So this is at least in part about the "Monty Hall Problem" and why it's solution not intuitive. The article missed an important angle: when the host opens a door, he's giving you more information, which explains why it's better to switch. If you're the host, you need to know which door the car is behind to do your job 2/3 of the time, to avoid revealing it.
It's this quality of unexpected information exchange that I find most fascinating about this particular puzzle!
It's this quality of unexpected information exchange that I find most fascinating about this particular puzzle!