Table of probabilities at 2% success chance

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.
1 2 3 4 5
10 18,3% 1,6% 0,1% 0,0% 0,0%
20 33,2% 6,0% 0,7% 0,1% 0,0%
50 63,6% 26,4% 7,8% 1,8% 0,3%
100 86,7% 59,7% 32,3% 14,1% 5,1%
150 95,2% 80,4% 57,9% 35,3% 18,3%
200 98,2% 91,1% 76,5% 56,9% 37,1%
250 99,4% 96,1% 87,8% 73,8% 56,1%
300 99,8% 98,3% 94,0% 85,1% 71,8%
400 100,0% 99,7% 98,7% 95,9% 90,3%
500 100,0% 100,0% 99,7% 99,0% 97,2%
600 100,0% 100,0% 100,0% 99,8% 99,3%
700 100,0% 100,0% 100,0% 100,0% 99,8%
800 100,0% 100,0% 100,0% 100,0% 100,0%
3 Likes

Ehhh… not sure how you got those numbers. But you can never has 0% nither 100%. That is not how it works

Also I think (but that would not change above) that there is 2% chance to drop uber. Not that every uber has 2% chance to drop.

7 Likes

like vlad said, no amount of runs will ever equal 100%. so your table is off.

6 Likes

Read the notes.

Again, read the notes. I mention there are 7 ubers.

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

2 Likes

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?

11 Likes

(1-0.98^x) is a special case that only would work for the first column. Generally it’s called binomial distribution.

Not just one, but one or more.

1 Like

right, i was just writing about the first column, it obviously doesnt work for 1+

that being said, how did you come up with the number for 2 and up? I dont understand.

like how did you know the chance of 2 uber dropping at the same time?

Imagine a dice with 100 faces. You need to roll 1 or 2 to get an uber.
Each time to summon Duriel, you roll that dice.

It’s statistically possible you will never get one :slight_smile:

2 Likes

he did say he rounded the numbers and explicitly stated that it will never be true 0 or 100…

4 Likes

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. :slight_smile:

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:

TIL, something new everyday <3

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.

1 Like

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%. :roll_eyes:

1 2 3 4 5
10 18,2927193% 1,6177641% 0,0863906% 0,0030506% 0,0000741%
20 33,2392028% 5,9898979% 0,7068693% 0,0599679% 0,0038591%
50 63,5830320% 26,4228606% 7,8427748% 1,7758081% 0,3209742%
100 86,7380444% 59,6728289% 32,3314378% 14,1038437% 5,0830445%
150 95,1703979% 80,3859016% 57,9074327% 35,2760491% 18,3025114%
200 98,2412053% 91,0624516% 76,4851864% 56,8505027% 37,1156420%
250 99,3595003% 96,0916448% 87,7886240% 73,7808067% 56,1280981%
300 99,7667494% 98,3386847% 93,9816302% 85,1489618% 71,7647654%
400 99,9690664% 99,7165473% 98,6884340% 95,9048345% 90,2666254%
500 99,9958976% 99,9540364% 99,7408859% 99,0187844% 97,1877414%
600 99,9994559% 99,9927940% 99,9520746% 99,7864270% 99,2818779%
700 99,9999278% 99,9988971% 99,9915451% 99,9566355% 99,8324929%
800 99,9999904% 99,9998342% 99,9985605% 99,9916460% 99,9635294%
900 99,9999987% 99,9999754% 99,9997616% 99,9984554% 99,9924776%
1000 99,9999998% 99,9999964% 99,9999614% 99,9997237% 99,9985146%
4 Likes

I’ve done 1500 or so runs on Eternal since Duriel was added and I’ve never once dropped a Shako, Doom, or Selig. So idk.

If I don’t get an Uber Unique in 800 runs I’m coming back to this thread, just saying.

3 Likes

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.

I think getting a normal unique from beast is 100x harder. Screw you ice beast

1 Like

Last season it took me 317 runs for my 1st uber. This season I am around 350 runs and have 5 ubers. RNGesus giveth and taketh away.

3 Likes

I’m calling shenanigans sir. You give those back right now so his table is correct on the percentages.