Ex Emerald
Ex Emerald contains no Gold Stars, but it is the first set to contain some kind of special cards (abbreviated “SP” in my rarity table) in the reverse slot. These are the six holographic Basic Energy cards. They appear in 1 in 3 packs, with all but one of the seven boxes opened on Youtube containing exactly 12 of them, and since their holofoil pattern is totaly different from that of the reverses, they must have been printed on a separate sheet. Aside from that, each box contains on average 9 holos and 3 Pokémon-ex, leading to the following rarity table (“O” is the box topper, Farfetch’d):
Since there are 11 holos and 11 Pokémon-ex, they likely all have the same pull rate; the sample showed nothing to the contrary, either. For the rares, the raw data looks as follows (dashed line indicating wheree the transition from R9 to R8 would occur:
Three of the (not so desirable) four rare Energy cards appeared the fewest times, which is probably no coincidence. The Darkness Energy may very well be a R8 card as well, despite being one of the cards showing up the most times; the sample is too small to rule it out.
For the holographic Energy cards, Water and Psychic Energies appeared the most often, but the sample is far too small to say which two are the SP19 Energy cards.
I looked at the reverses for 4 of the 7 boxes and it looks like they were still printed on a 110 card sheet, with 21 commons appearing on the sheet twice. The table below compares the sample data to models using a 110 and a 121 card sheet:
One note of interest: Since the Pokémon-ex appeared in 1 in 12 packs, and the holo Energy cards in 1 in 3, I wondered if there was any regularity as to whether packs could contain a Pokémon-ex and a holo Energy card. The result was interesting: In three of the four boxes, all packs containing Pokémon-ex also contained a holo Energy card; in the fourth one, none did. Since not all the boxes are the same, I would consider this more of a coincidental effect from the way the cards were printed than anything intentionally planned this way.
I reconstructed the commons sheet, which shows the 7 C3 cards to all be Pokémon of which there are two common versions in the set. I looked as follows:
† Baltoy, Makuhita, Electrike (Rear Kick), Larvitar, Doduo, Ralts, Gulpin, Spoink (Knock Away), Spoink (Lunge), Whismur, Pikachu, Feebas (Water Arrow), Electrike (Double Kick), Luvdisc, Mudkip, Meditite, Duskull, Pichu, Taillow, Torchic, Zigzagoon, Swablu, Snorunt, Cacnea, Shroomish, Whismur, Rhyhorn, Numel (Collect), Treecko, Vulpix, Baltoy, Larvitar, Makuhita, Ralts, Doduo, Gulpin, Electrike (Double Kick), Luvdisc, Torchic, Pichu, Spoink (Lunge), Taillow, Mudkip, Pikachu, Numel (Stampede), Duskull, Meditite, Electrike (Rear Kick), Numel (Collect), Snorunt, Spoink (Knock Away), Voltorb, Vulpix, Zigzagoon, Treecko, Feebas (Water Arrow), Shroomish, Swablu, Cacnea, Rhyhorn, Feebas (Submerge), Pikachu, Torchic, Taillow, Larvitar, Makuhita, Gulpin, Ralts, Voltorb, Doduo, Luvdisc, Pichu, Mudkip, Baltoy, Spoink (Lunge), Whismur, Vulpix, Electrike (Rear Kick), Meditite, Duskull, Snorunt, Zigzagoon, Voltorb, Treecko, Swablu, Shroomish, Cacnea, Spoink (Knock Away), Rhyhorn, Numel (Stampede), Electrike (Double Kick), Feebas (Water Arrow), Feebas (Submerge), Larvitar, Baltoy, Makuhita, Ralts, Torchic, Taillow, Doduo, Gulpin, Luvdisc, Pichu, Meditite, Mudkip, Pikachu, Spoink (Lunge), Duskull, Zigzagoon, Numel (Collect), Vulpix, Snorunt, Shroomish, Cacnea, Treecko, Whismur, Voltorb, Numel (Stampede), Rhyhorn, Swablu, Feebas (Submerge) †
Edit 2023/05/16: Corrected a mistake in the rarity table and text: The holofoil Energy Cards are 1 in 3 packs, not 1 in 4. I also added the reconstructed commons sheet.