Editing Backgammon (section)

== Studies and analysis ==

[[Image:GNU bg screenshot.png|thumb|240px|A screen shot of GNU Backgammon, showing an evaluation and rollout of possible moves]]

Backgammon has been studied considerably by computer scientists. [[Artificial neural network|Neural networks]] and other approaches have offered significant advances to software for gameplay and analysis. With 15 white and 15 black counters and 24 possible positions, backgammon has 18 quintillion possible legal positions.<ref name="UKBGF 2014">{{cite web | title=Developing Positional Awareness | website=UKBGF | date=2014-01-03 | url=https://ukbgf.com/developing-positional-awareness/ | access-date=2022-09-26|quote=There are 18,528,584,051,601,162,496 distinct backgammon positions.}}</ref>

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 game positions. Early versions of BKG played badly even against poor players, but Berliner noticed that its critical mistakes were always at transitional phases in the game. He applied principles of [[fuzzy logic]] to improve its play between phases, and by July 1979, BKG 9.8 was strong enough to play against the reigning world champion [[Luigi Villa]]. It won the match 7–1, becoming the first computer program to defeat a world champion in any board game. Berliner stated that the victory was largely a matter of luck, as the computer received more favorable dice rolls.<ref name="berliner-acm">{{cite journal|last=Berliner|first=Hans|title=Backgammon program beats world champ|journal=ACM SIGART Bulletin|issue=69|date=January 1980|pages=6–9|doi=10.1145/1056433.1056434|s2cid=36222242}}</ref>

In the late 1980s, backgammon programmers found more success with an approach based on [[artificial neural network]]s. [[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.<ref name="tesauro-acm">{{cite journal|last=Tesauro|first=Gerald|url=http://www.research.ibm.com/massive/tdl.html|title=Temporal difference learning and TD-Gammon|journal=Communications of the ACM|volume=38|issue=3|date=March 1995|pages=58–68|doi=10.1145/203330.203343|s2cid=8763243|doi-access=free}}</ref> According to assessments by [[Bill Robertie]] and [[Kit Woolsey]], TD-Gammon's play was at or above the level of the top human players in the world.<ref name="tesauro-acm"/> Woolsey said of the program that "There is no question in my mind that its positional judgment is far better than mine."<ref name="tesauro-acm"/>

Tesauro proposed using [[Rollout (backgammon)|rollout analysis]] to compare the performance of computer algorithms against human players.<ref name="Tesauro2002"/> In this method, a [[Monte Carlo method|Monte-Carlo evaluation]] of positions is conducted (typically thousands of trials) where different random dice sequences are simulated. The rollout score of the human (or the computer) is the difference of the average game results by following the selected move versus following the best move, then averaged for the entire set of taken moves.

Neural network research has resulted in three modern [[Proprietary software|proprietary programs]], JellyFish,<ref>{{cite web|url=http://www.backgammon.help/software.html|title=Backgammon software - Backgammon Online Guide|website=www.backgammon.help|access-date=2015-08-10|archive-url=https://web.archive.org/web/20150816163340/http://www.backgammon.help/software.html|archive-date=2015-08-16|url-status=dead}}</ref> Snowie<ref>{{cite web|url=http://www.bgsnowie.com|title=BackgammonSnowie - World class poker coaching software|website=www.bgsnowie.com}}</ref> and [[eXtreme Gammon]],<ref>{{cite web|url=http://www.extremegammon.com|title=eXtreme Gammon|website=www.extremegammon.com}}</ref> as well as the [[shareware]] BGBlitz<ref>{{cite web|url=http://www.bgblitz.com|title=BGBlitz|publisher=BGBlitz|access-date=2009-02-26|archive-url=https://web.archive.org/web/20090225122525/http://bgblitz.com/|archive-date=25 February 2009|url-status=live}}</ref> and the [[free software]] GNU Backgammon.<ref>{{Cite web|title=GNU Backgammon|url=https://www.gnu.org/software/gnubg/gnubg.html|access-date=2022-12-29|website=www.gnu.org}}</ref> These programs not only play the game, but offer tools for analyzing games and detailed comparisons of individual moves. The strength of these programs lies in their neural networks' weights tables, which are the result of months of training. Without them, these programs play no better than a human novice. For the bearoff phase, backgammon software usually relies on a database containing precomputed equities for all possible bearoff positions. There are 54,263 bearoff positions for each side. This means there are 54263<sup>2</sup> total bearoff positions (~3 billion positions). In 1981 Hugh Sconyers wrote a computer program that solved all positions with nine checkers or fewer for both sides.  In the early 1990s Hugh extended his results to all bearoff positions. For each position there are four results: no cube, roller's cube, center cube and opponent's cube. So, Hugh's bearoff database contains the exact answers to ~12 billion bearoff situations.

Another neural network software developed by Nikolaos Papachristou is Palamedes that was developed in the early 2000s and it can also play variations like Hypergammon, Portes, Plakoto, Fevga, Narde and has multiple engines for each one.<ref>{{Cite web|title=Palamedes |url=https://nikpapa.com/Palamedes/}}</ref>

Computer-versus-computer competitions are also held at [[Computer Olympiad#Backgammon|Computer Olympiad]] events.