Thanks all for these interesting analyses!
In conclusion, having Advantage almost perfectly counteracts the effects of Karmic Dice, except you get less crits.
For all other distributions, Karmic Dice seems to raise the average roll by 2, making it less likely that you'll roll numbers below ~9.
I’ve got a bit confused in amongst all the data whether this is the case for our party, enemies or both?
And whatever the answer, I guess the next question is whether this is what it is
supposed to do? Do we actually know for sure?
I think I recall in a PfH Larian said they introduced it partly in the hope that players who reloaded on failed checks might be able to use it to reduce save scumming, and I think someone else mentioned it was partly in response to players complaining they missed too frequently. I guess increasing the average roll for PCs and allies would be one way of addressing that, though not necessarily the best. And I guess extending the same advantage to enemies would be karmic, if that’s what is happening!
Good question. The data from @Hrungr is the AI rolling against the player. I'm not sure what rolls @DragonSnooz recorded..?? I assume you just recorded all rolls, player or AI? If so, then the fact that DragonSnooz's rolls matched Hrungr's means that it seems to work the same for AI or player.
I don't think Karmic dice is supposed to affect crits in this way. As I understand it, it originally was supposed to remove streaks, as players were unhappy at getting too many low rolls in a row (to be fair, Larian's original Patch 1-4 RNG system was actually bad). And then Larian changed it so that it would only act in the roller's favor (changing low rolls to high, but not vice versa). However, I couldn't figure out a simple way of creating a Karmic Dice distribution that actually matched the data...it certainly doesn't do any thing as simple as "if the previous roll was a 1-10, reroll and take the new result."
The frequency of Karmic Dice rolls is:
1 0.0448
2 0.0292
3 0.0292
4 0.0375
5 0.0260
6 0.0333
7 0.0333
8 0.0333
9 0.0396
10 0.0573
11 0.0469
12 0.0469
13 0.0615
14 0.0500
15 0.0625
16 0.0583
17 0.0625
18 0.0729
19 0.0781
20 0.0969
Higher numbers are progressively more and more likely, except it's not a
constant increase. There are jumps and , which may just be due to inherent randomness, or may be due to the actual code Larian is using. But it kind of looks like rolls from 2-8 have ~equal chances. And of course, the ~5% occurrence of natural 1s is an outlier.
