Sorry, I haven't kept up with it - tracking 200 here, and then 200 in three other games that use a d20, was about the limit of my stamina for this.
What I tracked here was the raw die roll, whether it was advantage or not, whether it was a hit or a miss, the creature it was on, and their remaining hp.

I'd recently also done a test of 100 + 100 rolls relating to skill checks, which I haven't spoken about yet because I can't be sure that something else isn't going on;



I performed 100 rolls against the necromancy book from Thay.... as large a sample size as I could stomach at the time.
I then took 100 more rolls against the book, but with Mystra's Bless on the rolling character.

What we would expect to see, with a fair RNG, would be a more or less even distribution of rolls across the 1-20 spectrum, and both sets of rolls being more or less indistinguishable from one another. To be clear, the results show the raw die roll - Bless and Mystra's bless affect only the modifiers, and supposedly should influence your 'roll target' as the game currently displays it. It should not affect the raw displayed roll.

So, When I started this experiment, I felt strongly that the base die roll was biased towards lower rolls for players for important checks like this book. The results, however, seem to prove me wrong: the unaltered roll, with no buffs, actually showed a good, even distribution of rolls over the course of the sample size. It's about dead on where you'd expect it to level out, more or less.

However, it's worth noting that as a result, over the course of 50 attempts at the book, my character succeeded only 2 times in total (!). Despite a fair distribution, we didn't meet the expected average for what is pitched by the game (and its base DCs) as a moderate-to-challenging save. This is an issue with Larian's design philosophy for checks and saves right now, which could be the subject of another thread. In short though: This is a check that they mean you to fail. They couldn't set a DC high enough that was still attainable, but also gave the desired abysmal success average they wanted, and so built a successive check, for which any failure at any point was an absolute and total failure, ensuring that short of dedicated save-scumming almost no-one will ever succeed this save, and those who try will just be in the same boat as those who don't. It's bad design, it's not interesting and it's not fun. No-one likes the DM who just throws you save after save Until you fail one, then to gleefully jump back to the failure dialogue they had intended to give you from the very start... this is what Larian does, and on more than one occasion.

The oddity came up here for the second set, using Mystra's Bless: the results were Heavily skewed. Over the full 100 roll sample, 40% of the rolls were in the very top 15-20 bracket, eleven 17s, nine 15s, and above expected average turn ours for 16, 18 and 20 as well.

So what's going on here? It cannot be that it's adding the Mystra bless bonus to our raw die roll – we never rolled over 20, and we got an extreme outlier of eight 2s, which, if it were adding the bless to the raw die roll, wouldn't line up unless we rolled 8 natural 1s... which is a sticker, because my character is a halfling; they'd need to be double 1s (there's a lot of evidence to suggest that Lucky isn't working correctly, but in these tests I received no natural 1s, in 200 rolls, so I can only conclude that in this test at least it was working. I've receive 1s before with my halfling, even on advantage rolls (which would require a quadruple 1), so there's still indication that it's buggy in some fashion). The final results also indicate that the modifiers were affecting the roll target, not the raw roll, as they do elsewhere, so it wasn't as though they were missing from where we'd expect to see them.

What we seem to be seeing here is that the character with the more favourable condition is actually getting a favoured roll on top of their buffs – an unseen bias on the die. That's not cool. It could be a bug, or something not applying correctly, but right now it looks suspicious.

Suffice to say I'm just about out of die-recording stamina for the time being...