Discovering the Ratios of Ultimates and Ghosts

Hello everyone! In this guide I want to present you all with the real ratios of getting a holo in a pack and the specific ratios for each rarity, using data I collected from videos on YouTube.

As you all may know, the ratios of getting a Super, Ultra or Secret Rare are 1/5, 1/12 and 1/24 respectively. But what about Ghost and Ultimate Rares? What are the odds of getting them in a pack?

It was this question that drove me to do a study, to try to figure out what are the odds of getting this rarities. After some reasearch, I discovered the following: Ultimate Rares should be about 1/16 packs and Ghost 1/36 BOXS, or 1/864 packs. I found that very fishy. Many people have Ghosts, so they shouldn't be that rare.

I started then to make a few studys: I watched 51 videos of Box openings on YouTube, ranging from The Duelist Genesis to Generation Force. I wrote what were their pulls, how many holos they got and what were the raritys. The videos I choosed were completely random (this means that I didn't saw any video knowing what it already contained, like if it said "good pulls" or "pulled a Ghost!" and stuff like that)

Here are the results:
SUPER RARES: 240
ULTRA RARES: 107
SECRET RARES: 53
ULTIMATE RARES: 51
GHOST RARES: 5

With these, we can draw simple conclusions (this is all in average):

• Secret Rares are present in every box and actually it is possible to get 2 secrets in a box.
  
• Ultimates are present in almost all boxes (almost)
  
• Ghost Rares aren't that rare.

But now the real Math enters. What are the odds of getting a specific rarity in a pack?
First, don't forget that these are boxes of 24 packs each. So in total here we have 51x24=1224 packs opened.
So we can say that the probabilities are:
SUPER RARES: 240/1224
ULTRA RARES: 107/1224
SECRET RARES: 53/1224
ULTIMATE RARES: 51/1224
GHOST RARES: 5/1224

Now rounded and in more acurate percentages:
SUPER RARES: 240/1224 = 19,61% ~ 1/5
ULTRA RARES: 107/1224 = 8,74 % ~ 1/11
SECRET RARES: 53/1224 = 4,33 % ~ 1/23
ULTIMATE RARES: 51/1224 = 4,17 ~ 1/24
GHOST RARES: 5/1224 = 0,41% ~ 1/245

Now what did I say in the beginning? I remember:
SUPER RARES: 1/5 = 20%
ULTRA RARES: 1/12 = 8,33%
SECRET RARES: 1/24 = 4,17%
ULTIMATE RARES: 1/16 = 6,25%
GHOST RARES: 1/864 = 0,12%

Checking if these numbers are correct, by comparing with the others above:
SUPER RARES: 19,61% - 20 = -0,39
ULTRA RARES: 8,74 - 8,33 = 0,41
SECRET RARES: 4,33 - 4,17 = 0,16
ULTIMATE RARES: 4,17 - 6,25 = -2,08
GHOST RARES: 0,41 - 0,12 = 0,29

Now how strange, Ultimates have a pretty big difference between the predicted and the actual ratios. Ghosts have too, but the difference is actually smaller than the difference in Supers or Ultras. The problem is: Super Rares are actually confirmed by Konami to be 1/5 packs and Ultras to be 1/12. The difference is just probabilities problems. However, the difference is pretty small and it checks out with the actual ratios for Supers, Ultras and Secrets.
What this confirms is: the ratio of a Ultimate isn't 1/16, it is the same as a Secret, 1/24.

Now Ghosts are a problem, because the probabilty is extremely low, so small differences matter. The more (random) videos I view, more Ghosts I get and more precise ratios too.
However, I can prove that a Ghost Rare isn't that rare. My current data says that the ratio of a Ghost is 1/10 Boxs, more precisely 1/245 packs, a number much lower than the original 1/864 that most people say.

Now the real interesting part: What is the probability of getting a holo in a pack?
Well, it is just adding all of them together. The result is 37,25% or almost 3/8. Then again, this is not entirely and precisely acurate.

This is all relative to packs. And what about boxes? Here are the ratios:
SUPER RARES: 4,95 per box ROUNDED 5
ULTRA RARES: 2,10 per box ROUNDED 2
SECRET RARES: 1,04 per box ROUNDED 1
ULTIMATE RARES: 1 per box ROUNDED 1
GHOST RARES: 0,10 per box or 10% chance
This is means that in average, you get 5 Supers, 2 Ultras and 1 Secret and a Ultimate and 10% of getting a Ghost. That results in a average of 9 holos per box (however, just note that this isn't always true. 1 of "my" boxes had 16 holos! And some have 4, which is actually lowered my average by 1% since the last update.) Remember the 5-2-1-1 when opening a box. That is how many cards you should pull.

I hope that my investigations could help some people realize that it isn't that difficult to pull a holo card in a pack, especially a Ghost.

And as always, happy dueling! Please comment.

Wow. These statistics are actually very nice for me. There are a few ghost cards that I want. Least I know how I should go about it!

nice calculations

but did u figure in somebody breaking a mirror thats 7 years bad luck xD
thats gotta lower the prob

I never expected this topic to be revived after weeks being ignored. I actually now have more boxes view, so now i have more accurate ratios. May update this today.