Backgammon

Backgammon -- Literature and Variants
compiled by Michael Keller

Thanks for assistance to Jerry Bailey.

The standard international game of backgammon is the most popular version of a group of related games sometimes called Tables. These games are remarkably consistent in being played on a board of 24 points, with 15 checkers per side. In a few older versions three dice are thrown per turn instead of two. Usually the 15 checkers per side begin off the board or piled up on a single starting point (one of the mysteries of backgammon is how, where and when the starting arrangement of today was developed). Movement also varies: in some versions players start in opposite corners and move in the same direction. Another major difference is hitting of blots: some variations do not allow landing on a point occupied by even one enemy checker; others allow a single enemy checker on a point to be landed on and pinned.

What is the essence of backgammon? What sets it apart from Pachisi and other race games? I think that the answer lies in the fact that a true backgammon variant needs a large number of checkers on each side (at least a dozen) in order to carry out the sophisticated blocking strategies which make backgammon so much more than a simple race game. Another element of the better variants of backgammon is that the sides move in opposite directions along what is essentially a one-dimensional track, with one side entering where the other side bears off. This leads to double-edged endgames of a kind which don't occur in any other game I can think of; the best-known such position is Le coup classique, with (say) Red, bearing off, having their last three checkers on their two point, and Black with a lone checker on Black's one point -- depending on what Red rolls next, the result can be anything from a Red backgammon to a win by Black.

Le coup classique: Red is forced to leave two blots

Backgammon is the rare race game which transcends pure dice-rolling and running. The doubling cube and the gambling element certainly have added to its enormous popularity, but it is a superb game even without them. Although it is a two-player game, the chouette allows many players to participate (both the chouette and the doubling cube are ideas which can be applied to other games).   A backgammon set requires a board, 15 pieces for each player, two dice for each player, two dice cups, and a doubling cube (a cube whose sides are marked with the numbers 2-4-8-16-32-64). A good backgammon board should be just the right size for six pieces to fit comfortably side by side on each half of the board, with a raised railing around the outside and a raised bar dividing the board in half. Most decent sets consist of a case which folds open to reveal the board, and closes with a latch to hold the components when not in use.   The modern case with trays to hold borne-off pieces (and store them when not in use) was patented in 1935 by Arthur Popper. Cardboard folding boards (like those found on the backs of many dime store checkerboards) are very poor for playing backgammon properly.

Modern Backgammon

The modern game of backgammon is actually a variant itself, based on the doubling cube.   This is a cube marked with numbers on each side (2, 4, 8, 16, 32, 64), which starts each game in the middle of the bar, turned to 64 (which represents 1 when it is in the center). Either player may, before rolling, offer to double the point value of the game by turning the cube to the next higher number and giving the cube to the opponent.   The opponent may resign the game at the current stake (drop) or accept (take) and take possession of the cube, continuing play at the increased value. Once a game has been doubled, only the player who last accepted (who is said to own the cube) can redouble. However, the game can be doubled any number of times as long as the doubles are offered in alternation.   The doubling cube, as a device to keep track of the current stake, might have been invented by Grosvenor Nicholas, who wrote the first modern book on backgammon in 1928, or W. Whitewright Watson, an early champion in 1925.   The idea of doubling itself may have come from older versions of the game, or from contract bridge.

A standard rule in tournament match play is the Crawford Rule: when a player reaches a score one short of victory (e.g. 24 points in a 25-point match), the opponent cannot double in the next game, This is sensible, as it gives the leader one game to close out a match without the game being doubled (after that, the lead is essentially cut in half, as the trailing player has no reason not to immediately double in every remaining game).

The chouette, which originated with backgammon, is a method of turning a two-player game into a multi-player game.   One player (said to be in the box) plays against all of the remaining players, headed by a player called the captain. The players on the team are ranked in an order (usually initially selected by lot) which determines how soon they will become captain. The captain has final say in the plays his team makes, but his teammates are free to discuss the situation, offer suggestions, and even try to talk the captain out of the move he has chosen. The player in the box wins or loses one point for each player opposing him (with the usual multipliers for doubles and gammons). If he wins, he remains in the box, the captain moves to the bottom of the team, and everyone else moves up in line (the player second in line becoming captain). If the man in the box loses, the captain takes over the box, and the loser moves to the bottom of the team as before. The winner at the end of a series of games is the player who is positive by the greatest number of points. Another way of playing with multiple players is the non-consulting partnership, in which each side of a two-player game is played by a team of two or more players, who make moves in rotation without discussing the situation with their teammates.

Backgammon was a well-known game long before the 20th century: Edmond Hoyle himself wrote a short booklet on the game in 1744, and almost every Hoyle up to the present has a short section on backgammon.   The doubling cube helped spark a gigantic craze in the late 20's, peaking in 1930 (at least a dozen books were published that year alone), but fizzling out a few years later.   Nevertheless it was one of the biggest game or puzzle fads of the 20th century, perhaps rivalled only by the Canasta boom of 1950 and the Rubik's Cube craze of 1980. Backgammon came into vogue again in the late 1970's; this boom lasted quite a bit longer, into the 1990's.   Possibly the rise of poker (especially Texas Hold'em) contributed to its decline, but it never went completely out of fashion as it did in the mid-1930's.   The internet has sparked another surge in recent years, with a new string of books on advanced strategy, helped by advanced computer analysis.

A Personal Viewpoint

I played very actively during the 1980's backgammon boom, and bought and read every book I could get my hands on.   Eventually the emphasis on money, and several bad experiences, turned me away from active play (I am not personally enthusiastic about gambling).   Frankly I am perfectly happy to play without the doubling cube at all, although there is no question it adds a strategic element to the game in matches.

Historical Variants (Tables)
Many early ancestors of backgammon were closer to pure race games: they used three dice, and started with all of the pieces off the board. See Salaamallah for accounts of many older variants.

Fayles is a three-dice version with each player having 13 checkers already on their six point, and the other two on the opponent's one point (perhaps the first inkling of the modern setup).   It had an unusual rule: a player who could not play all three numbers rolled, lost immediately.   Other rules were as modern backgammon.

Trictrac is a very strange forerunner of backgammon, a complicated game where hitting opposing pieces in particular ways, and making certain patterns of pieces on the board, scores points. David Levy has a detailed account.

Regional Variants
In most regional variants, players roll one die to see who moves first, but the winner rolls two dice again instead of playing the combined roll, so playing a double on the first turn is possible, unlike international backgammon.   Both gammons and backgammons count double (i.e. backgammons do not count triple).

In Iran (Takteh) and Turkey (Tavla), backgammon is played today by rules very similar to the standard international game, with the following exceptions: the player winning the opening roll does not play the two numbers rolled, but instead rolls again, so doubles are possible on the first move.   A checker which hits in its own home board cannot move again on the same roll (it can be covered).   When bearing off, pips cannot be wasted unnecessarily: a checker which can be borne off directly using the larger number cannot be moved forward with the smaller number and then borne off; it must be borne off first and the smaller number then played with another checker. There is no doubling cube, and backgammons count the same as gammons.

Tavla 1

               Tavla: Red cannot play 6-2*-1                                     Tavla: Red cannot play 6-5-off

Eureika
Bearing off practice for children. Each player starts with two checkers each on their 6,5,4 points and three each on 3,2,1.   A game of almost pure luck.

Blocking games
Moultezim (Fevga, Gioul, Narde, Tawla 31, and Tawula are regional subvariants)
Each player starts with 15 checkers on one point, diagonally opposite. Movement is anticlockwise: Black's first, second, third, and fourth quadrants correspond to White's third, fourth, first, and second. There is no hitting; a single checker (or more) on a point prevents the opponent from landing there.   As in regular backgammon, a player may begin to bear off once all their checkers are in their home quadrant.    A short article by John Mamoun on Fevga is available on Internet Archive; his full-length book was published in 2018 and is in print.

Gioul is a variant of Moultezim in which extra moves are given for doubles: a player throwing doubles plays that number four times, then each higher number four times, as long as possible.   If a player cannot complete all the moves up to 6-6-6-6, the opponent can play the remainder (as far as possible), then take a normal turn.   This obviously adds an enormous amount of luck.

Jacquet
The first checker moved (courier) must reach your home board before all other pieces can move.

Pinning games
Plakoto (Mahbooseh, Tsilido, and Tapa are regional subvariants)
Each player starts with 15 checkers on one point. Movement is as in backgammon (clockwise for one player, anticlockwise for the other).   There is no hitting, but a single checker on a point can be landed on by the opponent, pinning it (more checkers of the same color can also land on the pinned piece). The pinned checker cannot move until the opponent moves all of the covering checkers.

In Greece, matches (called Tavli) are played to a given number of points, consisting of three different games (Portes, Plakoto, and Fevga) played in succession, as many times as needed.   Portes is the Greek form of backgammon, played without a doubling cube and counting double for gammon, but not triple for backgammon. Players roll for first move, but the winner rolls again instead of playing the combined throw.

Saitek used to manufacture a handheld backgammon computer which played, in addition to the standard game, several alternate forms of backgammon: Jacquet, Tric Trac, and Moultezim.

Variants of the Modern Game

Positional variants

Acey-Deucy -- popular variant in the U.S. Navy. All pieces start off the board and enter in the opponent's home board (any pieces can be moved once entered, no matter how many are still off the board). 1-2 is a special roll which allows the player to play a normal 2-1, then play any number four times, then roll again.

Blast-off -- simplified variant invented by Oswald Jacoby and John R. Crawford, and published in their book.   The two checkers usually on each player's 24 point are placed instead on their 13 point.   Blots cannot be hit. It can help players learn when to double (and accept) in running games.

Hypergammon -- a miniature form of backgammon with only three checkers per player, starting on the 1,2,3 points in the opponent's home board.   It uses the doubling cube, but gammons and backgammons count only in doubled games (Jacoby Rule).   Hugh Sconyers programmed a computer to play perfectly, by calculating the equity value of every one of the more than 7 million possible positions. Tom Keith's Backgammon Galore has a detailed study of the game.

Longgammon -- Each player begins with all 15 checkers on his 24 point.

Nackgammon -- Nack Ballard modified the standard opening position, placing two checkers on each player's 23 point (the opponent's 2 point), and removing a checker from each player's 13 and 6 points. This is popular as a side event in tournaments, usually played with no doubling cube and with no gammons or backgammons counting.

Snake -- White starts in the normal position; Black has nine men on the bar and two each on White's first three points. It was designed as practice in playing (both sides of) back games.

Metavariants

Bazooki-Gammon -- Each player may call their dice roll once during each game. Another popular side event (my source is the flyer for the 1991 Midwest Backgammon Championships) played without a doubling cube or gammons.

Choose Roll vs. Double Roll -- a folk variation posted at least twice on the Usenet group rec.games.backgammon. One player is allowed to call any non-double dice roll every turn as their roll; the opponent gets to roll and play normally (including doubles) twice per turn.   Kit Woolsey posted that the double rool player is supposed to have a slight advantage.

Destructo -- (source: 2003 Boston Open flyer) Each player, once per game, may play the opponent's roll for them.

Duplicate -- adapted from contract bridge, and tried in both the 1930's (see Nicholas and Vaughan) and again in the 1970's during the second backgammon boom. It can be played two on two, or with a large field of players, with every game being played with the same dice rolls.   Unfortunately, it does not appear to work well (unlike bridge), as the positions diverge too quickly, so that the throws have completely different effects in different games (it is discussed in the book by Cooke and Orleans).

Exacto -- (source: 2003 Boston Open flyer) Bearing off must be by exact count (e.g. you must throw a two or 1-1 to bear off a checker from your 2 point).   In addition, the winner of the opening roll may reroll and play the new roll (including doubles), and any player throwing doubles plays and rolls again (as in Monopoly).

Misère -- like many games, backgammon (in most of its variants) can be played to lose, even with doubling and gammon bonuses if you prefer.   It can be a long-winded game.

House Rules

Many people play that a point may contain a maximum of five pieces. This doesn't effect the game much until the bearoff phase.    This is a standard rule in the Mexican variant of Acey-Deucy.

Turning a game of skill into a gambling game
A notable court case in 1982, Oregon v. Barr, resulted in a ruling that "backgammon is a not a game of chance but a game of skill".   Ted Barr, a noted player and writer, was arrested on gambling charges after running a tournament. He called expert witnesses, including Paul Magriel, and after four days, Judge Stephen Walker ruled in Barr's favor.   There is indeed a great deal of skill in backgammon, both in checker play and doubling, but all of the optional rules below heavily decrease the skill of the game and turn it into more of a gambling game.

Automatic doubles -- if both players roll the same number when rolling for first move, the doubling cube is turned to 2, but remains in the center available to both players.   This was a common house rule in the earliest days of modern backgammon, but even early writers like Nicholas and Hattersley disapproved, Hattersley correctly states (p. 38 of How To Play The New Backgammon) "... this automatic double, unlike the optional double, detracts from the science of the game ...".

Beavers (and other animals) -- a player who accepts a double may immediately redouble without giving up the cube (the player who just doubled may resign the game at the doubled stake).   Even more extreme variants are raccoons (immediate redouble by the first doubler) and higher redoubles with varying names.   Even more extreme is the Woodpecker.

Jacoby Rule -- gammons and backgammons only count as single games if the cube is still at 1.   Apparently almost universal in money games. It is not used in match play (e.g. tournaments). Supposedly introduced to speed up play, but a fatuous rule which reflects badly on the legendary games expert Oswald Jacoby.
(1) Why are you playing backgammon if it's boring? Even a long game is usually less than ten minutes.
(2) Back games are one of the most skillful aspects of backgammon, and often result in gammons and even backgammons.

Notable Computer Programs (currently available)

BGBlitz (Frank Berger, 1998)
Strong current program.

BKG 9.8 (Hans J. Berliner, 1979)
Early program by a well-known chess programmer.   Won an exhibition match 7-1 against Luigi Villa, who had won the World Championship the previous day. (This was the first victory by any game-playing program against a world champion.) Later analysis showed that Villa played better but had poorer dice rolls. BKG, however, made better cube decisions.

eXtreme Gammon (Xavier Dufaure de Citres, 2009)
As of 2012 this was rated as the strongest commercial program, in both checker and cube play.

GNU Backgammon (collective)

Jellyfish (Fredrik Dahl, 1995)
The first of the commercial NN programs (followed soon after by Snowie) to be used by top players to evaluate positions and develop new strategies.   One of the first programs to use automated rollouts to evalute different moves in a position.

Mloner (Harald Wittman, c. 1996)
Private NN program which was one of the top-ranked players on the First Internet Backgammon Server (FIBS).

Motif (Tom Keith)
Online program running in Java, which is not supported on present-day browsers.

MVP Backgammon (Justin Boyan, 1992)

Palamedes (Nikolaos Papahristou, 2024)
Freeware program which supports regional variants including Plakoto and Fevga, as well as modern variants like Nackgammon and Hypergammon.   Available for Windows and Android.

Silicon Highlands (Bob Landwehr)

Snowie (Olivier Egger and Johannes Levermann, 1997)
Another commercially released NN program with rollouts, among the strongest programs around the turn of the century.

TD-Gammon (Gerald Tesauro et al., 1992) -- the first backgammon program to use a neural network (NN), playing 1-1/2 million games against itself to teach itself how to play. It led to later NN programs Jellyfish and Snowie, all of which helped to reveal new strategies for the game which were quickly adopted by top human players. TD stands for Temporal Difference, a machine learning technique, which was later used by the chess program Deep Blue.

Commercial Variants

Four-handed variants with names like Quadro-Gammon and Multi-Gammon were published in 1931 during the backgammon boom.   Similar designs appeared in the 1980's and 1990's, along with many other commercial variants.

Nannon -- Nannon Technology Corporation, 2004
A miniature form of backgammon with three checkers per side, played on a board of only six points and one die per player.   Still in production, but the website is identified as not secure.

7-Sider Dice -- invented by Bernard Bereuter, bb Games Academy, 1992
   These are among the most unusual dice in the world: pentagonal prisms with seven sides. They are carefully designed to have equal chances for all seven sides to come up. Bereuter has designed several games using these dice. 7-Gammon is a backgammon variant played on a 28-point board, with 17 men per side. The 7-sided dice make it slightly harder to hit blots and easier to reenter from the bar, rewarding aggressive play.    [I have experimented with a similar variant played with octahedral (8-sided) dice and 20 men per side on a board 32 points long.]

Distant Relatives

Counterstrike -- Essex Games, 1978
Makhbusa
Marrakesh isn't really a backgammon variant, but we mention it here since it uses the bearing-off phase of backgammon as a mechanism.
Wykersham -- $38 from Land's End ?????

Bibliography

The literature of a game or puzzle enters an advanced stage of development when it progresses beyond general works, to books and articles on specialized aspects of the game. For example, chess and checkers books evolved from general manuals to detailed studies of openings, endgames, middle game tactics, positional play, and the like. Bridge books likewise progressed to the study of particular types of bids (doubles, preemptive bids) and card play (squeezes, opening leads). Backgammon entered this stage with the publication of books devoted to openings, endgames, back games, doubling strategy, etc.

1. Standard Backgammon

Hoyle, Edmond -- A Short Treatise on the Game of Back-Gammon, 1753, Ewing, 47pp.
Probably the first book in English on backgammon as we know it today, though without doubling (Charles Cotton's 1674 The Compleat Gamester has about a page, with an odd scoring variant, and warnings about "false dice").

Older Books from the 1930's craze

"Bar Point" -- Backgammon Up to Date, 1931, De La Rue, 53 pp.
Bond, Ralph A. -- Beginner's Book of Modern Backgammon, 1930, Sears, New York, 95 pp., hardback
Readable online at HathiTrust. (The publisher J.H Sears is apparently unrelated to the co-founder of Sears and Roebuck.)
Hattersley, Lelia -- How To Play The New Backgammon, A New Revised Edition, 1930, Doubleday, 136 pp., hardback
Longacre, John -- Backgammon of Today, 1930, John C. Winston, 1973, Bell, 132 pp., hardback
Nicholas, Grosvenor, and C. Wheaton Vaughan -- Winning Backgammon, Problems and Answers, 1930, D. Appleton, 103 pp., hardback
Possibly the first-ever book of problems.
Thorne, Harold -- Backgammon Tactics, 1931, E.P. Dutton, 80 pp., hardback

Introductory Books

Ball, Baron Vernon -- Alpha Backgammon, 1980, William Morrow, 224 pp., paperback, ISBN 0-688-08714-0, $5.95
   The author won the 1976 World Championship in the Bahamas.   The majority of the book is a reasonable strategy guide.   The last section attempts to show how you can win by controlling the dice with your mind.   Some reviewers took this seriously, others thought it ridiculous. Out of print and now rather pricey.
Becker, Bruce - Backgammon for Blood!, 1974, E.P. Dutton
   Much derided, particularly in its recommendations for opening moves.   I share his disdain, however, for the Jacoby Rule.
Bray, Chris -- Backgammon For Dummies, 2009, John Wiley & Sons, 259 pp., paperback, ISBN 978-0-470-77085-6, $14.99
Carter, Donald -- Backgammon: How To Play And Win, 1973, 1978, Holloway House, 247 pp., paperback, ISBN 0-87067-616-4, $2.00
Clay, Robin -- Backgammon, 1977, Teach Yourself, 164 pp., paperback, ISBN 0-340-22233-6, £1.75
Cooke, Barclay, and Jon Bradshaw -- Backgammon : The Cruelest Game, 1974, Random House, 210 pp., paperback, ISBN 0-394-73243-X[P], $5.95
Crane, Michael -- Teach Yourself Backgammon, 2006, Hodder, McGraw-Hill, 166pp., paperback, ISBN 0-07-148260-1, $10.95
New version of the Teach Yourself series, including some positions analyzed by Snowie.   Useful references, including software and websites.
Genud, Lee -- Lee Genud's Backgammon Book, 1974, 1975, Cliff House (Price/Stern/Sloan), 158 pp., paperback, ISBN 0-8431-0342-6
Deyong, Lewis -- Playboy's Book of Backgammon, 1977, Playboy, 295 pp., paperback, ISBN 0-87223-522-X
Dor-El, David -- The Clermont Book of Backgammon, 1975, Winchester, 147 pp., paperback, ISBN 0-87691-307-9, $6.95
Goren, Charles H., [Charles Papazian, Technical Consultant] -- Goren's Modern Backgammon Complete, 1974, Cornerstone, 192 pp., paperback, $2.95
Heyken, Enno, and Martin Fischer -- The Backgammon Handbook, 1989, 1990, Crowood, 232 pp., ISBN 1-85223-402-4
Holland, Tim -- Backgammon for People Who Hate to Lose, 1977, David McKay, 153 pp., hardback, ISBN 0-679-50652-7
Jacoby, James Oswald, and Mary Zita Jacoby -- The New York Times Book of Backgammon, 1973, Plume (Quadrangle), 175 pp., paperback, $2.95
Jacoby, Oswald, and John R. Crawford -- The Backgammon Book, 1970, Galahad Books (Viking), 224 pp., hardback, ISBN 670-14409-6
[Jacoby, Oswald, and John R. Crawford -- The Backgammon Book, 1970, Bantam, 244 pp., paperback, ISBN 0-533-13090-0, $2.95]
Kansil, Prince Djoli -- Backgammon!, 1974, Victoria, 80 pp., paperback
Lawrence, Michael S. -- Winning Backgammon, 1973, Pinnacle, 239 pp., paperback, ISBN 0-523-00860-4, $1.95
Obolensky, Prince Alexis, and Ted James -- Backgammon: The Action Game, 1969, Macmillan, 171 pp., hardback, $6.95
Reese, Terence, and Robert Brinig -- Backgammon: The Modern Game, 1976, Cornerstone, 141 pp., paperback, ISBN 346-12311-9, $2.95
Thompson, Dave -- Play Backgammon Tonight, 1976, Gambler's Book Club, 61 pp., paperback, ISBN 911996-58-3, $2.95
Tremaine, Jon -- The Amazing Book of Backgammon, 1996, Chartwell, 128 pp., hardback, ISBN 9780785805687
Woolsey, Kit, and Patti Beadles -- 52 Great Backgammon Tips, 2007, Batsford, 144 pp., paperback, ISBN 978-0-7134-9064-0, $12.95

Problem Collections

Cooke, Barclay -- Paradoxes and Probabilities: 168 Backgammon Problems, November 1978, Random House, 184 pp., hardback, ISBN 0-394-50126-8, $8.95
   A book whose reputation has suffered in the age of computerized rollouts.   Many of the solutions given by Cooke are now regarded as wrong, some badly so.
Dwek, Joe -- Backgammon For Profit, 1975, 1978, Scarborough, 191 pp., paperback, ISBN 0-8128-2313-3, $4.95
Holland, Tim -- Better Backgammon, 1974, Reiss, 122pp., hardback, ISBN 0-679-50501-6
Collection of 64 problems and variations.
Kansil, Prince Joli -- The Backgammon Quiz Book, 1978, Playboy Press, 288 pp., paperback, ISBN 0-872-16491-8, $2.50
112 problems, each with three different rolls to play.
Robertie, Bill -- Advanced Backgammon, 1984, Robertie, 298 pp., paperback, $30
Robertie won the World Championship himself in between his first two books.
[short review in WGR4:] Bill Robertie's second book on backgammon is a collection of problems. What sets this book apart from earlier problem books is the depth of the explanations of each problem, and the way in which the problems are connected together with general discussions into a coherent whole, which makes the book a textbook (in the mold of Paul Magriel's Backgammon) rather than just a problem collection. Robertie gives 241 problems, divided into twelve categories, along with quite a few tables and explanations of how to calculate various probabilities. Problem 28 is particularly interesting. Next to a diagram of the opening position, the problem reads "Black to play the opening roll." Instead of forcing his own recommendations on the reader, Robertie gives the results of a survey among 16 of the best players in the world. But he didn't get the results by asking them -- he compiled them from studying transcripts of actual tournament games played by each player.

Robertie, Bill -- 501 Essential Backgammon Problems, 2000, Robertie, 376 pp., paperback, ISBN 1-58042-019-2, $19.95

Tzannes, Nicolaos S., and Basil Tzannes -- How Good Are You At Backgammon?, 2001, Writers Club Press, 113 pp., paperback, ISBN 0-595-17462-9, $9.95
50 problems covering all stages of the game, including doubling.

Woolsey, Kit, and Hal Heinrich -- New Ideas In Backgammon, 2000, Gammon Press, 336 pp., paperback, ISBN 1-880604-10-8
The first problem collection where the solutions are verified by computerized rollouts.   104 problems are given, which the authors also posed to a panel of 8 experts. Detailed explanations of the best move in each position are given.   The last chapter gives statistics on the results of each move, as well as the number of experts who chose each move.

Advanced Strategy

Ballard, Nack, and Paul Weaver -- Backgammon Openings, Book A; 2007, The Backgammon Press, 126 pp., hardback, ISBN 978-0-9797053-0-4
First of a projected series covering every roll(!). The first volume covers the opening roll 3-1, with computer-backed recommendations on how to play 3-1 on the first three rolls, and general principles for later rolls.

Barr, Ted -- Barr on Backgammon, 1981, Writing Works, 202 pp., hardback, ISBN 0-916076-52-0
A collection of 90 columns from the author's regular feature in the Seattle Times.

Kleinman, Danny -- Vision Laughs At Counting with Advice to the Dicelorn, 1980, Kleinman, 2 volumes, 438 pp. total, single sided, paperback, $64
Kleinman, Danny -- Wonderful World of Backgammon, 1981, Kleinman, 132 pp., single sided, paperback, $18
Kleinman, Danny -- Meanwhile, Back At the Chouette, 1981, Kleinman, 142 pp., single sided, paperback, $20
Kleinman, Danny -- Double Sixes From The Bar, 1982, Kleinman, 135 pp., single sided, paperback, $19
Kleinman, Danny -- Is There Life After Backgammon?, 1983, Kleinman, 148 pp., single sided, paperback, $21
Kleinman, Danny -- How Can I Keep From Dancing?, 1983, Kleinman, 134 pp., single sided, paperback, $19
Kleinman, Danny -- The Dice Conquer All, 1984, Kleinman, 228 pp., spiral bound, $33
Kleinman, Danny -- How Little We Know About Backgammon, 1985, Kleinman, 168 pp., spiral bound, $25
Kleinman, Danny -- The Other Side of Midnight, 1986, Kleinman, 142 pp., spiral bound, $20
Kleinman, Danny -- But Only The Hogs Win Backgammons, 1991, Kleinman, 244 pp., spiral bound, $37
Kleinman, Danny -- A Backgammon Book For Gabriel, Kleinman, 1994, Larry Strommen, 144 pp., spiral bound
Kleinman, Danny -- Long Road to Gammon, Kleinman, 1995, 2003, 2007, Larry Strommen, 176 pp., spiral bound

Magriel, Paul -- Backgammon, 1976, Quadrangle (New York Times), 404 pp., hardback, ISBN 0-8129-0615-2
Still regarded by many as the definitive strategy guide.

Olsen Marc Brockmann -- Backgammon: From Basics to Badass, 2015, Olsen, 319 pp., paperback, ISBN 978-1512200447, $40

Trice, Walter -- Backgammon Boot Camp, 2004, Fortuitous Press, San Francisco, 339 pp., paperback, ISBN 0-943292-32-8, $40

Wachtel, Bob -- In the Game Until the End: Winning in Ace-Point Endgames, 1993, The Gammon Press, 103 pp., paperback, $25

Ward, Jeff -- Winning Is More Fun, 1982, Aquarian, 1988, Larry's Gammon Press, 164 pp., spiral bound
Ward, Jeff -- The Doubling Cube in Backgammon, Vol. I, 1982, Aquarian, 186 pp., paperback, ISBN 0-9609884-2-4, $24.95

Woolsey, Kit -- How To Play Tournament Backgammon, 1993, The Gammon Press, 50 pp., paperback, $20

Annotated Games

Cooke, Barclay, and René Orléan -- Championship Backgammon : Learning Through Master Play, 1980, Prentice-Hall, 338 pp., hardback, ISBN 0-13-126102-9, $19.95
Robertie, Bill -- Lee Genud vs. Joe Dwek: The 1981 World Championship of Backgammon, 1982, Robertie, 172 pp., paperback
Robertie, Bill -- Backgammon for Serious Players, 1997, 2003, Cardoza, 250 pp., paperback, ISBN 1-58042-077-X, $19.95
Five games played through and fully annotated.

Magazines

Backgammon Times

Chicago Point -- Bill Davis, ed., monthly, 6-12 pages, June 1988-January 2012 (236 issues)
The entire run of the magazine is available online.

Inside Backgammon -- Bill Robertie, 1991-1998

Leading Edge Backgammon -- Roy Friedman, 1991-1992?

Flint Area Backgammon News -- Carol Joy Cole, 1978-??

2. Historical and Regional Variants

Mamoun, Dr. John S. -- Plakoto Board Game Strategy. 2017, CreateSpace, 220 pp., paperback, ISBN 978-1976223761, $7.99
Mamoun, Dr. John S. -- Fevga or Moultezim Board Game Strategy. 2018, CreateSpace, 334 pp., paperback, ISBN 978-1723972379, $12.99

Salaamallah the Corpulent -- Medieval Games, 1982, Third Edition, 1995, Jeff DeLuca, 203 pp., spiral-bound
Comprehensive survey of traditional board games, including a survey of Tables, a family of games which was the forerunner of modern backgammon. Two dozen variants are described, played with a similar board and usually 15 checkers per side. At least one variation uses three dice instead of two.

Schmittberger, Wayne -- New Rules For Classic Games
Chapter 11, Beyond Backgammon, pp. 159-168, covers the doubling cube and chouettes, then moves on to a few historical and regional variants.

Tzannes, Nicolaos, and Basil Tzannes -- Backgammon Games and Strategies, 1977, A.S. Barnes, 267 pp., hardback, ISBN 0-498-01497-5, $9.95
   The first chapter describes standard backgammon (which the authors have dubbed Hit).   The next two chapters describe Plakoto and Moultezim, which they declare to be much better and deeper games than standard backgammon.   They also describe the much lighter variant Gioul.

Frantzis, Nicholas -- The Seven Popular Games of Backgammon, 1979, Exposition Press, 136pp., hardback, ISBN 0-682-49295-7
Out of print and rare.   The author describes: standard backgammon, Plakoto, a game of his own invention called the Never Finishing Game (players may either hit or pin opposing single checkers: a combination of backgammon and Plakoto), Gioul, Moultezim, Acey-Deucey, and the Blocking Express game.   [How can a game be popular before it is ever published?]

3. Modern Variants

Abak Evolution Backgammon is an unusual modern variant (invented by Samy Garib) with five new classes of checkers with special powers (Druid pins as in Plakoto, Guard can only be captured by two men or another Guard, General can move backward, etc.). The interactive website has a tutorial and allows you to play online against computer or human opponents.

Greenacre, David -- American-Backgammon, The Game and Its Rules, 1990, 59pp., spiralbound, ISBN 0-9693690-X
Bizarre, complicated, and long-winded variant by an inventor who admits he found the regular game boring.   Many rolls are excessively powerful; high luck factor.   A new edition (83pp.) was published in 1997, but the trademark was not renewed and also expired in 1997.   Copies exist in the Smithsonian Library and the Library and Archives Canada.   ISBN search comes up empty.

Molyneux, J. du. C. Vere -- Begin Backgammon, 1997, 1984, 2002, Elliot Right Way Books, 126 pp., hardback, ISBN 0-71602075-0
Chapter 10, The Tables' Family, describes Moultezim and Ghioul. Chapter 11, Experiments on the Backgammon Board, describe two variants designed by Matt Crispin:
(1) Tiles, where dominoes are used to determine the rolls. The 21 non-zero dominoes are distributed between the players, either randomly, or according to a balanced formula. Each domino can be played once, then the non doubles are exchanged between the two players (doubles are out of play for the rest of the game once played).
(2) Grasshopper, a diceless abstract game only distantly related to backgammon. Details are in the book, which can be viewed online.

Websites

Tom Keith's Backgammon Galore is the best information site on backgammon, with many articles on the standard game, including an up-to-date tutorial on opening rolls, links to other pages, a detailed page on variants, and transcripts of older books from the 1930's.

The Gammon Press is one of the major backgammon publishers, owned by two-time world champion and leading author Bill Robertie (also an expert in chess and poker).   They publish books by Robertie and other authors, and from 1991-1998 published Inside Backgammon, one of two major magazines devoted to backgammon theory.