This article originally appeared in the January 2003 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
Picture a well-timed back game which has just hit a shot:
Even though White has taken ten checkers off, in the hands on an expert Blue is a definite favorite. It is true that if Blue closes White out when White has ten checkers off that White has the edge, but there are other things which can happen. Blue's plan is to trap White behind the blockade and force White to jar more checkers loose. If Blue can pick up a second checker he will be a big favorite -- in fact, he will probably be able to claim on a recube. In the actual position Blue should probably play 24/19, 22/20* in order to take immediate advantage of White's inflexibility. If White rolls 3-1 or 3-2 he is forced to leave two blots, and Blue will already have a powerful recube which might not even be a take.
The above scenario is the ideal one for a back game. Unfortunately, not all back games are well-timed. Sometimes you are forced to crunch, and when you finally get your shot the position might look something like this:
Blue has hit, but the plan of containing the hit checker behind a prime and jarring a second checker loose isn't going to work. Blue has made his ace point and buried a couple of checkers in the process. What is Blue's game plan? Does he even have one?
Most players adopt a scramble approach. They try to spread their outfield men about to cover all parts of the board, and hope to keep hitting White as he comes around. The problem with this plan is that it almost can't work. White won't have much trouble entering and moving, and eventually something bad is likely to happen along the way. About the best that Blue can realistically hope for with this approach is to never miss a shot and eventually scramble off the gammon. Building up the inner board and containing the White checker sufficiently to win the game is a real longshot.
Does Blue have anything better? Maybe he does. Ideally he would like to jar another blot or two loose. If Blue can pick up another blot, he will have a decent chance to come out ahead in the ensuing free-for-all. But how can Blue pick up that second blot? He doesn't have a prime, nor does he have the ammunition to make one.
Picture the following position:
White is on roll. Offhand, it doesn't appear that Blue has done a very good job of positioning his checkers. He isn't blocking fives or sixes, and his men are on the same points rather than diversified to pick up White's fleeing checker. But wait! Blue has blocked sevens and eights. Is this important? Let's see. Suppose White rolls 6-1, 5-2, 4-3, 6-2, or 5-3. He has to move the large part of the roll with the outfield checker, and then he is forced to take the rest of the roll in his inner board since the outfield checker is now blocked. 6-2 and 5-2 force White to leave one blot and a double shot. 4-3, 6-1, and 5-3 are even better for Blue -- these force White to leave two blots. If White rolls one of these bad numbers and Blue hits a blot in White's inner board, Blue will have some real chances to win the game. One checker is difficult to keep contained with no prime, but with two checkers to batter around Blue will have a decent chance to keep White on the bar, bring his men around, and not only get off the gammon but quite possibly win the game.
Now we are starting to see a real winning plan for Blue. Instead of scattering his checkers around in the outfield, he should be trying to make points and hope that these points cause White to stub his toe bringing the back checker around. Almost any point may do the trick if White happens to bump his head into it at the wrong time. That is why it is called the random point.
Where should this random point be? Most of the time there won't be much choice -- just make some point in the outfield and hope for the best. Sometimes, however, there is a choice, and by carefully examining the opponent's bad rolls you can maximize his chances of having an accident.
Blue has his choice of points to make. Even though 18/13, 17/13 doesn't block big doubles, I believe this is his best play. This play leaves White the most root numbers -- 4-3, 5-2, and 6-1. Making the 12 point blocks boxes, but only 5-1 and 4-2 jar another checker loose. Blue may not get too many chances at that second checker, so he should make the most of what he has now.
While making inner board points is fine, Blue can't afford to take risks to do this. He must proceed slowly, covering the outfield and establish those random points.
Many player mistakenly try to rush things by playing 11/6*. This simply isn't the right approach. If Blue is to win this game, it will be in the outfield. The 11 point is a great asset, a random point which gives White 4-1 and 3-2 as root numbers. Blue can make another random point with 17/14, 16/14, adding 6-2 to the collection. The remaining back checkers give Blue sufficient outfield coverage.
When there is nothing to be done this roll, Blue must prepare for the future. A random point in his outer table is not something to be given up lightly. In addition to potentially being a root number for White in the future, Blue can make a new inner board point by rolling doubles or the point can just serve as a key blocking point at some future time.
Blue should not try to distribute builders to make an inner board point by playing 12/10, 12/9. He would have to roll perfectly to make an inner board point, and these blots may be targets at exactly the wrong time. Blue should hang onto his 12 point and hope it comes in handy in the future. Best is 24/19, which not only blocks 4-4 but creates 6-2 as a root number for White.
Blue wants to make any new inner board points, of course, but he can't afford to rush things. Slow and steady is the watchword. Every point counts.
It would be quite wrong to break the bar point in order to slot something inside. Blue doesn't have the ammunition to cover it. In addition, the bar point has plenty of value as a potential random point. White will probably be sent to the bar a couple of times in the future as Blue slowly brings his checkers around. Every time White tries to enter, as long as Blue has the bar point there is the possibility that White will roll 5-2 or 6-1 and the ball will pop loose.
Careful attention to root numbers can make a big difference. Take a look at the following position:
Obviously Blue will make the six point, but his other two aces don't appear to be too important. Actually, they are. If Blue keeps his current inner board structure, White's only really bad entering roll is 3-1. However, look what happens if Blue shifts with 7/6(2), 4/3(2). Now both 4-1 and 2-1 are disaster rolls for White. In addition, the shift takes away White's 3-3 joker which clears everything up immediately.
Another similar example:
Aces aren't particularly bad for White. If he is forced to play an ace in his inner board he will have to leave a shot, but it is only one blot and if Blue misses the shot White is in decent shape. Twos, on the other hand, are a major disaster for White. If Blue makes his six point and plays the rest of the roll in his outer board, White has only 4-2 as a disaster roll. However, if White shifts with 7/6(2), 3/2(2), now both 4-2 and 3-2 are disaster rolls. In addition, this shift takes away White's 2-2 joker. Since White will probably be entering from the bar several more times this game, every time he is on the bar he is threatened with these disaster rolls. That adds up quite quickly to a lot of potential for Blue.
Careful attention to details and root numbers can lead to some interesting plays.
Shifting with 6/5(2)* and playing two other aces is short-sighted. That will put White on the bar for a second, but it will not accomplish what Blue is trying to do. White can live with aces -- it is his twos which are the real root numbers. If Blue shifts, White doesn't have any bad twos. Right now there is immediate potential for some root number, since Blue's points are six and eight away from White's blot. The problem is that this is too efficient a configuration. If White rolls 6-2 he can't play the six at all, so he can play 20/18 safely. Blue needs to force White to play the whole number. His correct play is to shift the front point 11/10(2) and play the rest of the roll with his checkers in White's inner board. Now both 3-2 and 6-2 are root numbers for White. Note that 5-1 and 4-1 also force White to leave a blot, although Blue does much better if White has to double-blot.
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 well-placed random points, these positions can be won.