DeckDeDungeon2 is a deckbuilder cardgame that I've recently started playing. It's quite good.
Nice graphics and sound, the required amount (not too much) Engrish in it, and heaps of free content.
Think of Hearthstone brawls/adventures, but a bit more progressive-deckbuild'y in play. Lots of challenges with specific "world" rules that change how you play, all played vs the AI. Once you figure out what all the card's "thingies" mean, you'll have no trouble at all.
You start with 20 cards in your pre-made deck, and get to choose another card out of a selection of 5 after each monster you defeat. Dungeons are made up of 15 levels (ie, monster battles), with a mini-boss or two along the way. So you slowly add cards with good abilities that synergize well with your current cards, or that give you abilities that you're lacking in.
It's 5-draw per turn (mostly), with 20 power-points to "cast" cards with, each of them having a certain PP cost. You get 10 more PP a turn, but this REALLY isn't normal. There's several forms of card draw, lowering of PP costs, upping of PP limit and upping of PP refresh all available on cards.
There's a few types of damage (normal/set/poison/burning/etc), healing, shielding, guard, draw, but it's the interactions that are important. If something does "a thing" for 5 turns, then you may have boosted over half your deck with that one card. +3 normal damage every time you heal for 5 turns? Better get healing then, so you can boost your normal attack cards for a triumphant crescendo of a smackdown finish later on. There's plenty of types of cards, most with multiple abilities, and some with certain downsides (that can turn into upsides in certain missions).
And boy do they give you cards. I've been playing for a bit over a day and I've gotten ~15 free packs of 5 cards each from all the gems they give you, plenty of gold and fame, and more from dungeons I've beaten. Actually, they give you everything for free, and lots of it. There are some pay options, but it's strictly laziness-optional.
Since the cards you get as you play through each mission are from the entire pool, you'll end up being able to use all kinds of stuff you don't actually own, even the super-duper 5-star stuff. I've gotten a few of them already for free anyway, and certain cards are just plain good in certain decks regardless of their supposed power level, but you get to try out everything at some point. Yet while there's player progression, there's no paywall or tiering. There are better cards than others, but it's all highly situational depending on your build and expected synergies.
The internal synergies available are pretty amazing too. It's one of the most satisfying deckbuilders I've ever played, because when it all works together, it's awesome. And you can't just play one style, because certain challenge missions make it suicidal. "3-draw-only, no card draw, small damage reflect" in that mission? Don't bring your PP-boosting, card-draw-engine weeny deck, it won't work. But you'll have plenty of cards to try something else, especially with your picks along the way during the mission.
There's a bit of PG-rated TNA on some of the cards, but considering that this is a Japanese card game, it's pretty tastefully done.
It's fully playable, but there are some crash issues. Early'ish development maybe? There's also no exit button that I've found, so I just task-kill it. I think it might be online only (Deck De Dungeon1 wasn't, but that is a totally different and far simpler game), so plan on that. It takes up a fair bit of space on your phone, 240mb or so, because update data doesn't go to your SD card for some reason. It sort of dies if you don't have at least 100-150mb spare after this too (deck view crash issue). The long load times completely disappear after about 3 loads, but expect 5-15 minutes while it downloads and initializes everything the first few times. It's quick for me now. 15-30 seconds tops to start up.
Anyway, despite these faults, if you like deckbuilders, give it a go. This one's good. And free. Yay!
It makes you feel like you're a genius level deckbuilder within an hour or two, and takes all that away from you with the mission-types moments later. But it's free, balanced on progression, and has the awesome level of interactions that I've wanted from a game like this for so long. There's a "1000 damage in 1 turn" reward. Strangely enough, with the right cards and the right mission, I think that's totally possible. I haven't done it yet, but ~300+ is doable by me. High level cards do ~30 damage and cost 8-10 PP. But by the end of a level my cards usually cost negative PP, out of 50-100 of them a turn. So you can see the amazing setups possible to scale crap scarily well if you want to. My cost/card draw engine deck is actually too efficient, and could use some decent damage multipliers and enhancers. It's all about the deck and the interactions within it and the mission.