[Ygorl]

It's a hair less than 1/4 (it's 15/64 to get at least N1).
Pretty sure these "patterns" are just our human tendency to find order even when there isn't any. I remember some people did some experiments a while back and it is actually random (as you'd expect - it would be harder to program them to be semi-random, it's not something you'd do accidentally)

If you've got 30 Smiths and you're looking for nature, the chance of finding 0 with nature is about 2%. Unlikely, sure, but nowhere close to impossible. Given the number of statistics just like that one that you can come up with (number of nature sites found, number of nature-gem events, number of...) it's likely that some of them will work out in an unlikely way.

If there are 50 different weird crappy unusual things that one might notice in a particular game (if they did by some freak chance happen), and each only has a 2% chance of happening, there would still be about a 2/3 chance that at least one of them would happen. Then the tendency would be to think "But... That's so unlikely to happen! There must be something funny in the way the game does this..." Then, next game, you'd be wondering why you didn't get any national heroes until turn 80... Then the next game, you'd be wondering why you had five barbarian attacks in the first ten turns... Then the next game you'd be wondering why you couldn't get a single frickin' sage with blood... There are just so many things that can happen in this game that some of them are bound to turn out weird.