Rollouts

Computers and Rollouts  By Kit Woolsey (2000). A history of using computers to roll out backgammon positions, from Expert Backgammon to TD-Gammon, Jellyfish, and Snowie. Some of the advantages and disadvantages of using computer rollouts. And a look to the future. Variance Reduction By David Montgomery (2000). Variance reduction was a breakthrough in backgammon technology. A rollout of one hundred games using variance reduction might be just as accurate as a rollout of 2500 games done without variance reduction. What is "variance reduction"? How does it work? Why does it work? Questions and Answers about Variance Reduction By David Montgomery (2000). Jake Jacobs poses several interesting questions about variance reduction in computer rollouts and David Montgomery replies. How reliable is the "equivalent games" estimate? What is a "confidence interval"? Understanding Uncertainty By Chuck Bower (2001). How to tell if your rollout results are significant. When comparing the results of two plays, each of which has an associated random uncertainty (standard deviation), a joint standard deviation needs to be calculated. Then you use a table to find out if repeating the rollout is likely to produce the same result. Sample Size and Computer Roll-Outs By DeWayne Derryberry (2002). All sampling schemes, including computer rollouts, have a common statistical issue. Are apparent differences due primarily to chance variation, or a true difference, indicative of long-run behavior? This article presents some simple rules for determining when a rollout gives enough information that we can say one move is better than another. Articles on Rollouts By Tom Keith. Information on using and interpreting computer rollouts of backgammon positions. From the Backgammon Galore Forum Archive.

Analyzing Positions

Nordic Open Seminar 2004 By Karsten Nielsen (2004). For the Nordic Open 2004 I was asked to do the seminar and comment the finals live. The subject of the seminar was how to systemize your errors into groups. EMG Woes: Toward a More Consistent Normalization of Match-Play Errors By Jeremy Bagai (2007). EMG is a way of expressing match-winning chances (MWC) in a normalized form for easier comparison at different match scores. This article examines the history of the EMG normalization, highlights some dramatic inconsistencies within it, and discusses what might be involved in a new normalization which avoids those problems.

Programming

Temporal Difference Learning and TD-Gammon  By Gerald Tesauro (1995). TD-Gammon was the first computer program to achieve a level of play close to the best human players. The brains of the program is a neural network that was able to learn to play well by playing many times against itself and learning from the results. This article was originally published in Communications of the ACM, March 1995. Practical Issues in Temporal Difference Learning By Gerald Tesauro (1992). This paper is a predecessor to Tesauro's TD-Gammon article above. It examines whether Sutton's TD(lambda) algorithm can be used to train a neural network to play backgammon. Tesauro found that with zero built-in knowledge a TD(lambda) trained network is able to learn to play the entire game of backgammon at a fairly strong intermediate level. This article was originally published in Machine Learning journal. Reinforcement Learning: An Introduction By Richard S. Sutton and Andrew G. Barto (1998). The online version of a book published in 1998 by MIT Press. It covers learning techniques which can be applied to backgammon programs. One section describes Tesauro's TD-Gammon program. "One of the most impressive applications of reinforcement learning to date is that by Gerry Tesauro's to the game of backgammon." Motif Backgammon Player Engine By Tom Keith (1996). Motif is a Java Applet that you can play against on the internet. Here are some notes on how Motif chooses the moves it makes and how it learned to play. The Making of Bob's Backgammon By Bob Landwehr (2000). An overview the genetic algorithms used in Bob's Backgammon, and how they evolved through natural selection to improve over many generations in competition with other algorithms. The Neural Net Backgammon Programs By Jay Scott (1998). A survey of many of the top backgammon programs and how they work. "These programs excel at strategic and positional judgment; they are less skilled in technical positions such as bearing in against an anchor." Part of the web site Machine Learning in Games. Programming Backgammon By Tom Keith. Many articles on tips and techniques for programming backgammon. From the Backgammon Galore Forum Archive.

Computer Dice

Official Backgammon Software Complaint Form By Gary Wong (1998). Form to fill out if you feel your backgammon software is cheating you or the site you are playing on has biased dice. Does Your Bot Cheat? By Bill Robertie (2006). Why do people think bots cheat? Many are beginners who have never played serious backgammon. But they have managed to win a few sessions against friends and are convinced they are very fine backgammon players. This image is shattered the first time they play a decent backgammon program. Proving Your Bot Doesn't Cheat By Bill Robertie (2006). You don't have to take my word for it that bots don't cheat. The two best-selling commercial backgammon bots, Jellyfish and Snowie, both contains tools that allow you it to prove to yourself (if you're suspicious). Online Backgammon Dice By Hank Youngerman (2001). In the many years I have played online, there have been repeated allegations that online dice are somehow not random. I have never found this to be the case. I'd like to devote this article to a discussion of the reasons people believe this, and the facts. FIBS dice analysis By Patti Beadles (1995). Do doubles on FIBS occur much more frequently than expected? There was speculation that this might happen if both players were using automatic rolls and moves. Patti investigates to see if this is true. GamesGrid FAQ: Random Number Generator By GamesGrid (2005). What random number generator does GamesGrid use? How are the dice rolls generated? How Rolls Are Generated at GammonSite By GammonSite (2004). How the dice are generated. Why people see patterns in dice rolls. Common misconceptions about dice rolls in backgammon. Jellyfish 3.5 Dice Algorithm By Fredrik Dahl (1998). This memo explains how Jellyfish generates the random dice throws that it displays, and how you can verify that the dice are not generated to benefit the computer. Computer Dice Postings By Tom Keith. The most common and persistent theme of postings to rec.games.backgammon has to do with whether various backgammon programs cheat with their dice. Here is a small selection of those posts. (As far as I know, the dice in all major backgammon programs and on all backgammon play sites are random and fair.)

Gnu Backgammon

All About Gnu Backgammon  By Albert Silver (2006). Gnu Backgammon is a very strong computer program for playing and analyzing backgammon matches. It is available free for anyone to download and use. Albert Silver's guide takes you through all the features of the program and shows you how to use them. This is the best documentation available for the program. Getting started with GnuBG, a Guided Tour By Robert-Jan Veldhuizen (2006). GnuBG is a program that plays backgammon and analyzes matches. This tutorial shows you how to download GnuBG and install it on your computer, how to play a game against the program, and how to analyze your matches. Gnu Backgammon FAQ By Wiki. Answers to frequently asked questions about Gnu Backgammon. What it is? Where do I get it? How do you use it? Gnu Backgammon Manual By Wiki. Detailed information on using Gnu Backgammon: Introduction; Playing a game or match; Evaluation settings; Setting up a position; Working with matches; Rollouts; Customizing Gnu Backgammon; Advanced topics; Appendix. Articles on Gnu Backgammon By Tom Keith. Various articles and pointers on how to use Gnu Backgammon. From the Backgammon Galore Forum Archive.

Snowie

Snowie Home Page By Snowie Group. Snowie is the second commercial neural-net backgammon program. Snowie 4: Back to the 80s By Albert Silver (2002). Some observations on how Snowie 4 compares with its predecessor, Snowie 3. Snowie 4 seems to be far surer of itself in many positons where Snowie 3 was unable to give a confident evaluation. Primes and Snowie 4 By Johannes Levermann (2002). How Snowie was improved to recognize primes better. It was possible to trick Snowie 3 into a certain kinds of positions because it was some missing some information for its neural network. It could only recognize primes up to the 12-point and Snowie 3 very rarely saw a prime from the 7 to the 12-point during its training. Snowie Parameter Settings By Chuck Bower (2001). How do the various settings (lookahead, truncation, bearoff database, live cube, search space, and play according to score) affect the time it takes to do a rollout in Snowie? Articles on Snowie Backgammon By Tom Keith. Articles and pointers on using Snowie Backgammon. From the Backgammon Galore Forum Archive.

Other Bots

Bgblitz Home Page By Frank Berger. One of the strongest neural-net backgammon players and analyzers. Jellyfish Home Page By JellyFish AS. Jellyfish was the first commercial neural-net backgammon program. Articles about Jellyfish By Tom Keith. Comments, questions, and answers about the Jellyfish backgammon program. From the Backgammon Galore Forum Archive. Programs that Play and Analyze Positions By Tom Keith. Articles about programs that play and analyze backgammon games and matches. From the Backgammon Galore Forum Archive.

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Last updated: 11 Jul 2008