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Backgammon,
a turn-based two-player tables board game of chance and strategy with 15 checkers each on a board of 24 spaces or points. One moves according to rolls of a pair of dice, trying to bring own checkers home and bear them off before the opponent does [1]. Opponent checkers can be "hit" and returned to the start.

Backgammon programs were pioneered in the late 70s by Hans Berliner with focus on smooth evaluation, and by Gerald Tesauro from the late 80s, who successfully applied Neural Networks and Temporal Difference Learning to his Backgammon playing programs. Computer backgammon is regularly played at Computer Olympiads, organized by the ICGA [2].
A Backgammon Set [3]

Computer Olympiads


Photos

Backgammon2015.jpg
18th Computer Olympiad 2015, Backgammon medalists: Frank Berger (Bronze for BGBlitz),
Nikolaos Papahristou (Gold for Palamedes), and Nardy Pillards (Silver for GNU Backgammon) [4]

Evaluation

In the late 70s at Carnegie-Mellon University, Hans Berliner developed the Backgammon playing program BKG 9.8 for the PDP-10 to research the principles of evaluation for another game than chess with a much higher branching factor of more than 800 at every node [5]. Early versions of BKG played badly even against weak players, but Berliner noticed that its critical mistakes were always at transitions apparently due to evaluation discontinuity. 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 [6] [7].

Learning

In the late 80s, IBM researcher Gerald Tesauro pioneered in applying Neural Networks to Backgammon - first within his program Neurogammon, which won the Gold medal at the 1st Computer Olympiad 1989 - and further improved by TD-Lambda based Temporal Difference Learning within TD-Gammon [8].

Publications

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Forum Posts


External Links


Computer Backgammon

Backgammon Programs


References

  1. ^ Backgammon Galore
  2. ^ Backgammon (ICGA Tournaments)
  3. ^ A backgammon set, consisting of a board, two sets of 15 checkers, two pairs of dice, a doubling cube, and dice cups, Image by Ptkfgs, March 6, 2013, Backgammon from Wikipedia, Wikimedia Commons
  4. ^ 18th Computer Olympiad - Day 6 Photos by Jan Krabbenbos
  5. ^ Hans Berliner (1977). Experiences in Evaluation with BKG, a Program That Plays Backgammon. IJCAI, 1977, hosted by Backgammon Galore
  6. ^ Hans Berliner from Wikipedia
  7. ^ Hans Berliner (1980). Backgammon Computer Program Beats World Champion. Artificial Intelligence, Vol. 14
  8. ^ Richard Sutton, Andrew Barto (1998). Reinforcement Learning: An Introduction. MIT Press, 11.1 TD-Gammon
  9. ^ The hillclimbing HC-Gammon from Machine Learning in Games by Jay Scott
  10. ^ Plakoto from Wikipedia

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