Backgammon is a two-player, perfect information game of skill and luck. Its large branching factor (number of different position the game pieces can be in after each turn) means that it can't be solved by simply reasoning through all possible moves, and the uncertainty of dice rolls means that probabilities and contingencies must be factored into strategies.
Check out the Github repo for an implementation of TD-Gammon with TensorFlow. A few weeks ago AlphaGo won a historic tournament playing the game of Go against Lee Sedol, one of the top Go players in the world. Many people have compared AlphaGo to DeepBlue, which won a series of famous chess matches against Gary Kasparov, but a different comparison may be made for the game of backgammon. Before DeepMind tackled playing Atari games or built AlphaGo there was TD-Gammon, the first algorithm to reach an expert level of play in backgammon. Gerald Tesauro published his paper in 1992 describing TD-Gammon as a neural network trained with reinforcement learning.