While this has indeed been a solo project, no man really travels alone. I would like to take this opportunity to thank those who have encouraged and assisted me along the way.
Karl Kagarise, who taught me the joys and pain of backgammon. I'll never forget those crazy all night sessions. If you ever read this, call me collect.
Jeff and Jill Hu, proprietors of the Campbell Bridge & Backgammon Club, for running such a fine club in California, and to all the Campbell Club players who conspired to teach me humility and sharpen my game in the process.
Ron Karr, for providing much needed moral and programming support as well as being my most active and thorough Beta tester
Bill Kennedy, Danny Kleinman, Roy Friedman, Bill Davis and Ray Glaeser, for critiquing my program and giving me many helpful suggestions.
My family and friends for taking an interest, listening to my obsessive ramblings, and keeping me focused; especially Ramona Rodriguez, Adam Winkler, Ben Dubin and Gary Kremen.
And to all those who said it couldn't' t be done.
Foreword
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Backgammon is one of the oldest games in existence, dating back some 5000 years and believed to have been developed by the ancient Egyptians. It is not a game of luck as many believe, but a strategic game of war; in many ways as difficult to master as chess or Go. A random element (luck) is certainly involved, but a champion player also uses the laws of probability, intuition, imagination and psychology to outwit his opponent.
Trying to get a few thousand lines of code to logically analyze the nuances of trillions of positions has been a monumental task. The paradoxes in backgammon are seemingly endless and there are relatively few positions where there is an empirically correct move. Attempting to program such concepts as priming, flexibility and contact have been almost impossible. The frustration and sleepless nights spent balancing the myriad of variables in just the proper proportion have only been offset by watching my electronic student go from a bumbling beginner to an "intelligent" challenger capable of taking the initiative with daring, imaginative plays as well as waiting patiently for the right moment to strike. The resulting style of play is reminiscent of mine, naturally; but is unique in many ways.
While I have taught my computer to play, it has also taught me. When programming, I would try to calculate the best move for each position and adjust the logic accordingly. Interestingly enough, I found that some of my analysis was an almost robotic response to a familiar situation. Upon close examination, I found the computer's play to be superior to my own. I have had to reevaluate many commonly accepted strategies. How much have I learned ? An intermediate player when I started this project, I was rated # 22 in the world in 1992 for match play according to Kent Goulding's International Rating List .
Expert Backgammon™ was written with ZBasic™ and PG PRO™. It scans every possible move and some responses and evaluates each position weighing hundreds of variables. It is strongly geared towards structure and patterns and tends to play "pure". What makes it really tough though, are the facts that it never gets tired, intimidated, miscounts or "steams".
Are you bold enough to challenge?
Introduction
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I have played (been obsessed with) backgammon for over 14 years. I have condensed the knowledge and skill gained from playing many thousands of games into so many bytes of data.
It is difficult deciding when to release a program of this scope as it's never really finished. There is always some area to be improved or another feature to be added. It has been under development for over five years and I believe that it's time to unveil my brainchild.
I welcome all electronic challengers. Expert Backgammon is the only backgammon program to have ever won a tournament against seasoned human players. In Austin , Texas in May 1991, Expert Backgammon swept the field 9-0, 7-0, 9-0 and split the first place winnings with the other finalist who refused to play the diabolical machine. The dice were rolled by hand and the numbers entered manually.
In 1992, Expert Backgammon for the PC won the World Cup Computer Championship against the highly acclaimed TD Gammon, an artificial intelligence research project using neural newtorks and sponsored by the IBM Research Center. The code used in that version has been ported to the Macintosh along with many new improvements.
When last tested, Expert Backgammon was rated by two time World Champion, Bill Robertie as being 3 times stronger than the nearest commercial competitor as measured by average points lost against a world class player. Version 3 is even stronger than the last version rated.
Expert Backgammon is currently recoginized as the premier computer software tool for studying backgammon and has literally changed the way that the game is being played. Even the accepted opening moves and responses have changed because of new information gained by rolling out positions.
Thank you for buying Expert Backgammon™. You won't be disappointed.
Chapter 1 Backgammon basics
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Note: For playing in color, substitute the word blue for black and burgundy for white throughout the user's guide.
Each player starts with 15 checkers from a preset position on a board of 24 points (triangles) and each moves in an opposing direction. The main objective is to move all of you checkers (men) into your home board and to bear them off the board before your opponent. The points are numbered in reference to the player on roll's home board. In the diagram below, Black is about to play a 5,3. If White was on roll, the points would be numbered from 24 in the top right corner to 1 in the left corner. (See Point numbers under the Position menu.)
Diagram A
Opening roll
The possible moves are determined by rolling the dice. Each player has their own set of dice corresponding to the color of their checkers. On the first roll of every new game, each player rolls one die and the player rolling the larger number uses the value of both the black and the white dice for his move. Normally, if the value of both dice are the same, the players roll again. The color corresponding to the larger value of the two dice moves first. On subsequent rolls, each player will roll his own color dice on the player's respective right side of the board.
Moving the checkers
If a 5 3 was rolled, then you are allowed to move one man 5 pips (or points) and one man 3 pips; or you may move one man 8 pips. However, if you choose to move the same man 8 pips, you must treat it as two separate moves. You are not allowed to land on a point where there are two or more enemy checkers. If there is a single enemy checker on your landing spot, then he has been hit and is sent to the Bar where he must start all over again. (Refer to the diagram A.) Checkers on the Bar must be moved first before any other move is allowed.
Doubles
If both dice match, then doubles have been rolled and you are allowed four separate moves of the value of a single die. For example, if you rolled 2 2 then you can (provided all moves are legal):
1. move four checkers 2 pips each
2. move one checker 8 pips
3. move 2 checkers 4 pips each
4. move one checker 6 pips and one checker 2 pips.
Bearing off
Once all of your checkers are in your home board you may begin bearing them off the board. If your opponent has no checkers in your home board, it is almost always the correct play to take checkers off if you can. To do so, there must be one or more checkers on the point corresponding to the numbers on the dice. For example, if you roll a 5 1, you have several possible options:
1. If there are checkers on the 5 and 1 points you may bear one checker off each point.
2. If there is no checker on the five point, but there is a checker on the 6 point you may use the full roll to bear 1 checker off.
3. If there are no checkers on the 5 or 6 points you may use the 5 to bear a checker off the next highest point only.
4. You may play the roll as you would in a non-bear off position by just advancing your checkers.
Basic strategy
Single checkers (blots) on a point are vulnerable to enemy attack and must start over if hit by an opponent's checker. Two or more checkers on a point are safe from attack and can also be used for blocking or trapping your opponent.
Essentially backgammon is a race to see who takes off all of his checkers first. However, the shortest distance between two points is not always a straight line. Most beginners, rarely leave exposed checkers and hit as often as they can. As you will find out, this seemingly logical approach is not the best strategy. The following is a simplification of some of the factors that you should consider in forming a winning plan:
1. Distribution
Evenly divide your checkers among the points occupied. It is usually better to have 3 checkers each on two different points rather than 4 checkers on one and 2 checkers on the other. You should rarely have six checkers on a point and almost never have any more. A player with even distribution will seemingly get "luckier" dice than his less flexible opponent.
2. Exposure
Don't be afraid to leave shots early in the game to establish a strong offense or defense. Be more cautious as your enemy's home board gets stronger. The more points he has in his home board, the more difficult it will be for you to re-enter after being hit. Conversely, the more points that you control in your enemy's home board (anchors) the bolder you may play. Even if his board is weak, limit the number of blots (single checkers) to no more than four. If you are significantly ahead in the race or position, then restrict your exposure to maintain your lead.
4. Blocking and priming
Try to build points without gaps between them directly in front of the enemy checkers in your home board to prevent their escape. Establishing these critical points as early as possible in approximate order of importance: 5, 4, 7 to start your blockade. Six points in a row is called a prime. This makes it impossible for your opponent to escape for as long as you can maintain that structure.
5. Hitting
Try to hit checkers that are the most advanced or checkers that your opponent would like to cover to establish an important point. Attack only when it is advantageous to do so. For example, if you already have two enemy checkers on the bar, it is more critical to make another point in your home board than to hit a third checker. Also refrain from hitting it makes you more vulnerable than your opponent. Keep your objectives in mind and don't be side-tracked. However, there is an old backgammon adage that still carries weight, "When in doubt, hit."
6. Anchoring
Try to establish a defensive point (anchor) in your enemies home board. This gives you a landing spot to come in on should you get hit and prevents your opponent from making his home board. Early in the game try to establish anchors on the lower points (20,21). If you become significantly behind in the race, the higher points (22,23,24) have more value as your strategy is to build your home board and wait for a shot. If you have two anchors try to keep them on adjacent points.
These are just a few ideas for the beginner to get started and is not meant as a tutorial. There are many fine books available if you want more information. See the glossary at the end of the guide for a definition of some backgammon terminology.
Chapter 2 Playing Expert Backgammon
Insert the disk and double-click on the (REMark put actual ICON here) 64 icon to open the program. A backgammon board will appear and a window will open asking you to enter your name. Simply type in your name up to 15 characters long and then press return.
Rolling the dice
Pressing the space bar or clicking the mouse anywhere on the plaing surface will roll the dice. If the Dice sound option is checked, the computer will generate a dice shaking and rolling sound followed by a random number of dice displays before settling on the final roll.
The black dice roll on the right side of the screen and correspond to the black checkers (yours). The white checkers and dice belong to the computer and appear on the left half of the board. On the first roll of every new game, each player rolls one die and the player rolling the larger number uses the value of both the black and the white dice for his move. Normally, if both dice are the same the computer will not draw them and will internally generate a new roll. ( See Automatic under the Dice menu. ) The color corresponding to the larger value of the two dice moves first. On subsequent rolls, each player will roll his own color dice on his side of the board. You must press the space bar or click the mouse after the completion of each move to roll the dice again.
Moving the Checkers
Basic move
The basic move is executed by clicking on the checker that you wish to move. If it is possible to move that checker then a hand cursor will, a thup will sound, the checker will gray out and a transparent checker will appear. Keep the mouse button down and drag the checker to the point that you wish to move to, then release the button. The gray checker on the starting point will disappear and you will hear a checker move sound.
If there is only one move possible from the point selected, you may simply single-click on that point rather than clicking and dragging the checker. The computer will then move the checker for you.
More than 5 checkers on a point will be represented by numerals printed on top of the checkers. In the following diagram, Black has 7 checkers on his 1 point.
Diagram B
Notice how the dice fade after each portion of the move is completed. When doubles are rolled, one die will fade after two of the four moves are completed.
In Diagram D, Black has played a 2 and still has a 6 to play.
Diagram C
Shortcut moves
There are shortcuts to speed up the game. If you find them confusing, just use the basic move until you are thoroughly familiar with the new moves. To use a shortcut, you must click on the border directly under the lower triangle or over the upper triangle that you wish to move to. There are three variations; each of which has a different priority level. Note: you may not always be able to use a shortcut depending upon position.
Priority 1 Move two checkers to the selected point. To activate during bear-off, click under the bear-off tray.
Priority 2 Move one checker to the selected point.
Priority 3 Move one checker the full roll for non-doubles or part or all of the roll for doubles. If a hit is forced, the checker(s) will be automatically put on the bar. If the move is ambiguous and a hit is possible, but not forced, it is best to use the basic move.
Double move
Holding down he Shift key while position the mouse over the checkers and clicking will move two checkers from the starting point.
Hitting
No special maneuvers are required. Just move your checkers as described above. If there happens to be an enemy blot encamped on the point that you are moving to, a bonk will sound, and the checker will automatically be sent to the Bar point.
3.Legal moves
There are certain basic constraints on how the checkers are moved.
1. You may not move to a point where there is more than one enemy checker.
2. You must move any checkers on the bar first. If that is not possible, your turn has ended.
3. You must take the maximum roll value possible. Let's say you roll a 5 4 and can move either a 5 or a 4, but not both. Then you must play the 5.
4. You may not bear checkers off until all your men are in their home board.
5. To remove a checker during bear-off, the checker must be on the point number corresponding to the number on the dice or the dice value must be greater than the highest checker in your home board.
Expert Backgammon will play forced moves from the bar for you. If after rolling, no legal moves are possible, both dice will fade.
Attempting an illegal play will call up a dialog window reminding you to take the largest possible move.
Speed of play
After rolling the dice, the watch icon will appear letting you know that the computer is "thinking". As this is the most sophisticated commercial backgammon algorithm ever developed, it takes some time to look at all of the possibilities. Computing time is affected by several factors:
1. The type of processor and clock speed of your computer.
2. The level of play chosen. The lower the level the more variables that are evaluated which increases processing time.
3. Rolling doubles. As there are significantly more variations with doubles, it may take up to 6 times longer to evaluate a position than with non- doubles.
You may select this option at any time to start a new game. The checkers and cube will reset to the start position. The score will remain unaffected.
Save game
If this menu option is checked, then "A Save file as . . . " window will appear at the end of each game. This will prevent you from erasing a game that you would like to save. If you rarely save the game simply turn this option off.
Saving the game will store the dice rolls, the checker moves, the cube action, the player's name, the starting and ending score and the number of points in the match. Replaying another game, opening a position, or altering the position or player on roll in the middle of the game will corrupt the storage of the game in progress.
If you can't finish a game and have to quit this application, don't worry as the game played up to that position will automatically be saved in the EXBG prefs file.
Replay game
To replay a game, select Replay game, then choose from the list of your stored game files. Press the space bar to activate each roll and move of the game.
Type of game
There are two options, Match play or Money play. Match style play is used in tournaments around the world and is played to a fixed number of points. The optimum cube handling and checker play strategy is significantly different than in money style or "fun" games
Selecting match play opens this window:
This is the default window. You may set the match length from 2 to 25 points. Your score and my score must be less than the match length. Use the tab key to move to the different edit fields. Press the OK button when done.
Selecting money play opens this window:
Enter the amount desired between $1 and $100 per point. Then hit return.
New player
Clicking on this menu item will open a window asking you to input your name.
Type in your name up to 15 characters in length. The game in progress will be unaffected.
Quit
This will shut down the program and automatically save your preferences as well as the game in progress and position and dice data.
Chapter 3 Position Menu
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Save position
Opens the current folder and asks if you want to save the game using the suggested file name of your name and current game number. Saving the position takes a snapshot of the position, roll, score, setup and player's name and other options for later recall.
Open position
Opens the current folder to display any positions that you have previously stored. Double-click on your choice to open any position for further study. You may continue play from the stored position.
Pip count
A pip is the measure of one checker moving from one point to another point. This option displays the number of pips to bear all your men off and gives the same information about your opponent's position. This is essentially an indication of who is ahead in the race. This factor becomes more critical as the amount of interaction between opposing checkers decreases.
If you are using 13" or larger color or grayscale monitor, the pip count is continuously displayed at the bottom of the screen and this option is not needed.
Take back move
This will reset the checkers to the position at the beginning of the roll. The dice will be unaffected. To undo both the move and the dice roll, select Take back roll under the Dice menu. This is useful if you have made a mistake or changed your mind during you roll. Also you may take back the computer's move to study the position before the roll. You must then press the sapce bar to reactivate the computer's move.
Point numbers
Will display the numbers from 1 to 24 on the edge of the board as in Diagram A. This is a tool to acquaint the neophyte with the way that the board is laid out. The numbers will invert with each roll as they are referenced to the player on roll.
Chapter 4 Cube
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Playing with the cube (or doubler) is an integral part of modern backgammon and adds a whole new dimension to the complexity and intrigue of the game. Essentially it is a device used to double the stakes or point values. At the beginning of the game, the cube is in the middle of the board and neither party "owns" the cube. When one player feels that he has a significant advantage, he may double his opponent. The opponent then retains possession of the cube until the end of the game or until he redoubles. For instance, if the cube is at 2 and you win a gammon ( a double game) then your total win for that game is 4 points. The cube on a "real" backgammon board shows the starting value to be 64. Actually that represents a 1. Expert Backgammon limits the cube value to a maximum of 64.
Double D
This offers the cube to your opponent. All point values for wins and losses double. This option may also be activated by positioning the cursor on the cube and clicking the mouse. The Computer will display a window telling you of his decision. If he accepts, the game will continue with the cube at a higher value. If he declines you will be awrded the value of the cube before doubling and the game will end.
When the computer doubles you, a window will open as in Diagram X, asking if you accept or reject the double. Simply click on the YES or NO (or BEAVER if selected) button. Dropping the cube will end the game, awarding the point(s) to the computer.
Diagram X
Automatic
This is allowed only during money play. Many players prefer that when the dice numbers match on the first roll of a new game, the cube is automatically doubled and stays in the center of the board. This is simply a random way to increase the stakes.
Jacoby rule
This rule devised by the renowned champion, Oswald Jacoby, is favored by most money players. It states that a player may not win a gammon or backgammon unless the cube has been turned first (is no longer in the center of the board). This keeps the games shorter and generates more "action". This rule is never used in match play.
.Beaver
This is another option favored by money players. When one player doubles another, the player receiving the cube may instantly redouble and retain possession of the cube. Usually this is done to show disdain for the supposed superiority of the opponent's position. If the computer frequently Beavers your doubles, then it is safe to assume that you are doubling too early, meaning that your position is not yet strong enough. ( See Double.)
Crawford rule
This is a standard rule used in most tournaments. Simply stated, when the leading scorer is within one point of winning the match, the trailing player may not double during the first game that this situation occurs, but may do so in subsequent games. As the leading scorer gets no benefit from winning a doubled game in this position, this rule was established to protect him for one game. Most players agree that this is a fair arrangement.
Style
To make the game more fun and varied, I have added three styles of play when it comes to making cube decisions. If you have played for any length of time, I'm sure that you recognize a fellow player by one of the following descriptions.
Conservative
Wants the opponent to drop the cube. Will offer the double somewhat "late" to ensure a single win. Gives the opponent free rolls in which to consolidate his position. Is somewhat timid and will drop takeable doubles.
Balanced
Attempts to offer the cube at the precise moment when the situation is definitely in his favor, but there are chances for the opponent to turn it around. He doesn't care if the enemy takes or drops as takes as he has maximized his winning equity. Will not be intimidated when offered the cube, but neither is he foolhardy.
Aggressive
Basically a gambler. He doubles early and prefers that the opponent take the double as he would like to try for a gammon (double win) or at least play on for higher stakes. He takes cubes that should be declined because he likes the action.
Chapter 65 Level Menu
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These levels are not necessarily consistent with equivalent human levels. The lower the level , the more random the move and the less variables or positions considered.
Expert
Has the proper balance between attack and offense. Evaluates every variable and can play any position for maximum equity. Has keen insight into the flow of the game.
Advanced
Understands all the mechanics of the game. Strong consistent play in most situations.
Intermediate
Uses the concepts of priming and distribution. Has reasonable structure, but still overlooks many factors.
Novice
Has some concept of the game, but only considers the immediate move and not subsequent rolls. Plays extremely conservative (afraid of being hit).
Beginner
Knows the basic moves, but has minimal strategy. Inconsistent play; may not make the same move in the same situation.
Chapter 6 Options
Automatic concession
If this option is checked and the end result of a game is mathematically certain, then Expert Backgammon will automatically award a single, double (gammon) or triple (backgammon) game depending on number of checkers reamining and the checker placement.
Speed
You may select either Slow, Medium or Fast graphics mode. These speeds refer to the duration between checker moves. As you become more familiar with the interface you may want to increase the speed. Try them all and select to suit your taste. This option applies to the graphics only. Computational speed is unaffected.
Color graphics are somewhat slower than B&W graphics because of the amount of data handled, but this does not affect the time required to decide upon a move.
Zero the score
This resets both players score to zero and the game counter to 1.
Display score
This option shows the scores for both players, the game number, and the number of points in the match. For those using a 13" or larger color or grayscale monitor, this information is displayed continuously on the bottom of the screen.
Glossary
anchor - a defensive point in the enemy's home board.
back game - a position occurring when one player is trapped in the enemies' home board. The winning strategy is to maintain your anchors, build your home board and wait for a shot.
backgammon - a triple win occurring when one player has removed all of his checkers and his opponent still has one or more checkers in the enemy's home board.
bar - the center strip of the board where checkers are sent after being hit.
bear off - the final stage of the game, where a player takes his checkers off the board.
blot - a single checker on a point.
contact - any position where opposing checkers must cross paths to get home or bear checkers off. The more checkers that have to pass by enemy checkers the greater the amount of contact.
cover - to make a point by covering ( putting another checker on) a blot.
cube - the large die in the center of the board numbered from 2 to 64 used to double the point value of the game. It is sometimes referred to as the "doubler".
gammon - a double win occurring when on player bears off all of his checkers and all of the opponents checkers are still on the board.
hit - to land on the same point as an enemy blot sending him to the bar.
midpoint - the thirteen point. An important point to maintain through the middle game.
pip - the value of moving one checker one point.
pip count -the total number of pips required to bear all men off.
point - 1. refers to one of the 24 triangles plus the 2 bars on the board.
2. two or more checkers of the same color on a triangle forms a point, which is invulnerable to attack.
race - the difference in pip counts between opposing players. The player with the lower pip count is said to be ahead in the race.
shots - the number of dice roll combinations that will allow one player to hit the other. There are 36 shots maximum per roll.
slot - to start a point by putting a single checker on it, in the hope that you can make the point the following roll.
split - to break a point into two single checkers on two different points.
Afterward
I welcome feedback from players of all levels. This is your program as well as mine and has evolved to its current state in response to customer suggestions. Let me know what improvements that you would like to see and I will happily review your ideas.
This program is the work of one man, not a large corporation, who has spent over 10,000 hours to develop the best backgammon game possible for you. While I know that this is a fun game that you would like to share with your friends, please resist the temptation to pass along illegal copies. Not only is this an infringemnt on Federal copyright laws, but it will prevent me from being able to bing you new products or future enhancements to this one.
Make sure to send in your registration card so that I can send you information about new releases! Also let me know when you change your address so that I may keep my database up to date.
