HeartGold & SoulSilver
There is a lot to discuss for this set. As mentioned in my last post, I am assuming the box ratios to be 8.5 holos, 3 Pokémon Legend, 0.5 secret rares (Alph Lithograph ONE) and 6 Pokémon Prime (which come in the reverse slot). I think it is best to start with the rarity table, and then look at each sheet in order:
There are 13 “regular” holos, plus the Red Gyarados (with Thrash as its first attack). Gyarados is not a secret rare (it is numbered 123/123). The raw data for the holos looks as follows:
The first column of numbers shows the observed pulls from 25 boxes, the second normalizes this data to a sheet size of 121 cards. There are two reconstructions which appear the most plausible: One would be for all the “regular” holos to be printed 9 times on the sheet, and Red Gyarados 4 times, the other would have 12 holos printed 9 times, 1 printed 8 times and Red Gyarados printed 5 times. I went with the second, making Gyarados half as common as the most common holo rounded up.
Next, the rares. In my post on Neo Genesis, I pointed out that that set looked like it had artificial rarity differences between the holos - i.e. some holos were printed fewer than others intentionally, not just in order to fill out a sheet. For almost all other sets looked at so far, I didn’t see any indication of such artificial rarity differences - the Basic Energy Cards in Base Set and Base Set 2, and likely errors such as Dark Vaporeon in some print runs of Team Rocket and Lunatone in Great Encounters being the exceptions. Looking at the raw data for the rares, I think HeartGold & SoulSilver however does have such rarity differences:
The observed pulls for Feraligatr, Meganium and Typhlosion - the final evolutions of the Johto starters, which also feature in the Theme Decks as holos - appear to be too few to be explicable by coincidence. Pichu - a Pokémon which in a way also belongs to a starter family - seems to belong in the same group. Since I have observed similar constellations for some later sets, I don’t think this is coincidence. Thus in my model I am assuming these four cards are printed only 4 times on the sheet - making them half as common as the most common rares, rounded up (of the other cards, I am assuming 3 are printed 7 times on the sheet and 14 are printed 6 times).
I did not look at the uncommons, but reconstructed the commons sheet. Going by set number, the commons alternate between C4 and C3, with the exception that Wooper has C4 rarity. The Basic Energy Cards are printed only once on the sheet (C1), making them rather rare, but keep in mind they were also available in the Theme Decks. The commons sheet looks as follows (though there is a catch):
† Meowth, W Energy, Pikachu, Cyndaquil, Wooper, Girafarig, Ledyba, Caterpie, Snubbull, Hoppip, Koffing, Spinarak, Growlithe, Totodile, Phanpy, Drowzee, Meowth, P Energy, Sandshrew, Sunkern, Magikarp, Mareep, Slowpoke, Jigglypuff, Exeggcute, Vulpix, Sentret, Paras, Wooper, Jynx, Growlithe, L Energy, Cyndaquil, Chikorita, Chansey, Hoppip, Phanpy, Pikachu, Caterpie, Hoothoot, Snubbull, Meowth, Spinarak, Clefairy, Staryu, Sunkern, F Energy, Ledyba, Vulpix, Sandshrew, Koffing, Mareep, Magikarp, Hoppip, Girafarig, Cyndaquil, Sentret, Marill, Wooper, Growlithe, G Energy, Slowpoke, Totodile, Jigglypuff, Jynx, Exeggcute, Drowzee, Paras, Sandshrew, Spinarak, Sunkern, Meowth, Chansey, Chikorita, Vulpix, Snubbull, M Energy, Mareep, Marill, Exeggcute, Magikarp, Ledyba, Hoppip, Clefairy, Phanpy, Jynx, Slowpoke, Chikorita, R Energy, Spinarak, Girafarig, Paras, Hoothoot, Staryu, Pikachu, Jigglypuff, Ledyba, Sandshrew, Totodile, Sentret, Koffing, Growlithe, Wooper, D Energy, Caterpie, Drowzee, Cyndaquil, Sunkern, Slowpoke, Exeggcute, Phanpy, Hoothoot, Chikorita, Staryu, Mareep, Chansey, Jynx, Caterpie, Marill, Vulpix, Clefairy †
The catch is that there seem to be some locations on the sheet with a very strong tendency for the cards to get flipped in order, to such a degree that I am not completely sure which is the correct order. I chose the variant which I observed more often. These positions are underlined. Since they are generally 11 cards apart, it looks like a part of one column (possibly one on the edge of the sheet) had a tendency of getting flipped underneith the neighboring column when the cards got scooped up after cutting. Interestingly, it seems not to have affected the whole column, and even more interestingly, I never observed Drowzee and Paras being flipped, despite Cyndaquil and Sentret 11 cards before in the sequence and Mareep and Marill 11 cards afterwards being flipped multiple times in the videos I watched.
The raw data for the Pokémon LEGEND and Pokémon Prime is as follows:
As mentioned in my last post, I am assuming a 10x11 card sheet for the Pokémon LEGEND. I am also assuming the two cards printed 28 times and the two cards printed 27 times are matching pairs of top and bottom halves. For the Pokémon Prime, also as mentioned in my last post, I am assuming a 10x10 sheet.
I did not look at the reverses for this set, not because it wouln’t be interesting, but because I simply didn’t get around to doing it and I would like to get on with this guide. I will only note that Red Gyarados is included among the reverses, but the 8 Basic Energy Cards aren’t.
Edit 2023/09/09: Changed sheet size of Pokémon Prime to 10x11 (see introductory post on HeartGold & SoulSilver Series above)
Edit 2023/11/19: Changed sheet sized of Pokémon Prime to 10x10 on second thought (see introductory post above)