Opus I Statistics - What are the odds of getting a legendary foil?

According to a Kotaku article I've read, as of December 2017, there have been 3.5 million packs sold from Opus I. If we break that down, then we have a rough estimate of how many cards there are from the set. This does not include starter decks, because I do not have information on how many of those there are. Except foils. More on that later.

Based on the fact that 3.5 million packs have been sold, we can predict how many of each card there is on the fact that there are twelve cards in each pack: 7 commons, 3 rares, 1 hero/legendary (80% chance hero, 20% chance legendary), and 1 foil. This means there have been approximately 42 million cards opened since it's release into western markets. There should be:

• 24.5 million commons
• 10.5 million rares
• 2.8 million heroes
• 700 thousand legendaries
• 3.5 million foils

If we take this further, we know that there are 186 unique cards in Opus I, 216 including cards found only in starter decks. Because I don't have the figures on those, I can't even speculate on how many are out there. I would guess there are several million units sold of Opus  I starter decks.

Of the 186 unique cards, there are 78 commons, 60 rares, 34 heroes, and 14 legendaries. This means:

• of the 24.5 million commons, there are 314,102.56 each
• of the 10.5 million rares, there are 175,000 each
• of the 2.8 million heroes, there are 82,352.94 each
• of the 700 thousand legendaries, there are 50,000 each

When factoring foils, it gets complicated. I mean, if we assume an equal distribution where rarity is not a factor, then there would be 16,203.7 of each card, including those found in starter decks. However, when watching videos of Opus I booster box openings, we find a very uneven distribution by rarity.

I found 6 videos of people opening booster boxes. I could not find a video of someone opening more than a handful of packs, which means there's not enough packs to get a statistic, in my opinion. The following are openings from wave one (the very first packs, with mistakes):

1. Big Orbit Gaming:         18 C, 7 R, 5 H, 4 L, and 2 S.
2. MeatyOCore:                  17 C, 10 R, 1 H, 4 L, and 4 S.
3. PokeCastXVII:               11 C, 10 R, 9 H, 2 L, and 4 S.
4. Anti-Gravity Room:       16 C, 8 R, 5 H, 1 L, and 6 S.
5. Templar Card Gaming: 16 C, 10 R, 4 H, 3 L, and 3 S.
6. MST.TV:                           15 C, 10 R, 3 H, 2 L,, and 6 S.                

As a percentage, that's: 43% common, 25% rare, 13% hero, 7% legendary, and 12% starter. I've heard on Reddit that wave 2 increased your chances of getting legendary foils, but I haven't been able to validate that claim. But for wave one, the above should be somewhat accurate. If wave two is the same, this means there should be roughly:

• 1,505,000 common foils
• 875,000 rare foils
• 455,000 hero foils
• 245,000 legendary foils
• 420,000 starter foils

Last batch of numbers here. Assuming the above is true, we then have a basis to deduct the exact number of each card printed as foils. We simply divide the quantity of each card type by the number of cards of that type. Here's the results:

• 19,294.87 of each common
• 14,583.33 of each rare
• 13,382.35 of each hero
• 17,500 of each legendary
• 14,000 of each starter

I find it strange that there are more of each legendary foil than all other rarities, except common. But then again, there are much fewer legendaries overall (only 14 L, as opposed to 78 C, 60 R, 34 H, and 30 S).

Even though I've answered the odds of getting a legendary foil (7% chance), the odds of getting a particular legendary foil are 1 in 200. That is, if you were to open a random pack, there is a 1 in 200 chance of getting legendary Cloud as opposed to getting just any legendary. Here's for all of them:

• .55% chance of getting a particular common foil (93 by 216 by 78)
• .42% chance of getting a particular rare foil (55 by 216 by 60)
• .38% chance of getting a particular hero foil (27 by 216 by 39)
• .5% chance of getting a particular legendary foil (16 by 216 by 14)
• .4% chance of getting a particular starter foil (25 by 216 by 30)

I would like to do at least 4 more booster box openings to get a more accurate figure, so look forward for an update. I know there are a lot of collectors out there who would like to know as precisely as possible the odds of getting, say, a foil Shantotto. Feel free to send me links here, or at my Twitter.