Thanks for remining me about your data @Niara. Adding it to the unweighted sample, the data looks decently more uniform, but still statically inconsistent with a uniform distribution.
n=508
average=11.16 (The expected standard deviation of a n=508 sample is 0.256, putting our average 2.6-sigma off from the expected average of 10.5)
chi^2=30.89 (still greater than the critical value of 30.1, but significantly less so than the n=308 data)
Biggest Offenders
--1 appears 60% as often as it should, a 2.1-sigma difference from expectation
--6 appears 70% as often as it should, a 1.5-sigma difference
--17 appears 1.77x more often than it should, a 3.9-sigma difference
This goes to show the importance of sample size. Going from n=308 -> n=508:
-the data went from 99% confidence of inconsistency with uniform (chi^2=36.15) to 95% confidence (chi^2=30.89)
-the average went from 11.5 (3-sigma off from 10.5) to 11.16 (2.6-sigma off).
-all the offenders were less offensive
I will probably continue this analysis if I get more data, so if anyone has robust* die rolls from patch 4 or earlier, weighted or unweighted, please give them to me. 1I'd like to get 1000 rolls.
*Robust meaning following as many as possible of: recording all rolls, without reloading the game in between each roll, without advantage or disadvantage, not a halfling, etc.
**Extra points if you record the order of the rolls, like @Niara
***If you see an error with my stats, please let me know. I'm like 80% confident I'm doing things correctly.
