If you're wanting to actually improve over time, you'll have to drop a few. There's not enough time in the day to be a master of all trades. I'd suggest spending more time on Chess - Do a small learning component where you read a book or do some opening theory, then do a portion doing puzzles to learn tactics and spotting common positions in Chess games, then finally play some 10 minute games to put into action what you have practiced.

lichess.org's mobile version is great, you get the "play people worldwide" as well as puzzles and lessons etc, as well as the "improve over time" aspect.

Card games like spades,hearts or Gin Rummy have solid mobile versions and decent privacy.For classic arcade vibes,Tetris and pac-man still have active global leaderboards.

Man I was really hoping this was reminiscing about classic ipod games.

Anyways since no one is listing real games, I'll list 2 I enjoyed a lot.

- i dig it - zombie farm