Originally Posted by JellyWoW

The first issue, which is true for statistics in general, is that the 50% chance is only true over very large data sets. Thus everyone's individual rolls are not going to be true for that, by a long shot. Especially for the fact that rainbows are a 0.5% chance. You would need to pull gacha 1057 times to even start to get a good approximation (just trust the math, I rather not explain how you get the number).

What you're saying might be true or might be bull**** depending on what you mean. There is an approximate 52.226% chance on any set of 11 draws that at least one is a gold or rainbow. This is immutable fact so long as the chances provided are accurate representations of the actual chances to draw gold or rainbow. It is true that you'll only observe that over a large data set, but every 11-roll will have that chance of at least one gold or rainbow.

Though it's hardly impossible to go 33 draws without seeing either - there's still ~11% chance to not get any at that point.