PixlBit

Touch screens can wreak havoc with many genres but turn-based strategy, depending on the game, can actually be easier to play. Hoplite is a great little strategy game that plays really well. You play as a common Greek foot soldier (a "hoplite") who is descending into the underworld to retrieve the fleece of Yendor. This plays out on hex-based maps that all contain some bad guys, an altar you can receive an upgrade from, and a stairway down to the next floor. Movement is one-to-one with your enemies, which makes every turn an important strategic decision. The game seems pretty hard but fair. I've gotten down to the 7th floor before dying but to win the game you have to make to floor 16 and back. That's the quest mode but there's also a challenge mode that gives you a random assortment of upgrades. There are also daily challenges and leaderboards, if you're into that sort of thing. It's a fun game that offers good strategy in a small amount of time.

I couldn't find a launch trailer for Hoplite but here's one that shows some good gameplay. There's also a chatty guy in there for whatever that's worth.