The problem here is that the usual explanation sneaks in multiple rarely stated assumptions.
If Monty knows the door with the prize and is aiming for the game to continue, then you should switch. (This is the usual argument.)
If Monty doesn't know where the prize is, then you learned nothing. (Monty's result was luck, and he can't impart information that he doesn't have.)
If Monty knows where the prize is and wants you to lose, absolutely don't switch. (Monty will only drag the game out as a way to try to make you lose.)
The reasoning behind these statements is completely solid, and there are no hidden assumptions being snuck in.
I think, canonically, Monty always knows where the prize is, and will always eliminate all doors except for one, and will never eliminate a door with the prize, and will always give you a choice to switch. There's no room for Monty's motivation.
the assumption is told to you in that the game is expected to continue after monty opens a door. if he could open the prize door, the game would describe what happens when he does that
No. That condition holds in all three of the scenarios that I stated. And yet you have 3 different answers. Switching 2/3 win, 1/2 win, and 0/1 win respectively.
You specifically need information that we haven't been given about the counterfactuals. What might Monty have done in other scenarios that we have not yet observed? We don't know. And we're not actually told. That makes that an implicit assumption that wasn't specified.
They're not. It says he "opens another door, say No. 3, which has a goat". That could mean he deliberately chose a door with a goat or he chose one by some unstated process and it happened to have a goat by chance. It says he "knows what's behind the doors" but that statement means nothing because it doesn't say how he uses that knowledge, if at all. It's full of language ambiguity.
If Monty knows the door with the prize and is aiming for the game to continue, then you should switch. (This is the usual argument.)
If Monty doesn't know where the prize is, then you learned nothing. (Monty's result was luck, and he can't impart information that he doesn't have.)
If Monty knows where the prize is and wants you to lose, absolutely don't switch. (Monty will only drag the game out as a way to try to make you lose.)
The reasoning behind these statements is completely solid, and there are no hidden assumptions being snuck in.