The Backgammon Guide

Backgammon has been studied considerably by computer scientists. Neural networks and other approaches have offered significant advances to software both for gameplay and analysis.The first strong computer opponent was BKG 9.8. It was written by Hans Berliner in the late 1970s on a DEC PDP-10 as an experiment in evaluating board positions. Early versions of BKG played badly even against poor players, but Berliner noticed that its critical mistakes were always at phase changes. He applied principles of fuzzy logic to smooth out the transition between phases, and by July 1979, BKG 9.8 was strong enough to play against the ruling world champion Luigi Villa. It won the match, 7-1, becoming the first computer program to defeat a world champion in any game. Berliner states that the victory was largely a matter of luck, as the computer received more favorable dice rolls.Berliner, Hans, et. al. "Backgammon program beats world champ", ACM SIGART Bulletin, Issue 69. January 1980. pp 6-9.

Each side of the board has a track of twelve long triangles, called points. The points are considered to be connected across one edge of the board, forming a continuous track analogous to a horseshoe, numbered from 1 to 24. Each player begins with two checkers on his 24-point, three checkers on his 8-point, and five checkers each on his 13-point and his 6-point. The two players move their checkers in opposite directions, each from his own 24-point toward his 1-point. Robertie, Bill. Backgammon for Winners, Third Edition. 2002.
Points 1 to 6 are called the home board or inner board, and points 7 to 12 are called the outer board. The 7-point is referred to as the bar point and the 13-point as the mid point.Hoyle's Rules of Games, Eighty-second printing. 1983 Movement
At the start of the game, each player rolls one die, and the player with the higher number moves first. The players then alternate turns, rolling two dice at the beginning of each turn.After rolling the dice a player must, if possible, move checkers according to the number of pips showing on each die. For example, if he rolls a 6 and a 3 (noted as "6-3") he must move one checker six points forward, and another checker three points forward. The same checker may be moved twice as long as the two moves are distinct: six and then three, or three and then six, but not all nine at once. If a player rolls two of the same number (doubles) he must play each die twice. For example, upon rolling a 5-5 he must move four checkers forward five spaces each.
A checker may land on any point that is either unoccupied or is occupied only by a player's own checkers. It may also land on a point occupied by exactly one opposing checker; such a lone piece is called a blot. In the latter case, the blot has been hit, and is placed in the middle of the board on the bar, the divider between the home boards and the outer boards. A checker may never land on a point occupied by two or more opposing checkers, thus, no point is ever occupied by checkers from both players at the same time.

Backgammon has been studied considerably by computer scientists. Neural networks and other approaches have offered significant advances to software both for gameplay and analysis.The first strong computer opponent was BKG 9.8. It was written by Hans Berliner in the late 1970s on a DEC PDP-10 as an experiment in evaluating board positions. Early versions of BKG played badly even against poor players, but Berliner noticed that its critical mistakes were always at phase changes. He applied principles of fuzzy logic to smooth out the transition between phases, and by July 1979, BKG 9.8 was strong enough to play against the ruling world champion Luigi Villa. It won the match, 7-1, becoming the first computer program to defeat a world champion in any game. Berliner states that the victory was largely a matter of luck, as the computer received more favorable dice rolls.Berliner, Hans, et. al. "Backgammon program beats world champ", ACM SIGART Bulletin, Issue 69. January 1980. pp 6-9.

In the late 1980s, creators of backgammon software began to have more success with an approach based on neural networks. TD-Gammon, developed by Gerald Tesauro of IBM, was the first of these programs to play near the expert level. Its neural network was trained using temporal difference learning applied to data generated from self-play.Tesauro, Gerald. "Temporal difference learning and TD-Gammon", Communications of the ACM, 38:3. March 1995. pp 58-68. According to assessments by Bill Robertie and Kit Woolsey, TD-Gammon plays at or above the level of the top human players in the world.