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Pull ratios

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I was working on a spreadsheet for my person use, showing all the packs and all the cards in them and percentages showing the likelihood of pulling a specific card, and it was going well, using this site, until I came to the percentages.

I came across some of the pages like Rare, Super Rare, etc.. and some of them had useful information that included pull ratios. Some other varieties of rares did not, for example I never saw a ratio showing for Ultimate Rare cards. Some of these ratios didn't match up with my personal experiences of drawing (I buy boxes). Because of this I decided to find out where these ratios are coming from and since I didn't see any references I searched the web after pages and pages of searching for rarity and ratios all I found where 3 sites.

A Lot of redirecting me back to this site.

1. A wikipedia page on the Yu-Gi-Oh! card game, the rarity section also cited no references. (Note: the pages for rare cards on this site are almost verbatim what is on wikipedia, which seems a little strange/sketchy...)

2. This site, http://farmhobbies.weebly.com/yugioh---classifying-a-cards-rarity.html, which has quite a few similarities to both the wikipedia page and the wikia pages here. (I'm guessing this is the source site for the information).

3. Another site, I can't recall what it was called, and I didn't bookmark it for a sole reason, that being while although much of the data matched the data from other sites it also said that the probability of pulling Ghost Rare cards was 1:36 boxes... which I know to be absolutely false considering I pulled 3 in one box.

So none of this ratio data seems to be supported by any "real" evidence that I can find or see.

To solve this problem I thought of a solution that I remembered from another wikia I saw a few years ago. Take a look at this page. http://runescape.wikia.com/wiki/Basilisk#Charms

It's a drop ratio for a game my brother used to play. It's on a 90% confidence interval which is pretty good. If we can start a log like this for boosters (a pull log), then we could formulate our own percentages and ratios through original research that would likely be more accurate than the current ratios given which seem to have little evidence to support them.

In the end the final result would look something like this:

Pull percentages Rare: 66-67% Super Rare: 19-20% Ultra Rare: 7–8% Ultimate Rare: 5% Ghost Rare: 1%

Represents 90% confidence range, based on a sample of 44,267 booster packs opened. 1 rare is pulled at a time.

It sounded like a pretty good idea to me, so I thought I'd share it for submission. I don't know who would be able to do it, if any one has taken stats or something like that it could definitely help. (I've taken a course in it, I just don't recall a whole lot.)

I really don't know how to make a template though, and I don't understand html a whole lot.Dragula42 (talkcontribs) 00:04, July 21, 2011 (UTC)Dragula42

Already see a problem

Looking through my stats book I already see a problem with the current ratios given on the site. Not a large problem but a problem none the less.

It's Guaranteed that you will get 8 commons in a pack so the ratio for commons is obviously 8:1 you have a 100% chance of getting 8 commons in every pack.
The site states that rare cards have a 1:1 ratio, this can't be true if super rares, ultra rares, and secret rares are all competing for one spot in each pack, unless the ratio for super rares, ultra rares, and secret rares are all 0:1.
There is a 1:1 ratio that you will get a rare card of some sort, but not necessarily a rare itself.
To calculate we take the given ratios 1:31 = 3%(.0323), ultra rare 1:12 = 8%(.0833), and super rares 1:5 = 20%(.2) and subtract them all by 1, as there is only one spot available left in the pack.
1-.0323-.0833-.200=.6844 or a 68% chance of getting a rare card. which when we reduce the fraction we find that the ratio for a rare card is "really" 2:3.
This is of course assuming all the other information is correct, which we can't really know for sure.Dragula42 (talkcontribs) 22:47, July 21, 2011 (UTC)Dragula42

I know for a fact that when you pull certain rarities from packs for some booster sets, you are also guaranteed to pull a Rare. However, I cannot say if this is true for all rarer-than-Rare pulls (which would indeed mean a 1:1 pull ratio for Rares), or if it only starts at Ultra Rare pulls (I do remember with certainty that I've always pulled a Rare whenever I pulled an Ultra Rare, at least for recent sets), and if this is the way it's always been, or if it started with a specific set or whatever. I can also say that ratios have changed in the past, at least according to the ratios printed on every pack. I'm not sure if ratios were changed in response to Konami taking over worldwide distribution after the release of Crimson Crisis, though. One more point to keep in mind is that not all types of booster sets have the same ratios; Duelist Pack sets, for example, have their own set of ratios. ダイノガイ千?!? · ☎ Dinoguy1000 21:56, July 22, 2011 (UTC)
This seems to be becoming a very difficult problem to solve, I'm almost certain when I bought a Crossroads of Chaos box a few months ago that pulling a rarer-than rare card in the pack, the rarer-than rare had replaced the spot of the rare card. If older packs included a rare card and a rarer than rare card then I agree the rare ratio for those packs is definitely 1:1.
I had noticed that rarity changes from pack to pack and reflected that in my spreadsheet, however I thought I'd keep it a little simpler on this page.Dragula42 (talkcontribs) 22:58, July 22, 2011 (UTC)Dragula42
I'm 99.9% sure that I was pulling Rares alongside Ultra Rares in Storm of Ragnarok packs just a month or two ago, so it's not something that used to be done and then got stopped (unless Konami stopped doing so after STOR). ダイノガイ千?!? · ☎ Dinoguy1000 23:18, July 22, 2011 (UTC)

In packs starting with TDGS, you automatically get one Rare per pack. If there's a higher rarity card in there it replaces a common.BobaFett2 (talk)

Something to take note of for collectors

The ratios on the site are for the type of card themselves to calculate the chance you will pull a specific card you want is calculated differently.

Let's examine the pack Labyrinth of Nightmare

In a pack we have a 3% (1:31) chance of pulling a secret rare card, but lets say you want Gemini Elf specifically. We get 3%/2 the number of secret rares available giving us a rounded 2% in a pack and from the 77% chance from buying a box we get a 39% chance we will receive Gemini Elf.

Same would be true for Ultras, 8% in a pack, if we want Bazoo the Soul-Eater specifically our chances drop to a measly 1% in pack and from 200% from a box to 20%.

Yes, you actually have a better chance of getting the secret rare you want rather than the ultra you want.. amusing.
Super rare,20% per pack, Kycoo the Ghost Destroyer 20% per pack---> 2%. Box 480% ---> 48%.

Rare, 72% per pack, Tornado Bird 72% per pack----> 4%. Box 1723% ---> 101%.

And finally common, 800% per pack, Supply 800%----> 12%. Box 19200%--->291%.

Ultimately from buying a box we can expect with some confidence, assuming given ratios are correct, 1 secret rare, 2 Ultra rares, 4 Super rares, 17 Rares, and 192 commons.

  • Rare ratios for LON appear to be 5:7 (given that SR ratio is truly accurate)

Dragula42 (talkcontribs) 23:24, July 21, 2011 (UTC)Dragula42

Printed ratios

Historically, booster packs have had ratios for pulling everything more common than a Secret Rare printed directly on packs (this doesn't seem to be the case for new sets, though); this section should serve as a catalog of such printed ratios. ダイノガイ千?!? · ☎ Dinoguy1000 21:56, July 22, 2011 (UTC)

Set name (ABBR) #/Pack Commons Rares Super Rares Ultra Rares Secret Rares
Legend of Blue Eyes White Dragon (LOB) 9 82 (8:1) 22 (1:1) 10 (1:6) 10 (1:12)
Legend of Blue Eyes White Dragon (LOB-EN) 9 82 (8:1) 22 (1:1) 10 (1:6) 10 (1:12)
Metal Raiders (MRD) 9 100 (8:1) 22 (1:1) 10 (1:6) 10 (1:12)
Metal Raiders (MRD-EN) 9 100 (8:1) 22 (1:1) 10 (1:6) 10 (1:12)
Metal Raiders (MRD-E) 9 100 (8:1) 22 (1:1) 10 (1:6) 10 (1:12)
Magic Ruler (MRL) 9 65 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Pharaoh's Servant (PSV) 9 66 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Labyrinth of Nightmare (LON) 9 66 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Labyrinth of Nightmare (LON-EN) 9 66 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Legacy of Darkness (LOD) 9 62 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Legacy of Darkness (LOD-EN) 9 62 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Pharaonic Guardian (PGD) 9 69 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Magician's Force (MFC) 9 69 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Dark Crisis (DCR) 9 67 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Invasion of Chaos (IOC) 9 73 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Ancient Sanctuary (AST) 9 73 (8:1) 17 (1:1) 10 (1:6) 10 (1:12)
Soul of the Duelist (SOD-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Rise of Destiny (RDS-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Flaming Eternity (FET-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
The Lost Millennium (TLM-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Cybernetic Revolution (CRV-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Elemental Energy (EEN-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Shadow of Infinity (SOI-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Enemy of Justice (EOJ-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Power of the Duelist (POTD-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Cyberdark Impact (CDIP-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Strike of Neos (STON-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Force of the Breaker (FOTB-EN) 9 35 (8:1) 14 (1:1) 7 (1:6) 4 (1:24)
Tactical Evolution (TAEV-EN) 9 48 (8:1) 18 (1:1) 9 (1:5) 5 (1:12)
Gladiator's Assault (GLAS-EN)
Phantom Darkness (PTDN-EN) 9 48 (8:1) 20 (1:1) 12 (1:5) 10 (1:12)
Light of Destruction (LODT-EN) 9 48 (8:1) 20 (1:1) 12 (1:5) 10 (1:12)
The Duelist Genesis (TDGS-EN) 9 48 (8:1) 20 (1:1) 14 (1:5) 10 (1:12)
Crossroads of Chaos (CSOC-EN) 9 48 (8:1) 20 (1:1) 14 (1:5) 10 (1:12)
Crimson Crisis (CRMS-EN) 9 48 (8:1) 20 (1:1) 14 (1:5) 10 (1:12)
Raging Battle (RGBT-EN) 9 48 (8:1) 20 (1:1) 14 (1:5) 10 (1:12)
Ancient Prophecy (ANPR-EN) 9 48 (8:1) 20 (1:1) 14 (1:5) 10 (1:12)
Stardust Overdrive (SOVR-EN) 9 48 (8:1) 20 (1:1) 14 (1:5) 10 (1:12)
Absolute Powerforce (ABPF-EN)
The Shining Darkness (TSHD-EN)
Duelist Revolution (DREV-EN) 9 48 20 14 10 8
Starstrike Blast (STBL-EN)
Storm of Ragnarok (STOR-EN) 9 48 20 14 10 8
Extreme Victory (EXVR-EN)
Generation Force (GENF-EN)
Dark Beginning 1 (DB1) 13 185 (11:1) 30 (1:1) 20 (1:6) 15 (1:12)
Dark Beginning 2 (DB2) 13 185 (11:1) 30 (1:1) 20 (1:6) 15 (1:12)
Dark Revelation Volume 1 (DR1) 13 202 (11:1) 30 (1:1) 20 (1:6) 15 (1:12)
Dark Revelation Volume 2 (DR2) 13 159 (11:1) 30 (1:1) 20 (1:6) 15 (1:12)
Dark Revelation Volume 3 (DR03) 12 140 (11:1) 56 (1:1) 28 (1:6) 16 (1:12)
Dark Revelation Volume 4 (DR04) 12 140 (11:1) 56 (1:1) 28 (1:4) 16 (1:8)
Dark Legends (DLG1) 12 60 (11:1) 26 (1:1) 16 (1:5) 10 (1:12)
Duelist Pack 1: Jaden Yuki (DP1) 6 17 (4:1) 7 (1:1) 4 (1:6) 2 (1:24)
Duelist Pack 2: Chazz Princeton (DP2) 6 17 (4:1) 7 (1:1) 4 (1:6) 2 (1:24)
Duelist Pack 3: Jaden Yuki 2 (DP03) 6 17 (4:1) 7 (1:1) 4 (1:6) 2 (1:24)
Duelist Pack 4: Zane Truesdale (DP04) 6 17 (4:1) 7 (1:1) 4 (1:6) 2 (1:24)
Duelist Pack 5: Aster Phoenix (DP05) 6 17 (4:1) 7 (1:1) 4 (1:6) 2 (1:24)
Duelist Pack 6: Jaden Yuki 3 (DP06)
Duelist Pack 7: Jesse Anderson (DP07)
Duelist Pack 8: Yusei Fudo (DP08) 5 17 (4:1) 7 (1:1) 4 (1:5) 2 (1:15)
Duelist Pack 9: Yusei Fudo 2 (DP09) 5 17 (4:1) 7 (1:1) 4 (1:5) 2 (1:15)
Duelist Pack 10: Yusei Fudo 3 (DP10) 5 17 7 4 2
Duelist Pack 11: Crow (DP11)
Duelist Pack: Yugi (DPYG)
Duelist Pack: Kaiba (DPKB)
Premium Pack 1 (PP01) 5 7 (3:1) 8 (2:1)
Hidden Arsenal (HA01) 5 15 (4:1) 15 (1:1)
Hidden Arsenal 2 (HA02)
Hidden Arsenal 3 (HA03)
Hidden Arsenal 4: Trishula’s Triumph (HA04) 5 40 (4:1) 20 (1:1)
Retro Pack (RP01)
Retro Pack 2 (RP02) 9 48 (8:1) 24 (1:1) 10 (1:5) 8 (1:12)
Tournament Pack 5 (TP5) 3 11 (3:1) 4 (1:3) 4 (1:18) 1 (1:108)


Wow, I never actually read the packs so that's good to know, ty for that information.
There are still some issues I have though.
  1. If Secret Rare ratios aren't printed on the packs where is this information coming from?
  2. The ratios for Rare cards are still incorrect as I've proven with simple mathematics, and given that the rarity information is different for each packs the rarity of rare cards will be different for each pack.
  3. We really need to fix the rarity information pages to reflect this information.
Still I find this information useful and am thankful for your posting.
The solution I presented to determine the actual pull ratios still seems applicable to the squares not filled in so if you're reading this let me know what you think, and if you can help in forming a template for the idea. 174.24.99.41 (talk) 22:26, July 22, 2011 (UTC)Dragula42
Any Secret Rare ratios elsewhere on the wiki probably come from individuals observing how often they pulled Secret Rares from given sets. It's doubtful that any amount of rigor was applied to these, and it seems likely that a single ratio could have then been copied across a number of different sets (I've never done an audit of the ratio information across booster set pages here, so I don't know how many different ratios for Secret Rares are presented).
The "correctness" for the Rare ratios in the above table strictly depends on whether a pack that contains a Super, Ultra, Secret, etc. Rare card also contains a Rare card - if this is always true for a given set, then that set does indeed have a 1:1 pull ratio for Rare cards. If this is not true, however, it implies that Konami/UDE have been including all non-Common rarities under their "Rare" label. This being said, all the information in the above table is taken directly from the set packs themselves, and is therefore what Konami/UDE are claiming.
I think, for now, we should remove all non-official ratios from set pages. Once we can get a rigorous, multi-user, per-set investigation of pull ratios for unlisted rarities going, then we can start looking at re-adding such ratios to pages. Ultimately, we need a Pull ratio page (whether under that name or another, I'm not sure, but it seems the most obvious to me); it could list all such official ratios (for *all* regions, not just the English TCG ones) along with noting unofficial ratios and providing some other notes (for instance, in the interest of brevity, I omitted Tip/Strategy Card pull ratios from the above table; these are specifically included in the cards-per-pack counts and listed pull ratios on older reprint and Duelist Pack sets and would be noted on the actual article). ダイノガイ千?!? · ☎ Dinoguy1000 22:48, July 22, 2011 (UTC)
I completely agree and can't thank you enough for helping me with this issue! I think all of this information will become very helpful to multiple users once we finally get to the solution! I'm personally looking into buying another box of Yu-gi-oh! cards and in order to decide which box to buy (since many of them can be expensive) I had decided to make a spreadsheet reflecting the cards available in each pack, highlighting the cards I owned, and the cards I wished to own (to collect, for certain decks I wish to build, and cards I'd like to own more of), then my plan was to evaluate my chances of pulling each card. Letting me know if I should buy a box, a Special Edition, or just a booster pack for each pack and which pack/box/SE would be best to invest in for my next purchases. It's been A LOT of work but ultimately I feel that it will pay off largely not just for this next purchase but for future purchases as well. I'm really glad someone else is taking an interest in all of this. Thanks again.Dragula42 (talkcontribs) 23:06, July 22, 2011 (UTC)Dragula42
Have you been keeping track of the exact cards and rarities you've been pulling, per pack, in your spreadsheet? Ultimately, this is the level of detail we'll need for any sufficiently accurate investigation (especially for investigating the existence of Super Short Print cards from very old booster sets, considering Kevin Tewart claims there's never been any such rarity). This is actually something that has interested me for some time now, so I've put a reasonable amount of thought into it up to now.
Boxes aren't available to me where I live, so I don't know how much they generally run for, though obviously, if you're not worried about price, boxes will give you the best chance for pulling the cards you're after. Special Edition boxes are the only way to get SE cards (other than buying them individually from hobby stores or online, or trading for them; they have also, very rarely, been included in per-store repacks (this is how I got most of my older booster SE cards)), so if those are what you're after, your choices are rather limited. ;) For looking at pull ratios, though, boxes will get you the most packs at a time. ダイノガイ千?!? · ☎ Dinoguy1000 23:28, July 22, 2011 (UTC)
No I haven't been keeping track of my personal pulls yet, though that's what I was suggesting we all do in order to get to the bottom of this and then form like a running database for all of our data that anyone could add to. My spreadsheet is more for my personal use and looks more like this: each tab is devoted to a different pack, within each tab is the card list for the pack next to the card name is either an "x" showing I own the card or nothing showing that I do not own the card the column next to that shows the rarity of the card. The one adjacent to that has the equation for the % chance of pulling that card in one pack, next to that the % chance of pulling that card in one box.

Below the card list is an equation showing how many of the cards I own for that card set. Let's say it's LOB I own 112 of those cards using the countif function it does the counting for me. Then I have a box of information used to make the equations showing how many cards are available in each pack, how many packs in a box etc etc. It's all set up except for the actual ratios for pulling cards. I can show you if this thing has some sort of file share ability.Dragula42 (talkcontribs) 04:11, July 25, 2011 (UTC)Dragula42

No, that's all right, I got a pretty good picture of what you're doing from your description. =)
I think, for the database, we'll have a template for each pack, used something like {{... | setname = Foobar | setregion = NA/EN/EU/AU/... | card1 = Foo | card1number = FOO-999 | card1rarity = C/R/SR/... | card2 ... }} (I can scratch together a mockup/prototype if that wasn't clear enough); the template would display all the info and also tally up the rarities from that pack. There would be a second template for boxes allowing to specify, at minimum, the number of packs per box, and maybe one for Special Edition boxes and one for Collectors Tins as well. ダイノガイ千?!? · ☎ Dinoguy1000 18:10, July 25, 2011 (UTC)
Awesomeness! :D I think we can expect some definite changes for the better.Dragula42 (talkcontribs) 18:23, July 27, 2011 (UTC)Dragula42

Related discussions

Pull ratios have been discussed from time to time in random places on the wiki; known discussions are listed below:

There are probably more discussions strewn about in the forum and on user talk pages, but these are all I could find with the wiki search functionality (feel free to add others you may know about, though). ダイノガイ千?!? · ☎ Dinoguy1000 23:16, July 22, 2011 (UTC)

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