I think that's probably true for you and it's definitely true for some, but I've tutored many students in both algebra and discrete and am very familiar with th

I think that's probably true for you and it's definitely true for some, but I've tutored many students in both algebra and discrete and am very familiar with the failure modes of students' thinking. The "Door 53" example makes it very easy for people to understand that in the case of 100 doors they should switch. It doesn't, however, always get them to see that the issue is fundamentally choosing between odds of 1:X and (X-1):X (or even that they should also switch with only three doors).