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It's better to switch doors according to any statistical method, whether you're a frequentist or Bayesian does not matter. You can also show that you should switch doors by making an exhaustive truth table, by writing a computer program, or by experimentation, if you prefer these kind of approaches.

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A truth table doesn't necessarily get you to the right answer. There are 3 doors I could pick, 3 doors Monty could pick, and 3 doors the prize could be behind. If I make a truth table of all 27 possible combinations, there are 12 combinations where Monty doesn't choose the same door as the contestant or the prize. Of these 12 options, exactly 6 have the contestant choosing the right door and 6 have the contestant choosing the wrong door.

You can certainly create a different truth table that arrives at the correct answer, but the truth table approach does not help ensure you get to the right answer like the Bayesian approach does.

No method on earth necessarily gives you the right answer to a problem. You first have to represent the problem correctly, of course.

Check out Scenario 2 here https://medium.com/@ProfessorF/visualizing-the-solution-to-t... for a correct tree.

Neither method guarantees the right answer, but it's a lot easier to get it wrong with a truth table.

Maybe you're right, I'm not fully convinced.

I mentioned a full truth table/decision tree because a long time ago these gave me the insight why switching is the right solution in the standard formulation of the problem, and they also illustrate why the problem is a purely deductive/logical problem whose solution does not require any inductive inference.

Then, to me it was a valuable lesson to learn that the Monty Hall problem does not reveal any perceived or real fundamental problem of probability theory.

I made this very same point ;) they burned me at the stake.

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