This is at the heart of why so many people find this unintuitive. People who know the right answer are assuming that this is a repeated game, where every time M

This is at the heart of why so many people find this unintuitive. People who know the right answer are assuming that this is a repeated game, where every time Monty Hall does the same thing. Every instance given in the linked article includes the assumption that you will always have a choice. If you encounter this situation, how can you possibly know whether you would be offered the choice had you picked the wrong one?