Backgammon NJ is the strongest Android app out there, It's a very strong Nueral net. It has a tutor mode and reports your ER at end of match. It's $7.99
Alcacoops's "Backgammon Mobile" is built off of Gnu Backgammon. No Hints, tutor, or analysis, but it will connect to Fibs and Tigergammon. It plays pretty strong, but not too great with the cube. It's free and has very small adds.
And, NO, they don't cheat...they're just that good!