Bearing Off

Bearing Off

by Phil Simborg

Many games are lost because of mistakes made in bear off positions.  Most people think bearing off is pretty simple, and in a way it is, because on many rolls you have very little choice of what to play, and much of the time you only have two or three choices that make any sense at all, so you simply have to choose one of them.  Also, many times the choices are very close--making the wrong play may only be wrong by a tiny fraction.  But what surprises all but the truly expert players is that sometimes the differences can be huge and a mistake could cost you a game or an entire match.  Even those small differences, when you add up a bunch of them over the course of a match, could result in a huge loss of equity.

Bearing off is not a simple, quick subject, as there are many factors other than just the roll that determines how to bear off including the score, the strength of your opponent's board, if your opponent has checkers on the bar, and how many on the bar; the importance and odds of winning a gammon or backgammon; and if your opponent has checkers in your inner board, how many, and where.  And of course, the pip count is always a major factor.  And everything can change dramatically if your opponent has already borne off checkers, and the number off is key.

For example, how you bear off against an opponent holding your ace point can be very different from when he's on the bar, on your 2 point, or on another point.  If your opponent has a good board, you have to be more careful not to get hit, and if he has a crashed board, you can generally be more aggressive.  At DMP your bear off strategy is simply to win, but at other scores it can be right to risk some wins to get more gammons or backgammons.

With all these variables and factors, you can understand why we cannot offer complete advice on bearing off in just one article.  Bob Wachtel wrote a great book on the subject in 1993 and in a recent interview on this site, Bob said that he is very proud that his conclusions and advice have held up over time after being tested with the newest technology (extremeGammon is that technology, by the way).

Most players assume this is not that difficult an area to play right and therefore have not given it enough time or study.

Over the board, it can be tremendously time consuming and difficult to try to calculate the odds of one play being better than another, and even the best players in the world make mistakes when its close.  But one of the best ways to avoid major errors is to have some general reference positions, rules of thumb, and basic strategies that you can generally apply in given situations.  For example, it is generally right not to leave a shot when you have a choice, and generally right to make plays that are less likely to leave a shot on your next roll.  It's generally right to clear from the higher points first if your goal is to bear off safely.  If there is no contact, it is generally right to take as many checkers off as possible with each roll.  If you can hit your opponent while bearing off in order to slow him down, that is generally right.  Not leaving gaps is generally right.  And another generality:  when in doubt, take checkers off.  And again, all of these concepts are generally wrong in some situations! 

We mentioned reference positions.  Here's a couple that might be of great help to you, as these kinds of bearing off situations occur often.

Let’s take a look at a typical bear off situation in the position below just to illustrate why we need to study bearing off and how reference positions and rules of thumb can help us. 


It is DMP, so gammons do not matter, and white has a crashed board but little chance in a race, so Red’s only goal is to bear off safely—leave no blot.



The rule of thumb here is simply to clear from the top points, starting with the 6 point, as much as possible.   The reason for this is that there are generally fewer numbers that leave shots on the ensuing rolls, and also, your opponent might enter from the bar on the high points and your worries about leaving  future shots are over. 

Any rolls with a 2 or higher, you would simply move checkers off the 6 point, including any rolls of doubles.   But all 1’s create a problem.  6-1 is forced (two checkers off the 6 point), but all other 1’s offer choices.  With a 5-1 it is safer to take two checkers off the 5 point than to move two off the 6 point as the odds of leaving a shot on the next rolls are lower.  We can simply count the number of rolls that leave shots with each play.  If you move two checkers off the 6, you leave a shot the next time with 6-6, 5-5, 4-4, 6-5, 6-4, 6-3, 6-2, 5-4, 5-3, 5-2.  Remember, non-double rolls like 6-5 counts as two rolls, because 5-6 and 6-5 are two different, possible rolls of the dice.  So the total number of possible shots is 17 out of 36 possible rolls.  Almost half the time! 

If you move two checkers off the 5 point, the total number of shots is only 7 out of 36 6-6, 5-5, 4-4, 6-1, 5-1.  A huge difference!

With a 4-1 you should clear the 4 point for the same reasons…fewer shots.

What about 3-1?  This one is very close, but what has always helped me is a rule of thumb that Jake Jacobs taught me years ago.  He said that if your only concern is bearing off safely and you are not trying to win gammons, generally speaking, if you have a spare on your 3 point or higher, it is best to clear the 6 point.  In this position, if you move both checkers off the 6 point, your 3 play will create a spare on the 3 point and that makes Jake’s advice right.  This advice is key, and also applies when you already have spares (a third checker) on various points.  For example, if you rolled a 5-1 and there was already a spare on the 3, 4, or 5 point, then instead of clearing the 5 point you can clear the 6 point, and the same applies if you rolled a 4-1.

Finally, with a 2-1 you should clear the 6 point as the combination of future shot-leaving numbers and the odds of your opponent coming in and getting out of your hair completely make this play the best.

Again, change the score and the value of gammons; put more checkers on the bar; change White’s inner board; change the race; and it may well change some or all of these plays.  The main lesson for this week is to not take bearing off for granted.  If you want to bear off well, you need to study and practice.  The information is out there in books, articles, and from qualified teachers and coaches.