowledge is important." I include an example where the host has no knowledge, but has coincidentally revealed a goat, and the best strategy remains switching. In other words, antris says the host's knowledge is crucial and I'm saying the host's knowledge is irrelevant, what matters is what was revealed. If you are talking about some other scenario - then why? I've just explained what this thread is about. Why would you invent an alternate scenario, not tell anyone about your alternate scenario, and argue that correct interpretations of the scenario I laid out in [2] are wrong because they don't fit with your interpretation of your private variation? 1 - https://news.ycombinator.com/item?id=31684653 https://news.ycombinator.com/item?id=31684653 2 - https://news.ycombinator.com/item?id=31683850#31684801 https://news.ycombinator.com/item?id=31683850#31684801