probability of at least (k) URs in (n) tries

Thanks. Interestingly, I can see a double UR drop in a pity timer pack on your row 91 in second spreadsheet. This tells us that pity timer packs have regular pRNG dice throw. Otherwise, there won't be another UR.

And there might be a simpler way to check independence. With large enough sample, double UR drop rate average should be exactly 0.0625 if UR drop is 0.25. But accurate estimate at 99% needs data about 6000 packs roughly.

Ok, I put the gaps through an online KS calculator, I'll try something more advanced from home later but IDK what would work well with this dataset. I probably need to go back to your original dataset in the first file. And you have some weird outlier at 14 gap, not sure what was going on with this one, I just threw it out.

So, median is exactly 4.0 which means that chance of UR is about 0.25 consistent with other data. But variability is quite high, so streaks are very likely. Notice that I did not throw out pity timer results, I just replaced 10 gap with 9 gap and it has no effect on distribution. It says not normal but it looks pretty much normal to me, it all depends on P value, and 0.01 is good enough.



I checked also with xuru www.xuru.org/st/ds.asp and it uses Anderson-Darling test that says it is normal at P = 0.02.

You still have a pity timer Premium pack on 4/29 which has 2 UR.

Anyhow, did that. Anderson-Darling test for normality at xuru : P=0.01; means values are normally distributed.

For other normality tests, I used contchart.com/goodness-of-fit.aspx which is kind of messy and is known to produce strange data sometimes. Also, different calculators produce different resulting P values which obviously sucks.

Anyhow, for non-log tests, mostly normal I presume. Although there are some hiccups, probably due to larger streaks. So, pity drops do introduce some uncertainty at lower P values. Can't do nothing about it.



For log tests, I just replaced all zero values (double UR) with 0.3 values. Otherwise, it cannot calculate. And it does not seem that distribution is log-normal, less likely than simple normal. But this is introduced essentially by pity timer drops and by double UR drops which log-normal tests cannot process.