One more to add to the list:
Hong Kong Style Mahjong (13 tiles) by Paul Vella is an app that plays fairly well - especially when you kick up the level of the AI. I typically play 1 or 3 point minimum hands, with the highest AI level and medium speed,. I also like using the "Extra" tileset, which looks like the tiles were photographed.
Here's the App Store link: https://itunes.apple.com/us/app/hong-kong-style-mahjong/id916388468?mt=8
There are still some minor bugs in the game. I find that there's an issue with resuming a game; it seems to put some other hand there, and the game eventually crashes. That said, when playing a game from scratch, the app seems pretty stable.
It's a free app, but there's some small fee if you'd like to remove the ads that appear after a hand is won.