The problem with the 100 heads in a row analogy it muddies the water becauase people are focused on the fact tht it is the same result 100 times in a row. You have to add that the odds are the same for any described 100 result sequence. The odds of 100 heads in a row is just the same as getting a head then a tail then a head then a tail etc.. over a hundred flips.
If you ask that question to the average person and most will say the odds of the latter are more likely when they aren't.
You will also get clustering and clumping of numbers since random probability is not a uniform occurence.
I work in an industry that is ruled by probability (the slot machine industry)
The most interesting probability riddle to me is the one about how likely is it that 2 people share the same birthday in a room of 50 people.
Edit: I should add I am not a mathematician. I suck at math horribly. I just invent stuff.