Shadowverse

I lost the very first one to the infamous agro-Sylvan faction, this time with a fairly standard build (maybe he had some interesting cards, but I didn't get to see them).

The free run you get is saved and continues to the next day, as long as the stage hasn't changed.

Ah, I know that. I'm more talking about situations where you know you won't be playing today and probably not tomorrow, but you want to get value not only from tomorrow's free attempt but also from today's.
The stages are interesting. It reminded me of a situation from Hearthstone, when the Arena was free for some time (= unlimited), and then it was changed to a standard format (= rotation). But even a year later (!), you could easily encounter players with Goblin and Gnome cards in the Arena, which were rotated out before the Arena's transformation. Because if you built a deck and didn't play, it would still have the old cards.