Found this topic kind of interesting, so I wrote a (very simple) little console app to run some RNGs over x-number of samples within a given range to see average hits and determine how spot-on RNGs would be.
It's pretty unlucky to hit anywhere below 15%, even with only 300 samples. But any good number of samples (1K to 10K for example) with a default RNG gets pretty spot on the 20%. Only small sample numbers and a tight range of random values to sample from can cause those extremes below 15% or above 25%.
NOTE: I have occasionally spotted absurd gaps though. Once had a gap of 69 fails before I got a hit, but it's rare. Still, gaps of 20-40 are quite common.
One thing that did bother me during all these discussions here though (and I'm not sure if this is applicable), but didn't anybody consider the fact that crafting with companions could influence the outcome, as some companions are more likely to succeed with certain skills than others? Resulting quality of an item is something that can greatly influence the numbers and is something one simply can't test with just RNGing, without knowing what the real code does to factor in those companion stats. Or doesn't the quality of a crafted item not influence the chances during RE? (maybe I'm just misunderstanding those things)
If it does, wouldn't it be a matter of other factors influencing the formula, rather than of RNG?
If the quality of an item is irrelevant, the test at the very least shows how larger sample numbers and ranges indicate solid RNG average hit results.
PS: Please excuse if I get terminologies wrong. Not really a math guy and most of the time don't really care about the inner workings of stats that much,... usually.
Quick video capture of a few runs: watch/download