[taeric]

Thought even more on this. Did not get a chance to run a simulation, but thought of it while driving around.

It finally jives with me that your odds at swap time are only 50%. Seems kind of obvious when you think of it as random events and you are at the end with it definitely behind one of two doors. Either door is clearly as likely. Now, your odds of getting to this point are vanishingly slim, the more doors there are. Which makes sense.

I think my intuitive block comes in in that your odds of winning the game are not increased in this scenario at all. Which, I knew. I think I even stated it at some point. Still a hard block to get around.