There have been two versions of bg_player. When first put onto FIBS, it was a hand-crafted program, not a neural net. This version was rated at around 1220 with 180 experience. At that point Jeff switched it to the first neural net version, and its rating climbed quickly. Shortly after that, he added one-ply lookahead (its move plus the opponent's replies) and "corrected some design flaws". This version is currently rated at 1405 with 480 experience.
Jeff states that the program is in an early design stage and that he expects significant development to follow. He is in the process of building a page with information about bg_player. When it's ready I'll put a link here.