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 Backgammon Articles

 Probability Luck versus Skill Match Play Ratings

Probability

Dice and Shots
By Robert Townsend.

An introduction to calculating probability in backgammon. A key concept is the ability to understand how many rolls out of 36 allow you to do something you want to do. The article also looks at when you should offer and take a cube in a last-roll situation.

Dice Tables
By Sho Sengoku.

Sho Sengoku presents the table of 36 possible dice rolls and shows how to use it to count the number of rolls that achieve particular goals. Then he shows how to calculate the probability of hitting a single direct shot, a single indirect shot, and a double shot.

Introduction to Probability
By Jim Albert.

While not about backgammon specifically, this article provides an overview of probability that is useful in backgammon. It explains how to interpret odds, gives the basic rules of probability, and shows how to calculate probabilities by listing all possible outcomes.

Backgammon Probability Charts
By Ed Collins.

Charts showing the probability of entering from the bar and the chances of hitting a blot.

Dice Rolls and Probability in Backgammon
By Paul Stephens.

Understanding the true probabilities of dice rolls can greatly improve your tactical play, by letting you accurately assess the risk of leaving blots, and the chances of hitting and covering points.

Arithmetic techniques
Sho Sengoku.

Handy techniques for calculating terms that commonly come up in backgammon.

Probability and Statistics Posts
Articles on probability and statistics in backgammon. Collected postings from the rec.games.backgammon newsgroup.

Luck versus Skill

A Backgammon Gamble Pays Off
From the September 1982 issue of Games Magazine.

Is backgammon a game of skill or chance? In 1982, a U.S. court answered that question in a decision that may affect backgammon players and promoters throughout the country.

A Measure of Luck
By Douglas Zare.

Can we measure luck in backgammon? What criteria should a measure of luck satisfy? Zare defines how to measure luck in backgammon and gives some interesting properties of luck.

Luck-versus-Skill Postings
Articles about the role of luck and skill in backgammon. Collected postings from the rec.games.backgammon newsgroup.

Hedging Toward Skill
By Douglas Zare.

Zare shows how to use variance reduction to remove most of the luck from the game. This provides a way for a backgammon player (or program) to analyze games between stronger players. Zare also introduces "hedged backgammon," where you makes side-bets cancelling most of the luck of the game.

Match Play

Kit Woolsey's Match Equity Table
By Kit Woolsey.

A match equity table tells you your chance of winning the match at each different score. It is a useful tool in making doubling decisions. Woolsey's table is derived from a combination of empirical data and assumptions about gammon probability and the value of doubling potential. While it may not be totally accurate, the figures should be correct to within a percent or two. The table has proven to be of practical value, and is used by most experts today.

Double? Take? The Mathematical View
By Roy Hollands.

A quick introduction to making doubling decisions in match play. Hollands presents a match equity table and shows how to use it to estimate your take point in various match situations.

Calculating and Using Match Equities
By Stephen Turner.

Turner presents several formulas for estimating match equities at different scores, including his own formula which is noted for its easy calculation. The article goes on to give an example of using match equities to influence doubling decisions.

Match Equities: A Question of Simplification versus Accuracy
By Nigel Merrigan.

Nigel Merrigan compares three formulas for estimating match equity: Janowski's formula, Turner's formula, and his own Merrigan formula. He finds that his own formula does the best overall while still being reasonably easy to compute.

Graphical Match Equity Charts
By Sho Sengoku.

Using these charts, you can visualize important characteristics of the possible scores in a match.

How to Compute a Match Equity Table
By Tom Keith.

This article describes how a match equity table can be derived mathematically if you assume a constant gammon rate and efficient cube usage. Lots of diagrams show the process step by step.

Match Equities
Various match equity tables and formulas for estimating match equities collected from the rec.games.backgammon newsgroup.

Match Play Doubling Strategy
By Tom Keith.

In tournament play, where matches are played to a specified number of points, proper doubling strategy is different than when games are played for money. This article presents a number of the considerations a player must make when handling the cube in match play.

Match Play
Articles about doubling strategy in match play. Collected postings from the rec.games.backgammon newsgroup.

And the Trailer Doubles ...
By Anthony Patz.

Anthony Patz shows that when both players are two points away from winning the match, it can pay to double even when you are the underdog in the current game.

Match Play at 2-away/2-away
Articles posted to the rec.games.backgammon newsgroup about the correct doubling strategy when both players both have two points to go in the match.

Ratings

The FIBS Rating System
By Kevin Bastian.

How do ratings on FIBS work? This article explains the rating formula and shows how the length of the match, each player's experience, and the difference in the players' ratings affect your rating when you win or lose a match. A similar ratings system is used on many other backgammon play sites.

The Rating System on the Microsoft
Gaming Zone

By Hank Youngerman.

How do ratings work? What factors go into the ratings formula? What factors don't matter? What's the best way to increase my rating? Can ratings be manipulated?

Ratings: A Mathematical Study
By Douglas Zare and Adam Stocks.

Zare and Stocks investigate some of the properties of the ratings system used on FIBS and other backgammon servers. What is the half-life of a ratings change? How much can you expect your rating to vary over time?

Ratings Posts
Several good articles about the ratings system which have been posted to the rec.games.backgammon newsgroup.