return to indexThere is one theme which isn't well known, yet it is often as importantor more important than the other themes. Consider the following problem:
| 189 79 | White money game Blue |
The natural play is 10/6, 9/4. What could be more perfect -- fourcheckers on each of the five and four points. There are five checkerson 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 sixpoint in advance. There should be little difficulty bringing theoutfield checker home next turn.
What about 10/5, 9/5? Surely that can't be right. We are supposed to beconcentrating on a smooth structure. How can piling 6 checkers on onepoint conceivably be correct? Yet 10/5, 9/5 is the best play, and bya fair margin.
What is going on here? After Blue brings all of his checkers into his innerboard, he will be working on clearing the six point. While he is waitingfor a good roll to clear the point, he may have some problems. What arehis problem numbers? Fives and threes, of course. These are the numberswhich don't allow Blue to play from the six point. In fact, the only legalfives and threes are from the five point. If Blue rolls a bunch of fivesand threes before clearing the six point, what is going to happen? Thefive point will be stripped. Even worse, Blue may be forced to break thefive point before the six point is cleared. That is very bad. It maylead to multiple blots and shots.
Blue's number one priority should be to prevent his five point from beingstripped while he is trying to clear the six point. Since fives and threesplay only from the five point, that means that Blue needs to put as manycheckers on the five point as possible, in order to protect that pointagainst bad rolls while Blue is trying to clear the six point.
We now see that little known theme. When bearing in or off against ananchor or anchors, look for the problem number or numbers. These willbe the numbers which can't be played from the outermost point. Giveyourself as many of these numbers as possible.
One might wonder about the adviasbility of not getting a fourth checkeronto the four point. After all, once the six point is cleared thenBlue will be trying to clear the five point, and fours will become thebiggest problem number. Getting spares onto the four point is important,but it isn't necessary right now. Blue already has one spare there, andhe will probably roll a two somewhere along the line and be able to putanother spare on the four point. Even if Blue isn't able to get anotherchecker to the four point before the six point is cleared, all he will needto do to keep adequate protection on the four point is roll an Ace beforerolling a couple of fours. Most of the time the four point won't be aproblem. The five point is the major problem right now.
Here is another position with a similar theme:
| 192 79 | White money game Blue |
Right now Blue will have problems with fives and fours, since these arethe numbers which don't play from the six point. Once Blue clears thesix point, fours will still be a problem number. If Blue doesn't dosomething about it, he is likely to be forced to give up his four pointbefore he has cleared his five and six points. Now is the time to dosomething 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 pointdoesn't figure to be a problem. Blue won't have to worry about threesuntil he has clear his six point, and by then he will almost certainly havebeen able to dribble a checker or two onto the three point. It is thefour point which is the major potential problem.
Here is a very common type of position which illustrates the problem number theme:
| 142 76 | White money game Blue |
The instinctive play is to clear from the back with 8/7, 8/6, not leavingany gaps. This happens to be quite wrong. First of all, Blue has threecheckers on the bar point, so he won't be able to clear the point nextroll without rolling doubles. Look what happens if Blue rolls a coupleof fives on his next two rolls. It's bye-bye six point. In addition, ifBlue is forced down to two checkers on the six point and then rolls6-5 he leaves a Double shot. Fives are a very serious problem numberwhen bearing in against the two-point anchor with the bar point yet tobe 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 seriousa problem as might be imagined. Note that if Blue rolls a six (other than6-1) he doesn't have to play it at all, and small numbers can be played fromthe inner board points. Thus, 6-1 is the only roll which leaves a shotnext turn. There is no major problem number.
When looking for problem numbers, one must be sure that it is a real problemnumber before making unusual plays. For example:
| 107 56 | White money game Blue |
Twos are Blue's problem number. However, there is no reason not to riptwo checkers off here. Blue doesn't need extra spares on the five point,since he can handle any problem twos successfully from the three andtwo points. Taking two checkers off not only increases gammon chances, butit delays the day when Blue might have to leave a shot. If Blue is ableto delay long enough, White might be forced to run to avoid a gammon orBlue may have enough checkers off so he will have winning chances even ifhe is hit.
A slight change in the position can make a big difference.
| 109 56 | White money game Blue |
This time Blue's problem number is a three. The difference here is thatBlue doesn't have any comfortable threes to play with checkers behindWhite'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 stripsthe 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 hehas two spare checkers on the three point to swallow threes while waiting toclear the six point.
It should be noted that once Blue has cleared the six point when comingin against a three-point game, he no longer has any major problemnumbers. He will be unable to play twos from the five point, butassuming 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 leavea 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 thesix point successfully. Once that has been accomplished, the big dangerof being forced to leave a gap is passed.
Speaking of gaps, how serious is a gap? A gap directly in front of theenemy anchor is very bad. This gap will haunt you for every point youneed to clear. Other gaps may not be so bad. They mean that there isanother number which will not play safely when trying to clear the backpoint, but that is all. Sometimes it is better to have the gap thanto risk a disaster due to a problem number.
| 109 54 | White money game Blue |
4/0 takes a checker off, but threes become a big problem number with boththe five and four points stripped. 6/5, 4/1 gives Blue one three to playwith, but there are still plenty of potential problems. If Blue rollstwo moderatly sized numbers next turn he will have to play the sparesfrom the six and five points, leaving him with a completely stripped positionwhich is very dangerous. The best play is the unintuitive 5/4, 5/2. Thisgives 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 ableto 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 whichleave a shot are 6-1 and 5-1. Other aces can be handled safely. One otherconsideration in favor of clearing the five point is that the point is clearedfor good. If Blue does succeed in clearing the six point, he will no longerhave to face the problem of clearing the five point.
When comming home against a backgame, the question of problem numberscan be very tricky. One must look ahead to see what the real dangers are.
| 174 95 | White money game Blue |
Blue has several possibile plays here. He could hold everything byplaying 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 astripped 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 willbe 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 problemnumber, 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 handlethese future difficulties.In addition, sixes are an immediate problem, and Blue will have onlyone spare on the bar point to handle a six.
Clearing the eight point with 8/6, 8/5 is a bit better. At least thisputs a second spare on the five point. Also, the eight point is one ofthe points which is under double-attack. If Blue is forced to leave ashot 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, andsixes are an immediate problem.
The best play by far is to clear the bar point with 7/5, 7/4. This putsthat important spare checker on the four point, as well as another spareon the five point, instead of overloading the six point. As we have seen,clearing the bar point can be especially difficult against the two-pointanchor, 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 allblocked, so if he rolls 6-3, 6-4, 6-5 or 6-6 he won't have to play thesix. Thus, Blue is unlikely to be forced to leave a blot in the middleof his blockade. Note that the nine point is relatively easier to clearthan the eight or bar points, since these checkers aren't being blockedby two of Whites anchors. Thus, clearing the nine point safely with a gapis no more difficult than clearing the eight point or the bar point withno gap. In each case, there are four safe landing places.
It is easy to overdo the above theme. As always, careful attention todetail and problem numbers is the key. For example:
| 108 81 | White money game Blue |
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 getstwo checkers home for a faster bearoff. In this position, however, thestodgy 8/7, 8/5 is best. The key is that there are no serious problemnumbers from the bar point. Sixes don't play, and Blue has severalspares on the six point to handle fours. After 7/6, 7/4, Blue hasproblem 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 boardcheckers home. These factors are sufficient to make 8/7, 8/5 thesuperior play.
The following problem should be pretty easy after the previous discussion:
| 152 73 | White money game Blue |
It might seem as though Blue could play 9/8, 9/3, since he wouldn't haveto play 6-6 next roll so everything plays safely. If we look ahead, it isclear 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 whichplays -- the spare on the five point. Playing 6/5 with the ace gives Bluethat second important four, which could mean the difference betweenbeing able to bear in safely as opposed to being forced to leave a gap.
| 138 96 | White money game Blue |
At first glance it appears that 9/6, 7/1 leaves Blue with an awkwardposition -- five checkers on the six point and all the outer board pointsstripped. 9/3, 6/3 may seem more flexible. Now that we know to lookfor problem numbers, we see things in an entirely different light.Right now Blue's problem numbers are fives and fours. Once he clearsthe nine point fours and threes will be his problem numbers, and threeswill remain a problem number until both the eight and bar points arecleared. The only place that Blue will be able to play his threes fromwill be the six point, so Blue better pile as many checkers onto that pointas he can while he has the chance. 9/6, 7/1 is a far superior play to9/3, 6/3. You just can't have enough checkers on the six point in thissort of position.
The above examples should give you a good idea about the dangers ofproblem numbers when bearing in against an anchor or anchors. See what theproblem numbers are or are going to be in the future, and protect yourselfagainst these numbers by giving yourself as many of them to play aspossible.