Also, my analysis of these-plus-other rolls is that
Karmic Dice works similarly to Advantage (unless you roll a natural 1, in which case that result stands). Effectively, the Karmic Dice system gives you an X% chance to reroll if you miss attack, which obviously happens more often against higher AC creatures.
This is supported by the detail that, when using Karmic Dice while making attacks at Advantage, it doesn't give any significant benefit.
960 Normal Karmic Attack Rolls
Is inconsistent with a uniform distribution, showing too many 18s, 19s, and 20s, and too few 2s through 9s.
Average of 12.34 +/- 0.19, compared with an expected average of 10.5
224 Advantage Karmic Attack Rolls
Is overall statistically consistent with an Advantage distribution. However, there are 35% too few 20s, at 2.3-sigma.
Average of 13.96 +/- 0.28, compared with an expected average of 13.82.
224 Disadvantage Karmic Attack Rolls
Is statistically inconsistent with a Disadvantage distribution, with too few 1s through 4s.
Average of 9.45 +/- 0.37, compared with an expected average of 7.17.
With Karmic Dice, higher numbers are progressively more and more likely and on average results in a +2 bonus to your roll.
Having Advantage almost perfectly counteracts the effects of Karmic Dice, except you get less crits.
