What you're missing here is that you already have enough intuition to translate it into a more obvious statistical problem, but most people come across this as

What you're missing here is that you already have enough intuition to translate it into a more obvious statistical problem, but most people come across this as blank slates, and under very different framing. Even when relayed the right way and the wording isn't necessarily unclear or misleading per se, it is still framed in a particular way and context that pushes you to believe your choice is inconsequential, less about probability and math, and more for psychological games and dramatic effect in the context of a TV show. In your example, the fact that the presenter opens all 98 doors and not just one is telling. If they only opened 1, and then told you to stick to your original or open one of the remaining 98 doors, that he picks for you, would you change? This is what you're missing, I think. Most people don't even get to the point where they reframe the "would you change" question to "what are the chances my original choice was correct vs not". Most people get stuck on "He knows something; he clearly demonstrated very theatrically that he knew the car wouldn't be behind door No.2. And now he's asking me to swap my choice for door No.67. Why 67? Is he trying to trick me? Is this a psychological trick to get me to forfeit my door, which may be the right one? Should I trust him? After all, HOW IS MY DOOR ANY DIFFERENT THAN ALL THE OTHERS?" (the fallacious thinking, obviously, lying in the last part here)