I think the 100 door example is good, but is often not described in a way that was intuitive to me. I've added bit that I found very helpful. The entire trick

I think the 100 door example is good, but is often not described in a way that was intuitive to me. I've added bit that I found very helpful. The entire trick of the game is that Monty opens 1 (or 98) of the remaining doors. That is because it is completely irrelevant to the odds, but has big impact on the contestants perception. It is not obvious, but Monty actually does two separate and unrelated things: First, a step that basically goes unnoticed, is to propose a new game to the contestant in which the contestant opens either 1 door or 2 (99) doors chosen by Monty, rather than the original game which was to select 1 door out of 3 (100). Obviously, the new game gives them the chance to make a choice that has 2/3 odds (99/100) versus the original game whose odds were 1/3 (1/100). His second step, which is typically the only step noticed and which very effectively misleads the contestant, is to open 1 (98) of the doors he selected. The result is that clearly the 2nd game gives the contestant a definitively better choice, but this is obscured by the fact the contestant only sees two closed doors, so they believe they are comparing 1 door to another, and thus only have 50-50 odds.