This is a table of probabilities of finding at least n (columns 1-5) ubers within given amount of Duriel runs (rows 10-800).

Notes:

It is based on the assumption that the chance of success (single uber only) per run is 2%.

I’m not making any points here about the game. Just providing pure numbers (binomial distribution) for my own curiosity and because I’ve seen some wild claims here about how probability works.

The values are rounded to one decimal, nothing is truly 0% or 100%

As mentioned at the beginning, it’s at least n ubers, each colum is cumulative upwards. For example column (1) includes a chance of finding 5 or 10 ubers, it’s just unlikely at low number of runs. The chance of exactly 1 would be column (1) minus column (2). At 100 runs you are more than twice more likely to find 2 or more ubers than just 1.

There are 7 ubers. Depending on class 5 or 6 are available to find. So when finding a single uber there’s further 1/5 or 1/6 chance of it being the one you want (if you’re looking for only one).

Absolute worst case scenario is 600-800 runs, where you find 5 unwanted ubers, which you can then transform into the desired one.

i believe his math was 1- (0.98 ^ 10) for the 18.29% to show

so he is assuming the chances of not getting any uber is 98% each run, so the chances of not getting any uber in 10 runs would be 98% ^ 10 =81.7% and therefore the chance of getting 1 uber in 10 runs would be 1-81.7% = 18.3%?

quick napkin math so i might be wrong about his logic

He stated it’s rounded to the nearest .1, so 99.95 would round to 100% without actually being 100%. Why make conclusions about the work if you didn’t bother to read the explanation?

I mean you calculated the value correctly for one or more (same as in my table), but you stated incorrectly that it’s a probability for just one. 1 - chance_of_nothing isnt just 1, it’s any number.

As noted, I assume that Duriel can either drop one uber or not. There’s nothing here about dropping two at once.

Cases where something either can happen or not happen are what binomial distribution describes, There’s a formula for it: https://wikimedia.org/api/rest_v1/media/math/render/svg/b872c2c7bfaa26b16e8a82beaf72061b48daaf8e
But it’s easier to use BINOMDIST function in a spreadsheet and do some proper subtracting.

Are we talking within realms of theory or practicality? Theoretically you are right. Practically go back to the table. The thing is about how probable is a series of rolls not just one roll. And the longer the series the less probable it will be, because there are more and more possibilities.

If you want to learn some intuition about it, read this post:

Read the explanation. He rounded at 0,1%.
We all now that normal distribution tend to 100% for an infinite sigma value. But his point was to show how the chance to not find an uber is supposed to decrease with the number of roll iteration.

For some of you, who can’t take a hint, here are the same numbers formatted with more precision and extended to 1000 runs. I’m sure you’re not satisfied with those odds being interpreted as 100%.

This might mean 2% figure is not true (it’s just an unnoficial estimation by who knows whom). It also might mean you are discarding the validity and the amount of ubers which you don’t care about.