This article originally appeared in the November 2002 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
The problem of bearing in safely against an anchor or anchors comes up all
the time in backgammon. We are all familiar with many of the main
priorities. Clear from the back. Keep flexible and smooth. Avoid leaving
gaps. Stay even on the outer points (a very overdone theme, since it usually
There is one theme which isn't well known, yet it is often as important or more important than the other themes. Consider the following problem:
The natural play is 10/6, 9/4. What could be more perfect -- four checkers on each of the five and four points. There are five checkers on the six point, but that costs only if Blue rolls 6-6 next turn. A reasonable alternative is 9/4, 6/2. This starts to clear the six point in advance. There should be little difficulty bringing the outfield checker home next turn.
What about 10/5, 9/5? Surely that can't be right. We are supposed to be concentrating on a smooth structure. How can piling 6 checkers on one point conceivably be correct? Yet 10/5, 9/5 is the best play, and by a fair margin.
What is going on here? After Blue brings all of his checkers into his inner board, he will be working on clearing the six point. While he is waiting for a good roll to clear the point, he may have some problems. What are his problem numbers? Fives and threes, of course. These are the numbers which don't allow Blue to play from the six point. In fact, the only legal fives and threes are from the five point. If Blue rolls a bunch of fives and threes before clearing the six point, what is going to happen? The five point will be stripped. Even worse, Blue may be forced to break the five point before the six point is cleared. That is very bad. It may lead to multiple blots and shots.
Blue's number one priority should be to prevent his five point from being stripped while he is trying to clear the six point. Since fives and threes play only from the five point, that means that Blue needs to put as many checkers on the five point as possible, in order to protect that point against bad rolls while Blue is trying to clear the six point.
We now see that little known theme. When bearing in or off against an anchor or anchors, look for the problem number or numbers. These will be the numbers which can't be played from the outermost point. Give yourself as many of these numbers as possible.
One might wonder about the adviasbility of not getting a fourth checker onto the four point. After all, once the six point is cleared then Blue will be trying to clear the five point, and fours will become the biggest problem number. Getting spares onto the four point is important, but it isn't necessary right now. Blue already has one spare there, and he will probably roll a two somewhere along the line and be able to put another spare on the four point. Even if Blue isn't able to get another checker to the four point before the six point is cleared, all he will need to do to keep adequate protection on the four point is roll an ace before rolling a couple of fours. Most of the time the four point won't be a problem. The five point is the major problem right now.
Here is another position with a similar theme:
Right now Blue will have problems with fives and fours, since these are the numbers which don't play from the six point. Once Blue clears the six point, fours will still be a problem number. If Blue doesn't do something about it, he is likely to be forced to give up his four point before he has cleared his five and six points. Now is the time to do something about by stuffing the four point as full as possible with 9/4, 8/4, instead of the seemingly more natural 9/5, 8/3. The stripped three point doesn't figure to be a problem. Blue won't have to worry about threes until he has clear his six point, and by then he will almost certainly have been able to dribble a checker or two onto the three point. It is the four point which is the major potential problem.
Here is a very common type of position which illustrates the problem number theme:
The instinctive play is to clear from the back with 8/7, 8/6, not leaving any gaps. This happens to be quite wrong. First of all, Blue has three checkers on the bar point, so he won't be able to clear the point next roll without rolling doubles. Look what happens if Blue rolls a couple of fives on his next two rolls. It's bye-bye six point. In addition, if Blue is forced down to two checkers on the six point and then rolls 6-5 he leaves a double shot. Fives are a very serious problem number when bearing in against the two-point anchor with the bar point yet to be cleared, and three checkers on the six point aren't nearly sufficient. 7/6, 7/5 is much better. This does leave a gap, but the gap isn't as serious a problem as might be imagined. Note that if Blue rolls a six (other than 6-1) he doesn't have to play it at all, and small numbers can be played from the inner board points. Thus, 6-1 is the only roll which leaves a shot next turn. There is no major problem number.
When looking for problem numbers, one must be sure that it is a real problem number before making unusual plays. For example:
Twos are Blue's problem number. However, there is no reason not to rip two checkers off here. Blue doesn't need extra spares on the five point, since he can handle any problem twos successfully from the three and two points. Taking two checkers off not only increases gammon chances, but it delays the day when Blue might have to leave a shot. If Blue is able to delay long enough, White might be forced to run to avoid a gammon or Blue may have enough checkers off so he will have winning chances even if he is hit.
A slight change in the position can make a big difference.
This time Blue's problem number is a three. The difference here is that Blue doesn't have any comfortable threes to play with checkers behind White's anchor. He must play his threes from his five and four points. Therefore, it is not correct to rip two checkers off, since that strips the five and four points, and the next three would create a gap. Instead, Blue should just prepare to clear the six point with 6/4, 6/2. Now he has two spare checkers on the three point to swallow threes while waiting to clear the six point.
It should be noted that once Blue has cleared the six point when coming in against a three-point game, he no longer has any major problem numbers. He will be unable to play twos from the five point, but assuming he has some men on his two point this will not be a difficulty. Consequently, Blue will not be forced to break his four point and leave a gap, so he can afford to start ripping checkers off as fast as possible. The key bearing off against the three-point anchor is to clear the six point successfully. Once that has been accomplished, the big danger of being forced to leave a gap is passed.
Speaking of gaps, how serious is a gap? A gap directly in front of the enemy anchor is very bad. This gap will haunt you for every point you need to clear. Other gaps may not be so bad. They mean that there is another number which will not play safely when trying to clear the back point, but that is all. Sometimes it is better to have the gap than to risk a disaster due to a problem number.
4/0 takes a checker off, but threes become a big problem number with both the five and four points stripped. 6/5, 4/1 gives Blue one three to play with, but there are still plenty of potential problems. If Blue rolls two moderatly sized numbers next turn he will have to play the spares from the six and five points, leaving him with a completely stripped position which is very dangerous. The best play is the unintuitive 5/4, 5/2. This gives Blue two threes to play with while waiting to clear the six point, and that should be sufficient. The gap means that Blue will not be able to clear the six point safely with an ace, but this is not necessarily fatal. When Blue comes down to two checkers on the six point, the only aces which leave a shot are 6-1 and 5-1. Other aces can be handled safely. One other consideration in favor of clearing the five point is that the point is cleared for good. If Blue does succeed in clearing the six point, he will no longer have to face the problem of clearing the five point.
When comming home against a backgame, the question of problem numbers can be very tricky. One must look ahead to see what the real dangers are.
Blue has several possibile plays here. He could hold everything by playing 6/1. That may look pretty, but it isn't a very good play. Blue loses a valuable spare on the six point and remains with a stripped position. It is better to clear one of the outfield points. But which one?
9/7, 9/6 may look natural, but it is actually rather weak. There will be no spares on the four point and only one spare on the five point. Once Blue clears his eight point, fours are going to be a big problem number, and when the bar point is cleared then threes will be a problem. Blue will need plenty of checkers on the four and five points to handle these future difficulties. In addition, sixes are an immediate problem, and Blue will have only one spare on the bar point to handle a six.
Clearing the eight point with 8/6, 8/5 is a bit better. At least this puts a second spare on the five point. Also, the eight point is one of the points which is under double-attack. If Blue is forced to leave a shot on the nine point, at least it is only a single direct shot. However, many of the same problems still exist. The four point remains thin, and sixes are an immediate problem.
The best play by far is to clear the bar point with 7/5, 7/4. This puts that important spare checker on the four point, as well as another spare on the five point, instead of overloading the six point. As we have seen, clearing the bar point can be especially difficult against the two-point anchor, and this play solves the problem for good. Also, and very important, the difficulty with sixes is partly taken care of. Blue's sixes are now all blocked, so if he rolls 6-3, 6-4, 6-5 or 6-6 he won't have to play the six. Thus, Blue is unlikely to be forced to leave a blot in the middle of his blockade. Note that the nine point is relatively easier to clear than the eight or bar points, since these checkers aren't being blocked by two of Whites anchors. Thus, clearing the nine point safely with a gap is no more difficult than clearing the eight point or the bar point with no gap. In each case, there are four safe landing places.
It is easy to overdo the above theme. As always, careful attention to detail and problem numbers is the key. For example:
After the previous discussion, 7/6, 7/4 may look like the natural play. This clears the bar point, brings a spare to the four point, and gets two checkers home for a faster bearoff. In this position, however, the stodgy 8/7, 8/5 is best. The key is that there are no serious problem numbers from the bar point. Sixes don't play, and Blue has several spares on the six point to handle fours. After 7/6, 7/4, Blue has problem fives. 6-5, 5-4, and 5-5 all leave a shot. If Blue rolls an ace, he has to risk an indirect shot in order to bring one of the outer board checkers home. These factors are sufficient to make 8/7, 8/5 the superior play.
The following problem should be pretty easy after the previous discussion:
It might seem as though Blue could play 9/8, 9/3, since he wouldn't have to play 6-6 next roll so everything plays safely. If we look ahead, it is clear that 9/3, 6/5 is superior. After bringing all the checkers home, the problem number will be fours. Right now Blue has only one four which plays -- the spare on the five point. Playing 6/5 with the ace gives Blue that second important four, which could mean the difference between being able to bear in safely as opposed to being forced to leave a gap.
At first glance it appears that 9/6, 7/1 leaves Blue with an awkward position -- five checkers on the six point and all the outer board points stripped. 9/3, 6/3 may seem more flexible. Now that we know to look for problem numbers, we see things in an entirely different light. Right now Blue's problem numbers are fives and fours. Once he clears the nine point fours and threes will be his problem numbers, and threes will remain a problem number until both the eight and bar points are cleared. The only place that Blue will be able to play his threes from will be the six point, so Blue better pile as many checkers onto that point as he can while he has the chance. 9/6, 7/1 is a far superior play to 9/3, 6/3. You just can't have enough checkers on the six point in this sort of position.
The above examples should give you a good idea about the dangers of problem numbers when bearing in against an anchor or anchors. See what the problem numbers are or are going to be in the future, and protect yourself against these numbers by giving yourself as many of them to play as possible.