[alexti]

It doesn't look likely to happen, the sample needed to find anything with a reasonable probability of correctness seems to be too big. My test with sample of 3000 wasn't even close to the point when the distribution significantly condenses, in your 100000 sample result is still 0.5% off.

What is the size of the sample required to show that there's a problem (using duck number indicator) with a 99.99% probability?

I think we'd need the code of RNG to test it on large samples...