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.
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.