## The cost of a gammon

Most intermediate players, and many championship level players, do not truly understand how gammons affect their cube decisions. Maybe this will help shed some light on the subject for you.

We take or drop cubes based on the relative risk of winning and losing the game, and the relative risk of winning and losing gammons and backgammons. Basically, when we are doubled, we have two jobs: first, to make these estimates based on the position of the checkers on the board, and second, to factor in the match score to determine if this is a time we should take more or less risks than normal because of the score.

At any match score, every opponent has a “take-point.” The take point is that number that separates the proper takes from the drops. Since money game is always the same…around a 25% take point, most players use that as their basis for comparing cube decisions.

In a money game, the reason your take point is around 25% is because if you play 100 games where you are doubled, and you take them all, you will break even if you win 25% of the games you take. So if you are in a position that you think you would win 33% of the time, you are much better off taking than dropping…in the long run, you’ll lose less money.

The 25% number, however, does not consider gammons and backgammons. If you will win 25% of the games from a given position, but many of the 75% that you lose will be gammons, then it is foolish to take the cube. It is a big drop.

There is a “price” you pay for gammons, and in a money game, statistically, that price is .5 times the cube. In other words, if you think you would win 33%, but you get gammoned 26% of the time when you lose, you have to multiply the 26 by .5 to get 13, and that is your net loss from gammons. So you subtract 13 from 33, and that gives you 20, and since 20 is less than 25%, you should drop.

It’s not quite that simple, because you have to add back the price of gammons for the number of times you migh gammon your opponent. So in the above example, let’s say that you might win a gammon 10% of the games, you multiply that times .5 and that’s 5, and when you add the 5 back on to the 20, you are right at 25% and you can take the cube. (Most of the time we don’t estimate backgammons unless there is a clear, serious backgammon threat, because they are so rare.)

So that is the calculation that really top players do in their heads when they are doubled. Often experts don’t have to go through all of the estimates and numbers and match because most of the time they are doubled, the position is not that unusual and they can get a pretty good idea as to whether it is a take a drop just from having experienced playing similar positions so many times in the past. They have “reference” positions that help them decide.

Match play gets much more complex, as the take points vary depending on the score, and the price of gammons also vary depending on the score. Many top players do not know all these numbers…they are fairly complex and there are many numbers to learn, and even when you learn them, it is often tough to make accurate estimates of wins and losses and gammons over the board. But the very top players know these numbers and do these estimates very well…that’s one of the major reasons they are top players.

The secret is out…top backgammon players aren’t just people who are truly gifted at playing the game of backgammon—they are people who have studied the game and learned the numbers and also have the skills to remember them and apply them accurately over the board. Do you want to be a top player some day? You will have to study. No matter how talented you are, you need to have an excellent understanding of take points and the price of gammons in order to be a top player.

## Updated opening moves in backgammon

With the aid of the modern computer programs, there is now little doubt or debate about the opening moves in backgammon.

Here is the latest update (anno 2008)

6-5 run a back checker

6-4 There are 3 acceptable plays. You can make your two point; you can run a back checker all the way out to your 14 point; I prefer runnint a back checker out to your opponent’s bar (24-18), and then bring down one checker off your midpoint (13-9).

6-3 There are two plays: you can run a checker all the way off your 24 point; I prefer to run to your opponent’s bar and bring one down from your midpoint.

6-2 Two plays: run all the way; I prefer running to your opponent’s bar and bring one down 13-11.

5-4 Two plays: move a back checker up (24-20) and bring one down (13-8), or bring two down from the midpoint (13-8, 13-9). Most of the time it is right to play 24-20.

5-2 Two plays: I prefer to move a back checker 2 (24-22) and bring one down (13-8), or bring two down (13-8, 13-11)

5-1 Generally, it is right to split the back checker and bring one down (24-23, 13-8).

4-3 This move has the most possible variation, depending on score, but generally, the experts agree that it is best to move up 3 off your back point (24-21) and bring the 4 down (13-9). I like to bring both checkers down from my 13 most of the time.

4-1 Generally, it is right to split the back checker and bring one down (24-23, 13-9), but it is not a bad gambling play, when gammons are key, to bring one down and slot your 5 point.

3-2 This play also has many variations, but generally the experts agree that the best play is to bring you back checker up 3 (24-21) and bring a 2 down from the midpoint (13-11). I prefer to bring two down from the 13 point.

2-1 Two possibilities: split your back checkers (24-23) and bring one down (13-11); I prefer to play 13-11 6-5 and slot my 5 point.

The match score affects many of these opening moves, and the greatest difference depends on whether it is important to win or save gammons at a particular score.

## Opening Moves in Backgammon

There are two very important things you should know about opening moves in backgammon

The experts, having studied opening moves for many years, and having the benefit of experience, the use of advanced computer programs, in combination with tremendous personal skill and intuition, have basically all agreed on what are the best opening moves for every possible dice combination.

If you any move other than the ones that the experts recommend, you are reducing your chance of winning the game and match.

Its that simple. You must memorize the best opening moves, and play them. Of course it will help you greatly to also understand the reason behind each move, and it will help you to also go to the next step and know and understand what the experts recommend you do on the “next” roll in response to opening moves if/when your opponent gets the opening rolls. And of course , none of that will be of much help unless you understand how to play for the rest of the game.

But since it is impossible to learn the entire theory of how to become a backgammon expert from a single article, let me offer some help regarding the opening moves.

There is no question what to do with 3-1, 6-1, 4-2, 6-5. How to play these opening moves has been agreed to for a number of years, and the correct plays are correct for ANY match score, whether you are winning or losing by a little or a by a lot, or tied. For all other moves, there is some debate; there are some different plays depending on the score; and the decision is not less clear.

Let’s take care of the definite ones first. With 3-1 you create your 5 point. Not only do most experts agree that the 5 point is the most important point to make (for a multitude of reasons), but any other 3-1 play exposes you to an unnecessary chance of getting hit.

Why is getting hit so bad, especially early on in the game? Because one of the overriding principles of backgammon is that every game, no matter how complex, ends up as a race to see who can get his checkers around the board and bear off first.

Everything else that happens between the first roll and the removal of the last checker is just preparation for who the one is that gets to remove that last checker. Even games that end as a result of a double/drop are because the dropper determined that he is less likely to be the one removing their last checker first.

With 6-1 you make your bar point (7 point) as that is the second most important point, and again, any other move leaves exposed blots (single checkers on a point). With 4-2 you make your 4 point because that is also an important point, and again, you don’t want to be leaving blots. And with 6-5 you simply run a back checker all the way because it is very good for the race and again, you do not leave any exposed blots.

There used to be a lot of debate about how to play an opening of 5-3. Many experts in the 70’s and 80’s believed that making the 3 point was wrong. That they were better off making several other moves that provided them with more “flexibility” and put their checkers in better strategic places for the next move.

The problem with the others moves, however, is this :

First, it leaves exposed blots, and if hit, gives the opponent an immediate advantage, and second, an opportunity to make the 3-point has been passed up, and the 3-point, while not as critical as the bar, 5, and 4 points, is still a very good point to have. The experts of the new millennium virtually all agree with each other that it is right to make the 3 point with your 5-3, regardless of what the score is.

Here is the list of standard opening moves in backgammon with variations

6 – 5 run a back checker

6 – 4 There are three acceptable play in this situation. You can make your two point; you can run a back checker all the way out to your 14 point; you can run a back checker out to your opponent’s bar (24-18), and then bring down one checker off your midpoint (13-9).

6 – 3 There are two plays: you can either run a checker all the way off your 24 point, or you can run to your opponent’s bar and bring one down from your midpoint.

6 – 2 Two plays: run all the way, or run to the bar and bring one men down

6 – 1 Create your bar

5 – 4 Two plays: move a back checker up (24-20) and bring one down (13-8), or bring two down from the midpoint (13-8, 13-9)

5 – 3 Make your 3 point

5 – 2 Two plays: move a back checker 2 (24-22) and bring one down (13-8), or bring two down (13-8, 13-11)

5 – 1 Generally, it is cnsidered right to split the back checker and bring one down (24-23, 13-8). When behind in the match and a gammon win is a major plus, you might bring one down and slot your 5-point (13-8, 6-5).

4 – 3 This move has the most possible variations, depending on score, but generally, the experts agree that it is best to move up 3 off your back point (24-21) and bring the 4 down (13-9).

4 – 2 Create your 4 point.

4 – 1 Generally, it is right to split the back checker and bring one down (24-23, 13-9), but it is not a bad gambling play, when gammons are key, to bring one down and slot your 5 point.

3 – 2 This play also has many variations, but generally the experts agree that the best play is to bring you back checker up 3 (24-21) and bring a 2 down from the midpoint (13-11).

3 – 1 Make your 5 point

2 – 1 Split your back checkers (24-23) and bring one down (13-11). Here again, if you wish to gamble, bringing one down and slotting your 5 point is not a bad play.

Conclusion

Will you win more often if you make the above opening moves? Yes, you will. It has been proven, statistically.

With the aid of computer programs (Snowie and Jellyfish) we can take any move or position and play out thousands, and even millions of games to “prove” that over the long run, one play or cube decision is better than another.

So not only for the opening moves, but for EVERY MOVE, if you want to win more often, you must learn the correct move to play. It is IMPOSSIBLE to memorize the correct move for every possible position, but it certainly is possible to memorize the opening moves, so why not do so?

## Opening moves in Backgammon – Part 1

In this and subsequent articles we are going to be looking at the opening rolls in backgammon. As in other games like chess, opening rolls and the way we play them play a large part in defining the type of game that will develop.

Playing a game of backgammon , you will discover that opening rolls can be played either with an agressive or passive mindset and that in various in-game situations one of these is prefferable over the other.

The first thing we need to define is our goal when playing the opening moves .

Backgammon is principally a race but if that was all there was to this game nobody would play it.

There are many factors and strategies that will determine the winner of the race. In order to ensure that you the player can play effectively we need to create safe havens for your men, while you obstruct the plans of the opposition as much as possible. In an ideal game situation we would like to trap one or more of the opponenents checkers behind a blockade. This is done by creating primes with the ultimate prime consisting of 6 points in a row. Of course four and five point primes are very desirable also.

The two things we try to do from the outset , are creating new points and of course start the race for home. The most difficult men to get home are the 2 that are furthest away at the beginning of the game. It makes sense that if one moves men in the opening that those 2 should be given the highest priority.

Priority number three should be to unstack any points that are so called ‘Heavy’. In the initial setup position of the game we have five checkers on our midpoint and the six-point. Having too many checkers on a point is dreadfully inefficient and redistributing those should be a priority also.

As with any game with 2 dice, there are thirty-six (36) possible combinations. Since you cannot open with a double this, coupled with the fact that in backgammon 31 & 13 , 14 &41 etc are the same we are left with fifteen (15) opening rolls that we have to consider. These rolls divide into four tidy groups.

There are five rolls that are always played the same way :

65 – 61 – 53 – 42 & 31

We have 2 rolls for which the majority of players agree on how to play :

63 & 62

Three rolls on which opinion is divided :

51 – 41 & 21

And five rolls on which there is no general consensus at all :

64 – 54 – 52 – 43 & 32

It is perhaps surprising that after 3,000 years of play we still don’t know how to play some of the opening rolls!

Now let’s examine each of these groups in turn.

These 5 rolls are the best you can have because they give you an immediate solid asset. Four of them create a new point whilst the fifth gets one of the back men safely to the mid-point (your 13-pt).

31

The strongest roll of all is 31. This allows you to make your 5-pt by playing 8/5, 6/5 as shown below:

Of all the points on the board the two most important at the start of the game that you should strive to make are your own 5-pt and your opponent’s 5-pt. Long ago, Paul Magriel, one of the world’s finest players and certainly the best author/teacher for many years, coined the term ‘Golden Point’ for the 5-pt to reflect its importance and the name has stuck.

Why is it so important? It is a new point in your home board that will hamper your opponent’s entry should he have a man hit. Most importantly it forms the third point in a potential prime – all you need now is to make your bar-point (your 7-pt) to create a four-point prime.

A 31 opening roll will lead to you winning the game about 59% of the time.

42

The next best roll is 42 which is played 8/4, 6/4 to make your 4-pt as shown here:

Magriel named this the ‘Silver Point’. Whilst not quite as strong as the 5-pt it is still a powerful point to make and 42 is the second best opening roll.

The reason it is not as strong as 31 is the ‘gap’ between the 4-pt and the 6-pt. If you subsequently make your 5-pt you will have a very powerful position but if your opponent makes it he will have a strong defence.

A 42 opening roll will lead to you winning the game about 58% of the time.

53

The third opening roll that makes a home board point is 53 that is played 8/3, 5/3 as shown:

Any new point is an improvement and making the 3-pt is still a good start to the game. It is not as good as the 5-pt or 4-pt because there is now a ‘double gap’ between the new point and the 6-pt.

Back in the 1970’s 53 was played 13/8, 13/10 because it was felt that the 3-pt was too deep a point to make on the first roll of the game. However, Jason Lester, switched to making his 3-pt and noted that he was winning more games with this play than the old one and soon all the budding New York professionals changed to making the 3-pt.

Nowadays making the 3-pt is universal.

61

The last of the point making rolls is 61, played 13/7, 8/7:

Beginners often think that the bar-point is better than making the 5-pt but it isn’t for a number of reasons. Firstly all home board points are useful because they limit your opponent’s entering numbers when he has a checker hit. Making the bar-point doesn’t do anything to stop your opponent entering from the bar.

Secondly, the most difficult men to activate from the opening position are the five men on your 6-pt because they have so few possible destinations. 31, 42 and a 53 all make use of one of those men, 61 does not so whilst a 61 is definitely a good roll the structure that it leaves is not as good as after one of the other three rolls. On the up side it does create a three-point prime that can be extended in either direction.

65

The last of our ‘forced’ opening rolls is 65 which is played 24/13:

This is a good roll because it gets one of the two back checkers halfway home in complete safety. The move is known as ‘Lover’s Leap’. Once you have started with a 65 you have a fairly straightforward game plan presented to you – run the other man out as quickly as you can!

For many years it wasn’t appreciated how powerful it is to escape one checker completely so early in the game. It is far easier to escape one checker than two and to have 50% of the job done on move 1 is a distinct advantage.

These last three opening rolls, 53, 61 and 65 will all lead to you winning the game about 55% of the time.

Summary

Our objectives in the opening are:

• Mobilise the back checkers
• Unstack the heavy points
• Make new points

So far we have only looked at rolls where there is really no choice. Things get more interesting when we look at the remaining 10 opening rolls.

## Backgammon Notation

Dice rolls are usually shown as two numbers followed by a colon. The numbering of the points is based on the point of view of the player whose turn it is. Each point thus has two numbers, depending on who is on roll, e.g. white`s 4-point is black`s 21-point. Diagrams are usually numbered from the viewpoint of the player whose home board is at the bottom of the diagram.. Each movement is depicted by giving the start and end point of the checker separated by a `/`. If a player is on the bar and fails to enter, a 0 is used to represent his roll (sometimes the word fan is also used). If a player is on the bar against a closed board (when the opponent owns all six of his home board points), his move is left blank or noted as `no play`.

Hits are denoted by an asterisk. A move made from the bar has `bar` as its starting point. A move bearing off a checker has `off` as its ending point. Where more than one checker is moved identically, as is often the case when doubles are thrown then this fact will be indicated by showing the number of men moved in brackets after the move.

The doubling cube is denby a large block It is either in the centre or is `owned` by one of the players. The value of the cube is always shown.

## A comprehensive history of backgammon – Part II

Looking at our previous article in this series we could see that the game of backgammon was losing its appeal in the 1920’s. The game was seen as slow and it was difficult to bet large sums of money.

We can only wonder whether the game would have survived without two major changes that would come into the game around 1925.

The first and most important change came when unknown person(s) in Boston or New York came up with the notion of doubling the stakes. We assume that doubling was invented at the same time and there is no evidence to support that this was not the case.

The doubling cube did not arrive for several more years and initially matchsticks were used to record the stakes. The first type of doubling device was a dial.

It is not recorded on exactly which date the doubling cube did arrive.

The second change was the arrival of the multi-player version of the game that has always been known, even back in the 1920’s, as a chouette. Chouette is the French word meaning screech owl, a bird that is attacked by many of its own kind.

The popularity of backgammon rose immensly after this. Backgammon became the perfect game for the 1920’s.

It is safe to say that doubling,though solving the backgammon popularity problems of the day and introducing a whole new level of skill, was initially very poorly understood by those playing the game. Take a look at any backgammon publications from that era and you will find very bad doubling advice !

Georges Mabardi, who is the author of Vanity Fair’s “Backgammon to Win” (1930) had this view of Doubling: “If two absolutely perfect players engaged in a match, there would never be an accepted double.”

This did not stop people cashing in on teaching the game. Here is Leila Hattersley, author of “How to play the New Backgammon” (1930) teaching at a New York Club (Leila is standing back right).

Similarly the early rules for chouettes didn’t much resemble today’s game, which involves multiple cubes, but it created a form of the game that is still the most exciting way to play backgammon today !

It is not clear how quickly doubling and chouettes crossed the Atlantic but there are no comparable UK backgammon books dating from the 20’s and 30’s of the 20th century

Backgammon continued to gain popularity until 1929 when the Infamous Wall Street Crash occured. In Part III of the series we will look at backgammon in the modern age.

## A comprehensive history of backgammon – Part I

Backgammon is one of the oldest games in existence along with Go and Chess. It is likely about 5,000 years old and may well have originated in what today is Iraq – previously Mesopotamia. Recent evidence supporting this was found when these very early dice (made of human bones) were discovered in this area.

The board with its twenty-four points and thirty men(or pieces or checkers) has been around for a long time but the game has not always been known as backgammon. Other games which used the same board were Senet and Mancala. The Romans were the first to make it truly popular with their version called “Duodecum Scripta et Tabulae” or “Tables” for short.

Frescoes in many a Roman villa depicted the game in progress as can be seen in the illustration below which was found in Pompeii.

The Roman Emperor Claudius was a avid player – he had a special board built on the back of his chariot to relieve the tediousness of long journeys. Emperor Nero was a prodigious gambler. He played for what would be \$10,000 a game in current terms.

For many years there were different sets of rules depending upon one’s level in society. Whilst the officers wagered large stakes it became so popular during the Crusades that soldiers below a certain rank were barred from playing the game.

The history of any game can be tracked by looking for references in both art and literature. It is mentioned in early literature, both in Chaucer’s Canterbury Tales:

“They daucen, and they pleyen at ches and tables.”

and by Shakespeare in Love’s Labour’s Lost.

The word backgammon first appears in print in 1645. No one knows for sure where the name came from, but most scholars agree that is likely to derive from Middle English ‘baec’ = back and ‘gamen’ = game.

Backgammon appears consistently in art throughout the second millennium, most famously in “The Garden of Earthly Delights” by Hieronymus Bosch and “The Triumph of Death” by Pieter Brueghel. Often it appears in tavern scenes and often there is a fight occuring at the same time.

The game continued to be played throughout the latter stages of the last millennium but it was involved in constant battles with authorities and the church who wanted to ban it because of the gambling element – which is not too dissimilar to the current US situation.

Its popularity continued to grow through the Victorian era.

By the early 1920’s the game was quickly losing its appeal. In the Roaring Twenties in New York City the games were just taking too long to play and it was difficult to wager (and thus to win) large amounts of money. We will look at further development in part II of this series.

## Backgammon Explained

To understand backgammon it is important to learn a little bit about the history of this most ancient of skill games.

Backgammon is the oldest known game in the recorded history of mankind. It is widely accepted today that the origins of the game go back to ancient Mesopotamia . Backgammon was played using a wooden board , stones or small rocks as checkers or men, and numbered dice made from a wide range of ancient materials.

Throughout it history backgammon has been seen as a game of royalty and nobility. Archeologists have uncovered many ancient backgammon artifacts that indicate the popularity of the backgammon among the aristocrats and nobility of Rome, Greece, Persia, and the Far East.

In the 1st century AD, Romans introduced backgammon to the British Isles. The Romans introduced it to the locals as a game called “Tables”. Most historians believe that the name “Backgammon” derives from the two English Words: “Bac gamen” meaning “Back Game”, either referring to the re-entry of checkers or men from the “bar” , or the more advanced strategy of playing backgammon commonly referred to as the “Back Game”.

An Englishman named Edmond Hoyle was the first person to compose a standard set of rules for backgammon and publish a complete guide to the game. This contributed greatly to the popularity of backgammon and the game spread rapidly throughout the European continent. Although several variations to the game emerged at that time, for example “Tric-Trac” in France and “Puff” in Germany these variations still followed the rules set out by Hoyle.

These basic rules of backgammon remained unchanged until the year 1931 when in the rules of the game were revised to the rules to which we use to play the game today.

Today, there are many variation to the game of Backgammon which use the same board and number of checkers such as: “Kotra”, “Tabard”, “Sixy-Acey”, “Acey-Deucey”, the Greek “Plakot”, the Arabic “Jioul” and the multi-player “Chouette”.

### Backgammon Setup

The game of Backgammon is played by two players and it is played on a board which consists of 24 triangles called “Points”.

The narrow triangles are grouped into 6 triangles in each quadrant of the board. There are 4 quadrants on the board, 2 on each side and the triangles alternate in color (to help with the counting of the moves).

The quadrants are referred to as a player’s home board (the quadrant that is on your right) and outer board (the quadrant that is on your left), and the opponent’s home board and outer board.

The home and outer board are separated from each other by the seam of the board which goes down the center of the board called the bar.

Each of the points (the triangles) are numbered for each player starting in that player’s home board. The point starting from the right corner of the home board is the one point and the point directly opposite to the one point is the twenty-four point, which is also the opponent’s one point. Each player has fifteen checkers of his own color. The starting position of the men is as follows: two on each player’s twenty-four point, five on each player’s thirteen point, three on each player’s eight point, and five on each player’s six point.

### The Object of the Game

The object of the game is for a player to move all of his men into his own home board and then remove them off the board (referred to as “Bearing Off”). The first player to “bear off” all of his checkers will win the game.

The picture above shows the Direction of movement of White’s men starting at his 24 point (where he has 2 men on the starting position). Red’s men move in the opposite direction.

### Movement of Checkers

The game starts with the throw of one die by each of the players. This will decide which player will go first and the numbers that are to be played. If the same number comes up, then the players are to roll again until they roll different numbers. The player throwing the higher number now moves his men according to the numbers showing on both dice. After the first roll, the players throw the dice on their respective turn. The player is to move his men across the points, or pips according to the roll of the dice. The men are always moved forward to a lower-numbered point towards your home court. The moves that are allowed are as follows:
1) A single men may be moved only to an open point, which is not occupied by two or more opposing men.
2) The numbers that come out on the two dice indicate the moves that are available to the player. Each number on a dice is one move. For example, if a player rolls 4 and 2, he may move one man four spaces to an open point and another man two spaces to another open point, or he may choose to combine both numbers and move one man a total of six spaces to an open point, but only if the respective point in the middle of the move (either two or four spaces from the starting point) is also open.

This picture shows the 2 ways that White can play a roll of a 5 and a 3.

3) A player who rolls doubles plays the numbers that are shown on the dice twice. If on a throw a player rolls 5 and 5 means that the player has four moves of fives to use, and he may move any combination of men that he feels would be the best moves for that outcome. Just like in the first example, he can move 4 different men 5 points each or a combination of one man to a total of 20 points.
4) A player must use both of the numbers of a roll as long as it is legally possible (in case of a double, then all four numbers of that double). The player must play all his numbers, even if only one number is legally possible. If both numbers can be played individually but not both, then the player must always play the higher number. The player will forfeit hit turn if neither number can be played. In the case of a double, a player must play as many numbers possible if not all numbers can be played.

### Hitting and Entering

A “blot” is a single checker of either color occupying a single point. If the opposite player moves his man to land on that “blot”, then that is called a “hit” and the blot is removed and placed on the “bar”.
It is compulsary for a player when he has any number of men on the bar, to enter his men to the opposite home board (between the 18-24 point). For a player to re-enter his men into the opposite home board, he must roll a number on the dice that is open.
For example, if a player rolls 2 and 5, then the player may enter his man into either the two point or the five point on the opposite home board, as long as it is not filled with 2 or more of the opponent’s men.

This picture shows if White rolls a 4 and a 5 while having a man on the bar, he must enter the man onto Red’s Four point since Red’s Five point is occupied by two opposite men and therefore is not open.

A player will lose his turn his either of the points on the opposite home board are not open. If a player has more then one man on the bar, then he must try to enter as many men he can during any one turn. If he can only enter one man but still has men on the bar, then the player will forfeit the reminding roll.
Once all of the player’s men are entered to the opposite home board from the bar, then the player must use any remaining roll to move either the re-entered men or any other men on the board

### Bearing Off in Backgammon

Bearing off is possible once a player has moved all of his own checkers into his own home board. To bear off, a player must take out any man that corresponds to the number of the dice thrown. For example, rolling a 5 allows the player to remove a checker from the five point.

If on the roll, the number that comes out is not occupied by any men, then the player must make any legal move using any man on a higher numbered point. If there are no men on any higher-numbered points, the player will remove a man from the highest point available on which one of his men resides. Bearing off will be done under the discretion of the player and if the player can make any legal move without bearing off, he/she is entitled to do so.

This picture shows White rolling a 6 and a 4 therefore white bears off two men.

## How to set up a Backgammon board

Each player has five men on his 6 point, three men on his 8 point, five men on his 13-point and two men on his 24 point. A player`s 6-point and 8-point will always be on his near side of the board and his 13 and 24 points will always be on the far side. The point numbers are reversed from the point of view of the opposing player. Your 13-point is your opponent`s 12-point, your 3-point his 22-point, etc.

The board will always appear as a mirror image for the opposing player.. One players` 1-point will be to his left, while the other`s will be to his right. One player moves anti-clockwise and the other clockwise as indicated in the diagram The board can be set up either way.

The points are not actually numbered on backgammon boards. 3 The doubling cube starts in the centre as indicated, either set to the value of 64 (or 1).

## Jellyfish

JellyFish is a neural net based backgammon program that plays at a very high level. On the highest playing level it matches the best humans in the world, and on the very fast level 5 a top human will hardly win more than 55% of the time. Also, its use of the doubling cube is outstanding. JellyFish is able to play matches of any length, or ‘money games’ where each point is equally valuable.

JellyFish uses artificial neural networks, trained to play backgammon from self play. An artificial neural network is a model of how the human brain works on the level of individual brain cells. Fredrik Dahl developed the neural nets of JellyFish, and used the neural net compiler nn from Neureka ANS. This program can be used for fun, for testing your game, for analyzing recorded matches, or most importantly:

To improve your game. JellyFish can give a running commentary on the moves and cube decisions you make. You may play against JellyFish, or use the “2 Players” mode to have JellyFish keep track of the score and comment on both opponents play. It’s almost like having your own private professional to comment on your game.

There are four different versions of JellyFish:

• Light
• Player
• Tutor
• Analyzer

JellyFish Player 3.5 is commercially available, while the previous release (3.0) is available as freeware download
JellyFish Tutor 3.5 is only commercially available
JellyFish Analyzer 3.5 is only commercially available

Why is the software called “JellyFish”?

The name JellyFish comes from the neural net that the program is build over. A neural net is a simulation of a biologic brain, and like a human, JellyFish has learned the strategy of backgammon by experience, by playing itself a very large number of games.

The human brain, however, contains more than 100.000.000.000 neurons, and this is not possible to include into a computer program. The size of our programs “brain” is more the size of some of the lower organism – like a jellyfish. But – our JellyFish is hopefully a better backgammon player than the jellyfish you find in the sea…

System requirements:

JellyFish requires a PC running Windows95 or Windows NT

8 MB RAM

i486 processor (Pentium recommended for maximum benefit)

2 MB Disk space

CD-ROM Player

Prices & Ordering Information

JellyFish Analyzer 3.5

US \$ 220

JellyFish Tutor 3.5

US \$ 100

JellyFish Player 3.5

US \$ 35

Upgrade Analyzer 2.0 / 3.0 > Analyzer 3.5

US \$ 50

Upgrade Tutor 2.0 / 3.0 > Tutor 3.5

US \$ 25

Upgrade Player 2.0 / 3.0 > Player 3.5

US \$ 20

Upgrade Tutor 2.0 / 3.0 > Analyzer 3.5

US \$ 140

Upgrade Player 2.0 / 3.0 > Tutor 3.5

US \$ 85

Upgrade Player 2.0 / 3.0 > Analyzer 3.5

US \$ 205

Please note that the quoted prices are suggested prices only, and that the actual charge may vary between countries due to reseller practice, local taxes, etc. JellyFish AS accepts no responsibility if the products can not be bought at the prices quoted here. Prices may change without notice.

Distributors:

Americas:

Gammon Press
P O Box 294
Arlington, MA 02476
USA
Phone: + 1 781 641 2091
Fax: + 1 781 641 2660
Email: gammon.press@jelly.effect.no
Rest of the world:

A & K Klassische Spiele
Grüner Weg 14
34117 Kassel
Germany
Phone: + 49 561 89 87 68
Fax: + 49 561 989 20 71
Email: ak@jelly.effect.no