Three Curtains

Yes, the strategy followed by the host matters.In the standard problem it is assumed that the host ALWAYS reveals one of the prizes, and never reveals the car. In that case the solution is as has been stated.Observing the show is the only way to work out if there is a strategy, and what it might be.

For analysing the problem, I'd say that the more interesting questions are"is the car ever revealed?"and"what relationship, if any, is there between the choice to reveal and the contestant choosing correctly"If the presenter has a strategy, it can be exploited.

Curtains or doors, goats or nothing - those are details which don't change the mathematics of the problem, and looking at the general problem will help understand this one.If this is a one-time occurrence then we do need to know if the host is required to offer the choice to switch, and if not what criteria he uses to decide to offer the choice or not. Without that the problem is not solvable.

Then the question is unanswerable. Switching could be advantageous, it could be disadvantageous, There is no way to tell.

I was speaking loosely, but this is a rather different game. Switching has to be better or worse or the same as not switching. If it's the same (worst case for the contestant) then it's still a 50-50 guess. And even that's better than the 1/3 odds before revealing.

That's just another variation that makes no difference.

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Actually depending on the strategy in play, switching can be worse than 50/50 for the contestant.

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That's what I said. And that is why I've been saying that you need to know the strategy.Simply by choosing when to offer the chance to switch the host can trivially guarantee that a switch will always win or always lose.

Oh dear. The point is that offering the chance to choose the other two is no different from revealing one of the other two as losing and offering the chance to switch to the remaining one. So it doesn't change the analysis at all.

No, it depends on the host's strategy as I keep telling you.