Okay, I've given the potion problem some thought. The base one is 50 gran, or 1 and 2/3rd cards from the shop using either the packs or the lottery. Assuming the 20% is flat, that means there's an 83% chance you'll get a treasure battle you wouldn't have gotten otherwise, and a 67% chance you get two treasure battles you wouldn't have gotten otherwise. (Feel free to correct my math, I was an English major). Assuming a 50% chance of winning, and (maybe a bad idea) you are always average, you will get 2 extra treasure battles and win one of them. So, on average you are basically getting a card for 50 Gran instead of 30. Sounds like a bad deal, but the Japanese have told me that the chances of a high rarity card is much better from a treasure battle than from the lottery. So consider it a premium lottery with some extra work involved.
If any of you with a statistics degree want to redo my math with less "assuming" and more statistical sophistication, I'm all ears.
Now, I wanted to see this myself, so I checked out a random sampling of cards that you guys have gotten from lotteries and from treasure battles so far, and it looks to me like treasure battles really are better. Still, the sample size is a little small so far.
I'll see if I can get some numbers from the Japanese (sorry, I can't share them if I do!) and run some more math. If potions really are unfair, I'll petition them to change something. I wouldn't count on it though, every time I try and call them on something it turns out that they've put a lot more thought into it than I have and they make me look stupid.
"Scissors are overpowered. Rock is fine." -Paper