I wanted to test the RNG to see if it was as wonky as I thought and it turns out... not so much. At the link below, you can see the numbers I rolled in the order I rolled them.https://docs.google.com/spreadsheets/d/1-iI05GHtKHhccnT8bQZPen-S-VoaaPABUrRXNq24K2U/edit?usp=sharing
As a test, I used an interaction where I had both the option to Intimidate and use Persuasion. I didn't care about target number, what my stat added or subtracted, etc. I just cared about the number it ended up on.
I also didn't want to do this in combat because a) there are modifiers such as high/low ground, lighting, etc. that I have no control over and b) I can't see the actual dice roll it's making. By using a skill check, I can see the die itself and did the following.
If I passed on my first Intimidate, I'd reload.
If I failed on my first Intimidate, I'd use the re-roll option.
If I passed on my second Intimidate, I'd reload.
If I failed on my second Intimidate, I'd try Persuade.
Whether or not I passed or failed Persuasion, I'd reload.
I did this until I had 100 rolls total.
I rolled the following totals:
20s - 5
19s - 7
18s - 7
17s - 3
16s - 4
15s - 4
14s - 4
13s - 5
12s - 7
11s - 4
10s - 7
9s - 2
8s - 4
7s - 1
6s - 7
5s - 6
4s - 4
3s - 6
2s - 6
1s - 7
That's a pretty even spread. Not perfect, especially for a computer program, but about what I'd expect to roll at the table.
Also, the average roll for a d20 is 10.5. For this spread, the average was 10.35. Again, not perfect but pretty darned close.
Overall, I've got to say I'm surprised by this. I was convinced the game was rolling low or high too often and wasn't truly random. And while it still may, for my taste, the fact that the overall average is pretty much spot-on, it's taught me to just take my lumps and move on.
Oh and feel free to pick apart this highly unscientific test.