I went 4 generations in a row with all 3 children I could select from having the exact same trait. How is it generating these traits? Are they totally random? It seems statistically improbable unless it is "inheriting" these? I'm wondering if anyone knows how this is done as far as this game is concerned. Thanks!

You can find a lot of useful information here

But I must admit that your situation sounds really strange and improbable. A wild guess: perhaps you have some software that suffers from memory leak problem. For example I have one dictionary that is just terrible in that respect (I like it because it contains a lot of words, including slangs and informal language but it was coded poorly). 70% of games won't even start when this dictionary is running, others can be played but with a number of issues. For example:
- Warlords Battlecry 2 - healing spells don't work
- FTL: sectors layouts are not randomized (I mean positions of bacons are always the same, what you can find there is, however, random)
On top of that most of those games crashes a lot.

So yes, it's possible that you have the same situation.