This app was mentioned in 23 comments, with an average of 1.48 upvotes
The problem with this and all CCG/TCG whether digital or physical is the very foundation of the business model is p2w.... (they can still be a lot of fun!)
That is besides a few exceptions like - Hidden Dimensions 3 - offline and singleplayer only, 100% free.
And Epic Card Game - physical and soon to be Android & iOS. Pay once and own all the cards.
Great thread.
Hidden Dimensions 3 - single player CCG with over 500 cards, free, no ads and no iap.
Onirim - single player card game with set collection and puzzlelike mechanics. Free game with no ads.
Hidden Dimensions 3. It isn't the prettiest game, but the gameplay is great. Several different races, and campaign challenges for each one. I've been playing it on and off for years.
https://play.google.com/store/apps/details?id=net.nulll.hd3.android
Admittedly, I've barely played most of them, so I can't give anything really useful.
Shadowverse is the one I've put the most time into. It's a Hearthstone-like with less RNG, but I've never played HS. There are seven characters and they each have their own cards they can use (with an eighth Neutral faction). The story cutscenes are voice acted and so are the cards. You are able to Evolve your cards after a certain amount of turns and you have only so many Evolve Points, so there's some strategy in that. Last I heard, the online was dominated by Dragon/Shadow meta, but I haven't done that either. Or played anyone but Forestcraft for the first couple of story missions. Still stuck but I have a lot more cards now.
I haven't played it yet, but Hidden Dimensions 3 is supposed to be pretty robust, offline, and zero IAPs.
Mage VS Mage is kinda interesting. You sacrifice cards to increase your maximum mana, and then you play a card on one of the 12 spaces on your field to intercept enemy attacks and attack the enemy leader. The game helpfully tells you what to do for each step of combat, though it takes a little getting used to for the mechanics (I think there was a tutorial though). World of Mages by the same dev is a little different. You have six mana colors that +1 every turn, and you're allowed to play one card provided you meet that card's cost. There are only five panels on each side to attack or intercept. You gain stars for winning and can use those for passive benefits.
Triple Triad is...not by Square Enix and it's got a lite version of FF8's combat system as well as the actual card game in it, for what it's worth.
Both DeckDeDungeon games are dungeon crawlers using cards, but I can't seem to get the second one to successfully load at all.
Shadow Keep isn't on the Play Store anymore, but it was kinda interesting. You have three elements used to play cards with them regenerating each round, and then you have your tower and a wall on the left with the enemy's wall and tower on the right. Cards that do only damage will hit the wall first before hitting the tower, but some only damage the wall, some only the tower, and some do different things like damaging and healing your wall/tower and so on. I haven't gotten far in it but it's pretty simple to understand it seems.
It's not in the picture, but I used to play a bit of Autoraid several months ago. A card game with an idler, set up a team and have them try to conquer a dungeon while you watch them succeed or fail. There are several races and several jobs are shared between them, but they differ by skills. There are different rarities of cards too and naturally the rarer, the better. Some fights needed specific loadouts of cards, so it might not be possible to steamroll the game with a deck of Legendaries.
I played Androminion for the first time last night and I got my ass kicked because I wasn't sure what to do. You sacrifice treasure cards to be able to buy from a community pile, and use those cards to fight/defend yourself and buy properties for Victory Points. I'll probably need to play a lot to figure out a strategy here.
Hidden Dimensions 3 completely free singleplayer CCG
Star Realms
and
Race for the Galaxy
are not CCG's but they are card games that offer great multiplayer.
Hidden Dimensions 3 is a lesser known, space themed single player ccg
https://play.google.com/store/apps/details?id=net.nulll.hd3.android
Personally, I like CCG games made by nullvoid
http://www.kongregate.com/games/nulllvoid/hd-xyth flash version
and latest game on steam http://store.steampowered.com/app/531540/
android https://play.google.com/store/apps/details?id=net.nulll.hd3.android