Although your conclusion is correct for most decks in general, there are some decks, like this Pokémon-e Starter Deck, which are a bit odd in that regard. If you take a look at its Bulbapedia page, you will see the following:
So the Deck contained 9 cards from the ‘deck’-set of 29. And 8 cards from (the first 32 cards of) the Base Expansion Pack set.
This information on Bulbapedia also explains why we see the starter Pokémon probably more often.
Assuming only 50 unlimited edition versions of this Deck have indeed been released, dividing everything equal there should be the following amounts of each card:
- 8⅓ Decks will contain one of the six possible Starter Evolution lines from the ‘deck’-set of 29
- All 50 Decks will contain the five Trainer cards from the ‘deck’-set of 29
- 4 Decks will contain 8 of the 32 other cards of the regular set, divided among the 50 decks
Considering @thecardcenter already owns four Cyndaquil and three Chikorita from the 8⅓ available, and I’ve seen the Chikorita at least three times before in unlimited edition from other sources (one can be seen in a picture on page 2), I think there might be more than fifty Decks out there, OR (perhaps more likely) the random Decks had more of one evolution line than another in their randomly generated decks.
All and all I see my chances of getting an unlimited edition E1 Pikachu pretty slim if there are indeed just 4 out there, considering I’ve already seen two pictures from different sources online, and I know a fellow Pikachu collector who has one as well.
So for my sake, I hope there are a lot more. Regardless of how many there really are, they are definitely the rarest unlimited edition Japanese cards and very hard to find (especially for a specific card like the Pikachu I’m looking for), although the WCP and L2/L3 sets, and some of the BW/XY-era sets perhaps, are pretty hard to track down in unlimited edition as well.
Greetz,
Quuador