Burning Shadows
For this set, as shown in my introductory post to the Sun & Moon series, I will be assuming 4.0 “regular” Pokémon-GX 1.1 full art Pokémon-GX and 1.3 full art Trainers/secret rares; on this last sheet, each of the 22 secret rares is assumed to be printed 3 times. This leads to the following rarity table:
For the non-holo rares, it appears Lycanroc and Alolan Ninetales, which are featured as theme deck exclusive holos, are artificially short-printed. The raw data for the various sheets is shown below (dashed lines indicating where the transition from H10 to H9, etc., would occur):
I reconstructed the commons and uncommons sheets. The commons sheet looks as follows (the dagger marks indicate it is unclear where it begins and ends):
† Magikarp, Croagunk, Pikachu, Pansear, Charmander, Alolan Rattata, Porygon, Panpour, Pansage, Espurr, Sawk, Noibat, Stufful, Mudbray, Tynamo, Oddish, Duskull, Morelull, Caterpie, Marill, Rhyhorn, Sandygast, Hoothoot, Tangela, Dewpider, Inkay, Ralts, Crabrawler, Sneasel, Venipede, Horsea, Cutiefly, Ledyba, Alolan Grimer, Riolu, Meowth, Alolan Vulpix, Wimpod, Togedemaru, Croagunk, Pansear, Magikarp, Mudbray, Alolan Rattata, Panpour, Caterpie, Porygon, Sawk, Oddish, Charmander, Marill, Pansage, Espurr, Pikachu, Noibat, Dewpider, Tangela, Rhyhorn, Riolu, Cutiefly, Tynamo, Duskull, Inkay, Stufful, Crabrawler, Morelull, Sandygast, Venipede, Horsea, Mudbray, Ledyba, Hoothoot, Alolan Vulpix, Ralts, Alolan Grimer, Sneasel, Charmander, Crabrawler, Meowth, Stufful, Pansage, Croagunk, Pikachu, Panpour, Cutiefly, Pansear, Magikarp, Alolan Rattata, Wimpod, Togedemaru, Sawk, Mudbray, Oddish, Duskull, Espurr, Morelull, Charmander, Porygon, Marill, Hoothoot, Rhyhorn, Ralts, Tangela, Tynamo, Crabrawler, Inkay, Ledyba, Caterpie, Sandygast, Venipede, Sneasel, Alolan Vulpix, Horsea, Noibat, Alolan Grimer, Riolu, Cutiefly, Dewpider, Togedemaru, Wimpod, Meowth †
And this is the uncommons sheet:
† Guzma, Whirlipede, Tormenting Spray, Simisage, Kirlia, Heatmor, Weakness Policy, Po Town, Rotom Dex, Simisear, Electabuzz, Lana, Metapod, Porygon2, Kiawe, Olivia, Bouffalant, Charmeleon, Rhydon, Noctowl, Mount Lanakila, Simisear, Dusclops, Acerola, Bodybuilding Dumbells, Seadra, Gloom, Lunatone, Wicke, Wishful Baton, Ribombee, Sophocles, Escape Rope, Rotom Dex, Seviper, Super Scoop Up, Simipour, Plumeria, Solrock, Guzma, Eelektrik, Wobbuffet, Whirlipede, Charmeleon, Seadra, Lunatone, Rhydon, Kiawe, Olivia, Kirlia, Ribombee, Po Town, Weakness Policy, Heatmor, Tormenting Spray, Lana, Seviper, Gloom, Acerola, Wobbuffet, Charmeleon, Porygon2, Simisear, Metapod, Dusclops, Noctowl, Simisage, Eelektrik, Bouffalant, Escape Rope, Wicke, Mount Lanakila, Wishful Baton, Solrock, Simipour, Bodybuilding Dumbells, Sophocles, Electabuzz, Super Scoop Up, Rotom Dex, Seadra, Plumeria, Lunatone, Olivia, Kirlia, Ribombee, Guzma, Whirlipede, Simisage, Weakness Policy, Porygon2, Po Town, Dusclops, Charmeleon, Tormenting Spray, Lana, Heatmor, Simisear, Kiawe, Mount Lanakila, Electabuzz, Noctowl, Simipour, Bouffalant, Eelektrik, Rhydon, Bodybuilding Dumbells, Metapod, Wishful Baton, Acerola, Gloom, Escape Rope, Solrock, Ribombee, Sophocles, Seviper, Wicke, Wobbuffet, Seadra, Plumeria, Super Scoop Up †
Edit 2024/02/25: Added info that my model for Ultra Prism does in fact use a sequence length of 360 packs instead of 180, though that for Burning Shadows continues to use 180.
Edit 2024/03/24: Increased sequence length from 180 to 360; changed box ratios for full art Pokémon and full art Trainers/secret rares from 1.0 and 1.4, respectively, to 1.1 and 1.3, respectively. Also removed a bunch of unnecessary information from the text.
Edit 2024/04/06: Added reconstruction of uncommons sheet.