Plague Inc.
Be a disease and kill the world! You pay if you want early access to other types of diseases, or you can play and unlock the virus, prion diseases, parasite etc. stages by beating the game. I haven't paid a penny in micro-transactions, and there's a great sense of achievement when you do unlock a stage. :)

Last Christmas I showed it to the family and pretty much everybody then went quiet as they were all playing the game. There was a great swapping of tablets and smartphones as not everyone had one.

These are a couple of my favorite

- Fallout Shelter


- Order & Chaos stuff


- Puzzles & Dragons


- Pretty much anything by Gameloft


- Grand Theft Auto any


- Tap Titans

Maybe the Trese Brothers games? I played a bit of Heroes of Steel and it was okay, but also really boring and repetitive (I have a video of the PC version here, but the mobile version is identical). Still, lots of people seem to have liked it and the other games they made. There are also Android versions of games like Braveland and other games inspired by Heroes of Might and Magic like Heroes: A Grail Quest. Rebuild and Rebuild 3 are also on Google Play and supposedly solid strategy games.

Haven't played any of that stuff beyond Heroes of Steel, personally. Turn-based strategy is an area where both iOS and Android really suffer (in my opinion), but the reviews for those are solid enough. Then again, after the terrible experience Lifeline gave me I've learned not to trust reviews, so I'd recommend doing fairly exhaustive research before diving in to any of those. People's standards when it comes to apps tend to be frustratingly lax.

you can do a trick with your phone date my friend in real life do it and it work fine ;) so you dont have to pay just change your date one day ahead :D

Pocket Tactics and Quarter to Three are sites I check as they somewhat focus on strategy and mobile.

IF you like $x TBS in space you should also check Birth of the Empires ported by a forumer.

The Bards Tale is really good on phone & tablet, it is the ARPG released by Inxile, they updated it to include the original trilogy emulated for the Apple 2

https://play.google.com/store/apps/details?id=com.inxile.BardTale&hl=en_GB

A friend of mine also released a game a few month back called Catflap, fun little game that is a great time waster, there is a free trial version of it and if you like it only costs 50 pence :

https://play.google.com/store/apps/details?id=com.japsters.cavern.catflap

Pixel Dungeon (my favourite)
Legends of Yore
Andor's Trail
Organ Trail
Robo Miner
Poll Billiards Pro
Bad Piggies

and of course..
Solitaire Free (AI Factory)
Chess Free (AI Factory)

I don't have a tablet myself and my smartphone is not good enough for games, but apart from the already mentioned "Monument Valley", a friend of mine also recommended "Duet" to me.