On first pass, Benford’s Law looks a lot like Zipf’s Law.
What differentiates Benford’s Law from Zipf’s Law?
> It has been argued that Benford's law is a special bounded case of Zipf's law,[22] with the connection between these two laws being explained by their both originating from scale invariant functional relations from statistical physics and critical phenomena.[24] The ratios of probabilities in Benford's law are not constant. The leading digits of data satisfying Zipf's law with s = 1 satisfy Benford's law.
I’ll take some time to try and better understand your post.
(Since we can reasonably assume that randomNumber is a binary number, and thus would be balanced over 8 values instead of 6.)
[0] https://en.wikipedia.org/wiki/Linear_congruential_generator#...
2. The dice roll example is not uniform distribution, I think this is a common pitfall when generating random integers of a range. `randomNumber % 6` results in a slight bias towards 0 and 1, since 2^31 % 6 == 2, there are more numbers in the range [0, 2^31-1] that map to 0 and 1 than those that map to 2...5. To make it uniform, for example, you should always discard if `randomNumber < 2` and regenerate another number for use.