Hiroshi Minagawa, Lead UI artist for FFXIV, basically broke down how 'rng' works and how your brain lies to you about it on the forums. A fun read, I think:

So to start off, I’ll lay out the essential points quickly.

A. The standard random number programs used by FFXIV, and other modern games, generate practical “true random numbers”.

B. With a range of trial numbers that can be understood by a person, because it’s a true random number bias arises.

C. Since our brains are very adept in their capability to detect bias as abnormal or a singularity, we perceive true random numbers as abnormal.

Hmm, interesting read. Just my thoughts:

The Atma drop rate formula is not really disclosed (does Fate lvl affect drop rates, does gold/silver/bronze impact drop rates)? So, that can easily explain the difference of seeing an Atma after 2 fates vs. 200 fates

I do agree with sample sets being extremely small. Even sample sizes of 50 or 100 samples is not statistically relevant in regards to the number of total fates being completed game wide. I would guess 50-100 fates is roughly 4-15 (?) hours of fating for a single person. So, I agree a confirmation bias definitely exists.

Though, it doesn't answer whether they use a uniform random numbers and normal random numbers.

It is very possible that the RNG is not working properly.

True RNG is really annoying cuz you cant force it to be fair to everybody. But if you add some security program to make sure it is TRUE rng, it is not the TRUE rng anymore. :p Paradox