A Puella Magi Madoka Magica mobage!
It's very cutesy, aimed at teenage Japanese girls and horny otaku boys, so I'm not likely to play very long, but I really did enjoy the anime series. If you haven't seen it yet, go watch that at the very least up to episode 4. Then it flips from "magical girls" to cute Lovecraftian horror and you'll be hooked to get to the end.
You don't play as the main characters from the anime, but entirely new characters. The main is very Madoka-like, except she took her contract, and the Homura-like Yachiyo antagonist/rival is great, a menacing rational magical girl. Kyubey is not yet a terrible existential threat.
There's the usual very long tutorial where you hit the buttons they tell you to. Eventually it lets you use the menu and go home and play around with the app. I don't even mind doing a campaign, but I want the ability to jump to home and change things, which tutorials prevent.
It's gachapon, and I haven't got enough for a 10-pull yet, so I dunno what the other characters are like. My free pull was a ★★★ tree-element flower girl, who's fine as long as she's not facing fire, which is like 50% of the fights where she's useless. I could reroll, but I never do that, I just grind a bit more.
Combat is turn-based, with 5 elements: Fire beats Tree beats Water beats Fire, and Light beats Shadow beats Light. There's a random selection of maneuvers that affect parts of an enemy formation or give bonus magia or damage, plus skills, plus
limit breaks Magia Specials.
There's no equipment? But you can power up your magical girls with various gems, which seems much the same. It's a rich character development system, for sure. There's a bit of cheesecake in the costumes, which verges on lolicon already.
It's free to play, just don't buy anything from the store if you're not into blowing money on this kind of thing; you can apparently grind out most of the content free.