How Should We Handle Variants of the Monty Hall Problem?

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The discussion revolves around variants of the Monty Hall problem, particularly focusing on scenarios where Monty's intentions are unclear. Participants question how to approach the problem if Monty is smart but does not necessarily open a door after a selection is made. Key points include the implications of Monty's potential intentions—whether he wants the contestant to find the car or not—and the uncertainty of his actions. The conversation highlights the need for clarity in the problem's setup to determine the best strategy. Overall, the ambiguity surrounding Monty's behavior complicates the decision-making process for contestants.
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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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