For the 3 case, since 2/3 is relatively close to 1/2, it's hard to build intuition from just a few examples.

The N=100 build intuition very quickly. I disagree that it doesn't explain anything. After playing, people quickly understand that the likelihood that they chose the correct door initially is very small and when all 98 other doors are revealed, the remaining door provides a red flag that their intuition is off.

Note that often I would explain the logic behind switching and still have them not believe me. Their intuition wouldn't be shaken by arguments or even small demonstration. Only when actually playing an the N=100 case would they start to understand.