I've a soft spot for card solitaires, not least because they tend to be close to the infinite game ideal. Archimedean Solitaire presents a simple variant, relying on your ability to recognise card pairs that add up to '13', but it's nicely implemented, with only one gotcha at the end....
Here's Archimedean Solitaire in action:
There's an animated tutorial at the start, showing you the general scoring system and idea - essentially, you have to manipulate and tap on card pairs that add up to 13 (Kings get dismissed on their own).
Strategy comes in where you have several options - the idea then is to uncover cards that you think you might need next. Cards from the draw and waste pile can also be used as needed, but when the draw pile is empty, you have to 'deal again'. Run out of deals and it's game over.
As you might expect, there's a lot of luck involved, but also some strategy and the main goal, that of amusing yourself in some downtime, is accomplished. Oddly, I found one quirk in that when the game was over and I was left with no options left and no deals left, the game didn't step in to tell me - it was left to me to remember my score and also restart the game in order to start again. Hopefully the developer will fix this in an update!