So, thinking about it really hard and reading about it online:
My comment was definitely wrong: If Monty could have opened a car door, but just didn't, then duh the probabilities for the car to be behind the doors are different than if Monty always opens a goat door. So in that way, the intentions of Monty, meaning how he chooses, definitely matter.
But I think your example here doesn't show that? Are you trying to illustrate the Monty Fall variation?
Sorry it took me so long to get back to this; real life intervenes sometimes.
I think what I was trying to do was frame the original Monty Hall problem as a variant of Monty Fall, in a way that (I hoped) makes it clear where Monty is doing work to convert some outcomes into other outcomes (and therefore producing different likelihoods).
My comment was definitely wrong: If Monty could have opened a car door, but just didn't, then duh the probabilities for the car to be behind the doors are different than if Monty always opens a goat door. So in that way, the intentions of Monty, meaning how he chooses, definitely matter.
But I think your example here doesn't show that? Are you trying to illustrate the Monty Fall variation?