Backgammon NJ HD
https://itunes.apple.com/us/app/back...371380665?mt=8
XG Mobile Backgammon
https://itunes.apple.com/us/app/xg-m...536774050?mt=8
I have read that these two are among the best. They will both beat you, but only because they are just that good.
Caveat: I don't own an iPhone or iPad, so you should take these recommendations with a grain of salt.
Mike