Hidden Fates
Next up for discussion is Hidden Fates, one of the most popular special sets of all times. Before going into the details of pull rates, we need to look into the different kinds of cards, and different kinds of sheets they were likely printed on:
- Commons, uncommons, rares, rare holos, and reverses: These are present just as in the main expansions. For the reverses, note that just like previous special sets, Hidden Fates includes reverse holo Basic Energies. Also, just like Dragon Majesty, the total number of reverses is 65, meening the 121 card sheet should include 56 printed twice and 9 printed once. I wouldn’t be surprised if these 9 were the 9 Basic Energies, but did not attempt any statistical analysis counting how many reverse Basic Energies appear in Youtube samples.
- “Regular” Pokémon-GX: also the same as in other sets.
- Full art Pokémon-GX: There is only one (Moltres, Zapdos & Articuno GX), which I assume is printed on its own sheet.
- Full art Trainers and secret rares: In am assuming a sheet for the main set including the two full art Trainers (Giovanni’s Exile and Jessie & James) and the rainbow rare Moltres, Zapdos & Articuno GX. As the full art trainers from the Shiny Vault come in the reverse slot, they can’t have been printed on the same sheet. (Extremely random side note: I am already thinking about how the cards in the “god packs” from Pokémon 151 were printed, it is a very interesting question.)
- “Baby shinies”: These cards from the Shiny Vault will have been printed on their own sheet. Due to the uniformly yellow borders, there is no reason to assume the cards were spaced on the print sheet, so I am assuming an 11x11 sheet, just as I did for the Prism Star cards.
- Shiny Pokémon-GX, full art Trainers from the Shiny Vault, and full-gold cards (Tapu Koko GX, Tapu Lele GX, Tapu Bulu GX, Tapu Fini GX). Here is where things get really interesting.
-As I personally don’t collect modern English cards (kind of ironic given I am writing this elaborate guide) I don’t have any on hand to check if there are any differences in texture or holofoil pattern which would preclude these being printed on the same sheet. Any information on this topic would be very welcome! For now, I am assuming there isn’t - the texture and holofoil pattern for the Shiny Pokémon-GX seems very similar to that of the rainbow rares which are generally printed on the same sheet as full art Trainers and other secret rares, and the full-gold cards appear generally the same as those featured in Ultra Prism and Dragon Majesty which I am also assuming to be printed on the same sheet as full art Trainers, rainbow rares and other secret rares.
-Due to the observed pull rates (see below) however, I have come to the conclusion that these cards were not all printed on the same sheet; I am assuming one sheet for the Shiny Pokémon-GX and another for the full art Trainers and gold cards.
Now, to the pull rates. For these, I have three main sources: my own Youtube samples (1), data on 1,480 packs by Derium (4) and the thread by @burpies Pull Rates in Sun & Moon - Sword & Shield Sets (2). The latter source, for all its merits, unfortunately does not distinguish between full art Trainers from the main set and those from the Shiny Vault, so the data is not completely comparable. (There is also a post on Reddit by “cardzard.com”, based on 2,350 packs, which arrived at a pull rate of 1/4 for baby shinies, 1/9 for Shiny Pokémon-GX, 1/73 for Shiny Vault full art Trainers, and 1/57 for full-gold cards.)
Here is the data:
From left to right, the columns show:
- number of packs in the sample
- holos (only looked at in my own sample)
- “regular” Pokémon-GX
- full arts from the main set (greyed out as it doesn’t correspond to a single sheet)
- full art Pokémon from the main set (Moltres, Zapdos & Articuno GX)
- full art Trainers from the main set (greyed out as it doesn’t correspond to a single sheet)
- secret rares from the main set (Moltres, Zapdos & Articuno GX) (greyed out as it doesn’t correspond to a single sheet)
- combined full art Trainers/secret rares from the main set
- “baby shinies”
- Shiny Pokémon-GX (assumed to be on a sheet of their own)
- full art Trainers from the Shiny Vault (greyed out as it doesn’t correspond to a single sheet)
- full-gold cards from the Shiny Vault (greyed out as it doesn’t correspond to a single sheet)
- combined full art Trainers/full-gold cards from the Shiny Vault (assumed to be on a sheet of their own)
- full art Trainers (all) (for comparison only, greyed out as it doesn’t correspond to a single sheet)
At the bottom, the model I am assuming for “box” ratios is shown (Hidden Fates wasn’t sold in boxes, but the ratio of cards per 36 packs is simply very usefull for comparing with other sets). The philosophy behind the model is that it appears that there is about a 1 in 3 (12 in 36) chance in getting a premium card in the reverse slot, and a 2 in 5 (14.4 in 36) chance of getting one in the rare slot. This latter ratio is what is standard for the Sword & Shield series. Everything else in the model is basically just chosen to best fit the raw data.
Now, why am I assuming the Shiny Pokémon-GX were printed separately from the full art Trainers and the full-gold cards from the Shiny Vault? Well, it has to do with sheet composition. There are 35 of the former, and 14 of the latter, so the most intuitive way to print them on one sheet would be for 47 of these 49 cards to be printed twice and the remaining two 3 times on a 10x10 sheet. Depending on whether these two cards were Shiny Pokémon-GX or other cards, the Shiny Pokémon-GX would make up 70-72% of the cards on the sheet, and should make up approximately that amount of the pulls (though previous experience writing this guide indicates uncertainty tends to be high in this regard). Assuming the full art Trainers and full-gold cards all only printed once and the rest of the sheet filled out with Shiny Pokémon-GX would lead to 86% of the sheet being taken up by Shiny Pokémon-GX.
Looking at the available data, my own sample yields 82% Shiny Pokémon-GX, Derium’s 76% and cardzard.com’s (from Reddit) 1 / 9 / (1 /9 + 1 / 57 + 1 / 73) = 78%. Were it only for Derium’s data, I would say it’s within the margin of error, but all in all the only way I could see all these cards printed on the same sheet would be if some of Shiny Pokémon-GX were printed on the sheet 3 times and some of the full art Trainers/full-gold cards only once. All in all, a strange way of composing a sheet which I am not fond of assuming in my model, which is why I am assuming two sheets.
For the rarity table below, I have designated the baby shinies as SPa, the Shiny Pokémon-GX as SPb and the Shiny Vault full art Trainers and full-gold cards SPc:
A note on rainbow rare Moltres, Zapdos & Articuno GX: I have no indication it is significantly rarer than the two full art Trainers; I am arbitrarily assuming it has FT33 rarity.
The raw data for the various types of cards is shown below:
I’ll conclude with two observations regarding individual card rarities: Looking at the raw data for Shiny Pokémon-GX, it looks like Charizard GX is not among the rarer cards. However, observed data can be very random, as is shown by Naganadel GX: In my own sample, it’s the most common Shiny Pokémon-GX, while in Derium’s it’s among the rarest ones.