alanback: Apparently you are correct in your assertion. I found a number of sources calling Backgammon a perfect information game. Perfect information games are divided into two categories. Those with no luck in them, which are called predeterministic, and those with luck in them, which are called either non-predeterministic or stochastic.

The definition seems to be if you can see every move made in the game and know where every game piece is and what they can do, the game is a perfect information game.

Thank you for making me learn something today. :) Now I know.