Please be truthful with us...

[Silverbane]

What I am saying is - your sample sizes are WAY too small to mean anything. Come back and complain when you miss 25% things more than 250,000 times out of 1,000,000.

Don't be ridiculous, that's an absurd requirement. Depending on how tight you want the error bars to be, the quality of an RNG can be determined with orders of magnitude fewer samples. For example, a mere 665 carefully collected samples was enough to establish the rate of G/E procs for L58 mats to within +/-2.7% with 93% confidence. (http://forum.square-enix.com/ffxiv/t...ar-L60-recipes)

So please don't make statements about things you don't understand. You're not going to convince anyone that the FFXIV RNG is a good one by demanding impossible numbers of samples for proof. Instead, you should encourage them to carefully collect a few thousand samples and share the results. Then we'll have some good scientific data to discuss, instead of dueling beliefs.

For example, if someone wants to craft a large number of items to 50% HQ chance and record how many come out HQ, whether the actual odds are near 50% (say, between 48 and 52%: close enough, I think) can be determined with 95% confidence by a mere 2500 craftings. Alternatively, you could determine if the true odds are in the 47 to 53% range with a 95% confidence with under a thousand craftings -- the less tight a bound you want and the less confidence you require, the fewer samples you need.

You see the results you personally get. You hear about the results that others get. But you cannot, I cannot, no one can see ALL the results of ALL the RNG calls

If the RNG is worth a damn, this critique is irrelevant. Any valid sample of the RNG, any at all, should have the same statistical qualities as any other sample or of all other samples of the same size. Not the same results, of course, but the same statistical qualities. That's basic statistics.