If you're looking for a very strong computer AI, our app, Backgammon NJ, plays on the level of GNU Backgammon (an open source desktop program that plays at world-class levels). It also includes features that can help you learn to play better by showing you the best moves to make in each situation. Backgammon NJ is relatively new, first released on 9/1/09.
I liked your post, so I bought it. $4.99 is really pricey though for a backgammon game. I would suggest a firesale, even though I realise it's a new app and it's hard to compromise when it's your sweat and tears.