
General Tactics


The Overstretched Position
By Bill Robertie (2007).
One of the most dangerous positions in backgammon is that of the outtimed and rapidly deteriorating position. These stretched positions usually arise when one side has built a great front position at the cost of leaving one or more stragglers disconnected from the main force.


The European Split
By Kit Woolsey (2002).
The question of what to do with a lone back checker can be very tricky. Ideally you would like to get it out and safely home. But is it worth moving the checker up partway in the opponent's home board, subjecting it to attack? That can be a difficult problem.


Cube Based Checker Plays
By Bill Robertie (2007).
In most positions, the correct play is the same regardless of the position of the doubling cube. This isn't always the case, and a good player needs to be alert to situations where the position of the cube makes a difference.


The Squeeze Play
By Kit Woolsey (2002).
A squeeze play is often correct when the opponent has a crunched board. The idea is to force the opponent to break off his anchor without letting him escape, so you can go after him with all your guns. Squeezes are unnaturallooking plays, since we are used to playing safe, but if you search for them you can find them.


Saving Sixes
By Kit Woolsey (2001).
Saving sixes is an important concept which should be in every player's arsenal. But it is important not to overdo it. Smoothness and flexibility usually have a higher priority, and the sixes that are saved can come back to haunt you later.


The Ace Point
By Kit Woolsey (2003).
Pros and cons of making your own ace point. In the 70's, the ace point was called the guff and making it was the mark of a beginner. Today, we know the ace point is more useful than we once thought.


Communication and Dyscommunication
By Danny Kleinman (1982).
Two men at a distance of fewer than 6 pips may be brought together to form new points; the closer the communication, the better the prospect for forming new points. But a distance of 6 does not foster the creation of new points. Kleinman calls this "dyscommunication," worse than no communication at all.


Conserving Energy
By Mike Senkiewicz (1982).
Conservation and saving energy are such commonplace ideas in modern life that they are taken for granted. Backgammon experts also practice conserving energy in a manner of speaking.


A Failure to Communicate?
By Mike Senkiewicz (1981).
Communication (keeping checkers within 6 pips of each other) is a positional concept and its implementation borders on a philosophical approach to certain positions as much as anything else. Therefore actual communication moves sometimes look nonsensical, and even antipositional. They are the "mystery" moves of backgammon.


It All Depends: A Guide for Evaluating Positions
By Mike Senkiewicz (1982).
There are no easy answers to finding good moves at backgammon. Experience and familiarity merely enable the expert to find good moves more easily. Each position must be broken down to its essentials, with the relevant factors weighed against each other to eventually arrive at a decision.


Equity Temperature Map: Introduction
By Sho Sengoku (2001).
This is the first description of a temperature map. A temperature map is a graphical representation of the distribution of equities of a position according to the next roll. Each of the 6 × 6 rolls is shown as a color — lighter for lower equities and darker for higher equities.


Communication and Control
By Antonio Ortega (1993).
When checkers lie six or fewer pips apart, they are said to "communicate." Put your checkers in communication with each other when you seek safety or want to cover blots. Control compliments communication. Checkers are spaced relatively far apart control a larger portion of the board. Seek control when it is your opponent who requires safety.



Probability


Introduction to Probability
By Jim Albert (1996).
While not about backgammon specifically, this article provides an overview of probability that is useful in backgammon. It explains how to interpret odds, gives the basic rules of probability, and shows how to calculate probabilities by listing all possible outcomes.


Backgammon Mathematics
By Kit Woolsey (2001).
How one can simplify the mental arithmetic sometimes required in backgammon so it can be done at the table: pip counting, match equity, shot counting, racing plays, and case counting.


Dice and Shots
By Robert Townsend (2007).
Introduction to counting shots and figuring probability. How to use this information to reduce wastage when bearing off or to calculate your probability of winning in a lastroll doubling position.


Dice and the Laws of Probability
By Ed Collins (2005).
Charts showing the probability of entering from the bar and the chances of hitting a blot.


Dice Tables
By Sho Sengoku (2003).
Sho Sengoku presents the table of 36 possible dice rolls and shows how to use it to count the number of rolls that achieve particular goals. Then he shows how to calculate the probability of hitting a single direct shot, a single indirect shot, and a double shot.


Arithmetic Techniques
By Sho Sengoku (2002).
Handy techniques for calculating terms that commonly come up in backgammon.


Dice Rolls and Probability in Backgammon
By Paul Stephens (2005).
Understanding the true probabilities of dice rolls can greatly improve your tactical play, by letting you accurately assess the risk of leaving blots, and the chances of hitting and covering points.


Basic Probabilities, Dice, and the Doubling Cube
By Hank Youngerman (1999).
Basic facts of probabilities associated with dice and the doubling cube.


Basic Probability
By Oswald Jacoby and John R. Crawford (1970).
A look at the 36 possible rolls of the dice and how they relate to the probability of entering from the bar, hitting a blot, or bearing off your last two checkers. (From The Backgammon Book, Chapter 4.)


If You Can Count to 36, ...
By Bruce Becker (1974).
Probability is a science and, when properly applied in a game, can be of inestimable value in helping you to win. When you know which move of several is the best one because of the odds of being hit, or because of the odds of covering a blot, then you will be playing backgammon with skill. (From Backgammon for Blood, Chapter 3.)


Probability and Statistics Posts
By Tom Keith.
Articles on probability and statistics in backgammon. From the Backgammon Galore Forum Archive.



Playing for/Saving Gammon


Oink Oink!
By Kit Woolsey (2002).
One difference between computer and human play is the bots play very aggressively to get gammons. They take chances that human experts would never take, risking an almost sure victory in order to increase gammon chances. We humans have been playing too conservatively. The bots love pigging it for the gammon.


Maximizing Gammon Chances
By Max Levenstein (2011).
Here is a tricky bearoff position where you want to maximize your gammon chances without unduly risking the game. What is the best approach in this type of situation?


Gammon Price
By Douglas Zare (2001).
The gammon price is a useful idea. It tells you how valuable it is to win a gammon at the current level of the cube. Often one has the chance to risk some wins in exchange for some gammons. The gammon price suggests how many wins you can accept converting to losses in exchange for each win that becomes a gammon.


Advanced Gammon Avoidance
By Bob Floyd (1983).
When analyzing a gammonavoidance position, you should first try to estimate how likely the gammon is. Your correct play depends very much on whether you can be optimistic or not.


The Rule of Sevens
By Jeff Ward (1982).
When trying to save gammon, it is usually best to play each roll entirely within the outer boards, either moving men closer to home or moving them to the 6point. However there are exceptions to this general principle.


The Rule of Sevens Revisited
By Jeff Ward (1982).
Some exceptions to Ward's "Rule of Sevens."


The Last Act of a Desperate Man
By Jeff Ward (1980).
As the game draws to a conclusion, each of the two players, Black and White, have several turns left with the dice, beginning with a roll for Black. Your goal is to give Black the best chance to save the gammon at the end of the game.


The Price Of Gammons
By Danny Kleinman (1980).
There are many situations where it is useful to know the price of gammons. For example, when our opponent turns the cube, his gammon threat may pose a problem for us when without the gammon threat our own winning chances would suffice for a take.



Taking Risks


Volunteering a Shot
By Bill Robertie (2006).
Sometimes there aren't any safe plays that make progress. Then you may start looking at plays that leave a direct shot. These plays may be costly if your opponent hits, but they may improve your position if your opponent misses. Here are some criteria for deciding whether to leave a direct shot.


The Aggression Coefficient Formula for Safe or Bold Bearins
By François Tardieu (2006).
A formula which indicates when to play boldly or safely when your opponent has been hit while bearing off and has a checker sitting on the bar.


Extra Shots
By Kit Woolsey (2001).
A number of positions where you have a choice between leaving a few extra shots to gain a small advantage when the shot is missed. How do you decide whether the risk is worth the reward? Knowing the concept of deciding how happy you are when things go right versus how unhappy you are when things go wrong often leads to the right conclusion.


Two Blots
By Walter Trice (2006).
Wouldn't it be nice if you could just move your checkers to where they would be most effective, without having to worry about getting a blot hit? Alas, most of the time backgammon cannot be played this way, and shortterm safety ranks prominently among the tactical priorities.


Considering Potential Gain Versus Potential Loss
By Gaby Horowitz and Bruce Roman (1982).
A common foible of even experienced players is the tendency to "enjoy the lead," attempting to protect it at any cost. This precipitates poor evaluation of the score at hand, followed by passive moves and feeble game plans.


Strategy for the 80's
By Gaby Horowitz and Bruce Roman (1983).
Much has been written by us and others concerning the liabilities of playing a backgame. A point which has not been mentioned is that the backgame can be a very effective transitory tactic. A simultaneous backwardforward game is an extremely flexible position from which to play until it becomes clear that either a forward or backgame is optimum.


Slot That Checker: A Basic Guide to Slotting
By Mike Senkiewicz (1982).
The expert player slots when he wants to improve his position by building a blockade. Suffice it to say that slotting is a sound and often necessary tactic in backgammon. The problem then is knowing when to, and when not to, slot.


Pay Me Now or Pay Me Later
By Kit Woolsey (1981).
The problem of whether to pay now or pay later  that is, whether to take a chance now or play safe for the roll at the possible cost of taking a greater risk later  recurs constantly in backgammon.



Duplication


Duplication
By Bill Robertie (2006).
Duplication is a cute idea which can lead to the right play in many situations. The idea is simple. You find yourself in a position where no matter how you move, your opponent will have some bad things he can do to you next turn. You want to minimize the number of his rolls that can hurt you.


More on Duplication
By Bill Robertie (2006).
Duplication is one of the crucial tactical ideas in backgammon. Look for your opponent's numbers that already play well, and remember that plays which expose blots to those very same numbers elsewhere on the board become stronger than they at first appear.


Duplication
By Kit Woolsey (2002).
We try to choose our plays so as to maximize the number of good rolls for our side and minimize the number of good rolls for the opponent. The latter can often be accomplished by duplication. If the same number is of use for the opponent in two places, then he can't do everything he wants to do unless he is fortunate enough to roll doubles.


Duplication
By Antonio Ortega (1993).
When you must expose more than one blot but you have a choice of where to leave your blots, you often want to minimize shots. You can always count the number of shots left by each play, but sometimes you can spare yourself this effort by applying the concept of duplication.



Hitting


The Tempo Hit
By Bill Robertie (2007).
When you make a tempo hit, your plan is to prevent the opponent from using his whole roll to do something good. By hitting (usually in your home board), you force him to spend half his roll coming in from the bar, so he's not in position to do something devastating elsewhere on the board.


Late Loose Hits
By Douglas Zare (2007).
According to Walter Trice, failing to hit loose in the late game is one of the most common errors. Zare looks at one particular situation: loose hits late in the game when you have a 5 point board. This can happen after your opponent breaks a high anchor.


Hit or No Hit?
By Bill Robertie (2006).
For a hit in your inner board to be correct, one of two reasons usually applies: (1) you're hitting on a key blocking or priming point, or (2) your opponent has so many threats that a tempo play is necessary.


More about Hitting
By Bill Robertie (2006).
Some key questions to ask when hitting on your own side of the board: Am I hitting on a key point? Am I unstacking when I hit? Do I already have a good anchor?



Containment


Committing to Containment
By Mary Hickey (2006).
Whenever you have trapped an enemy checker but still have contact with his other men, you have to choose between trying to capture a second prisoner, or just hanging on to the one you have.


Containment
By Kit Woolsey (2002).
You are playing a holding game. Finally, a late shot has been hit and your board is in disarray, either not put together yet or partially crunched. You are still well behind in the race and somehow you must contain the hit checker to prevent your opponent from completing his bearoff. This is one of the most difficult parts of the game.


The Random Point
By Kit Woolsey (2003).
This article deals with how to best contain a hit checker. The next time you hit a shot from a badly timed back game, don't just scatter your checkers around the board without a plan. With the help of a couple of wellplaced random points, these positions can be won.


The Monday Night Football Fatality
By Gaby Horowitz and Bruce Roman (1982).
Did Gaby's student learn the wrong lesson? "You taught us to save the gammon first and then try to win. I did exactly what you taught. It was the lecture on minimizing losses. I have it all in my notes. I can show you."


Off the Bar and Out?
By Jerry Nathan (1983).
Black is trying to contain White's last checker. How should White move to best facilitate his escape?



AcePoint Games


Bear Essentials
By Fran Goldfarb (1982).
Bearing in and off against opposition looks deceptively simple, but it's not. How many games have you lost by leaving a shot and how many gammons has your opponent saved because you played too safely? Ace point games come up so often that it's important to learn how to bear in and off correctly against them.


A Matter of Judgment
By Kathy Posner (1982).
What's the best to maximize your chances of getting a shot when opponent's in the last stages of bearing off?


Do You Know Your AcePoint Game?
By Kit Woolsey (1983).
One of the programs I have written analyzes the bearoff against an acepoint game. Here is a quiz involving some of its results. In each case, rate the four given choices from best to worst, and see how well you know your acepoint game.



Unequal Players


Handling Your Superior Opponent
By Gaby Horowitz and Bruce Roman (1981).
The most common strategical error committed by the weaker player is trying to "hang in" the match as long as possible. This results in overly conservative checker movement and cube action and a complete unwillingness to "put the match on the line."



Racing


Bearoff Tips at DMP
By François Tardieu (2007).
During bearoff, you must often choose between playing safe or taking off the maximum number of checkers. To figure out your best play, you have to be able to count shots (the easy part) and then estimate your chances of winning when you are hit.


Bearing in Safely
By Kit Woolsey (2002).
We are familiar with the priorities when bearing in against opposing anchors: Clear from the back; keep flexible and smooth; avoid leaving gaps; stay even on the outer points (often overdone). There is one theme which isn't well known: Look for numbers which can't be played from the outermost point and give yourself as many of these numbers to play as possible.


The Racer's Edge
By Kit Woolsey (2003).
The race is the most common position type we see except for the opening position. Since it is so common, it is worth knowing how to play it correctly. The principles outlined in this article will enable you to play races quickly and efficiently.


Burying vs. Bearing In
By Douglas Zare (2001).
A tutorial for players who don't know the theory of bearing in yet. Why it is bad to move checkers deep into your board while bearing in? Why you want to aim for a 753 checker distribution on your high home points.


Ideal Racing Positions
By Mike Mannon (2011).
By systematically choosing positions that are as close to ideal as possible, we can minimize the average number of rolls in a bear off. To this end, I have produced the tables that show the ideal racing position for each pip count and number of checkers still in play.


Inside Bearoff
By JeanLuc Seret and Bernard Bigot (2003).
With some experience, one can become almost infallible in the bearoff checker play. Nevertheless some bewildering plays exist that may occasionally be overlooked in practical play.


Bearing Off
By Tom Keith.
After breaking contact with your opponent, you want to bear your checkers in and off in such a way as to "waste" as few pips as possible. Here are some articles that explain wastage and how to minimize it. From the Backgammon Galore Forum Archive.


The Importance of Middlemen
By Jeff Ward (1983).
Near the end of a close, exciting race, it can be difficult to patiently examine all possible moves and accurately count the number of winning doubles for each. To help in this situation, the Ward has devised a shortcut method of finding the play that maximizes the number of winning doubles when there are exactly three men left in a player's home board.


The Magic Triangle
By Jeff Ward (1984).
In bearing off, many players do not know how to arrange their last two men correctly. This situation led me to discover a simple approach with no exceptions: the "magic triangle."


Smoothing
By Antonio Ortega (1993).
During the bear in, when you bring your last checkers home into your inner board, you do best to spread them evenly among your six, five, and four points. Likewise, while bearing off, you will do best to use the numbers which miss to smooth by filling empty and thin points.



Last updated: 24 May 2017
