There is a genuine human language problem here, NOT A MATH PROBLEM, which accounts for two differing but self-consistent views. It is a legitimate difference in

There is a genuine human language problem here, NOT A MATH PROBLEM, which accounts for two differing but self-consistent views. It is a legitimate difference in views because human language is genuinely ambiguous. "You pick a door, the host opens another door and reveals a goat. Should you switch?" Does this mean you are in one particular situation where the host opened a 2nd door, with a goat? Or does it mean the host always opens a 2nd door with a goat? If the host always opens a 2nd door, showing a goat, you should switch to the third unopened door. If all you know, is this time you picked a door, then the host revealed a goat, you don't know what to do. Maybe this host only opens goat doors after you pick the right door, in order to trick you into switching? In that case switching would be the worst thing you could do. A host with that strategy is a special case, but special cases where a potential general solution (always switch) doesn't work, are all you need to disprove the general solution. It cannot be a general solution if their is even one special case it doesn't work. Most people interpret the problem to mean the host always reveals goats. But if the language isn't clear on that, then you do have a different problem, whose solution is really impossible to optimize for without some more information on general host behavior or strategies. Without that information, all you can do is flip a coin. Or always stay, or always switch. You have no means to improve your odds whatever you do.