How Should We Handle Variants of the Monty Hall Problem?

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SUMMARY

The discussion centers on variants of the Monty Hall problem, specifically scenarios where Monty may or may not open a door after a contestant makes a selection. Key questions include how to strategize if Monty wants the contestant to find the car, if he does not, or if his intentions are unclear. Participants emphasize the ambiguity of Monty's actions and the implications for decision-making in these variants. The conversation highlights the need for a clear understanding of Monty's role in the game to determine optimal strategies.

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I have a couple of variants of the http://en.wikipedia.org/wiki/Monty_Hall_problem" that I have a hard time to figure out how to handle.

What if Monty doesn't have to open the door. All we know is that he is smart. How should we then behave if
1) he wants us to find the car?
2) he does not want us to find the car?
3) we don't know if he wants us to find the car or not, or maybe he doesn't have any intentions?

Do you have any ideas?
 
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If he doesn't open a door after you made your selection, then it may not matter. Are you assuming he opens a door sometimes? Your question is vague.
 

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