Your logic is correct but you are a making a different assumption, that Monty treats each door symmetrically. For example let's say Monty's strategy is to alway

Your logic is correct but you are a making a different assumption, that Monty treats each door symmetrically. For example let's say Monty's strategy is to always open door #3 if he has a choice. Then if your choice is to switch to door #3 or to stay, you should choose "stay".