This article originally appeared in the June 1999 (Demo) issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
If you have ever watched a top-flight pool player, you will notice that
most of his shots seem very easy. There are very few bank shots or other
difficult shots as the player runs the table. Almost all of his shots are
head-on shots. The reason is that the expert pool player plans ahead. He
doesn't think of just the current shot; he considers the next two or three
shots and plays to position the cue ball where he will want it to set up
those future shots.
It is the same for backgammon. Somehow, the expert doesn't appear to have difficult rolls to play. Pretty much regardless of the dice, his plays are usually natural and easy to find. The intermediate player, on the other hand, will often be struggling play after play. The reason is that the expert backgammon player is positioning his checkers much in the same way that the expert pool player positions the cue ball.
It might seem impossible to plan ahead in backgammon, since one can't forsee what the upcoming dice rolls will be. To some extent this is true. What one must do is position the checkers so the largest number of future rolls play comfortably. This is what is called flexibility, but there is more involved than that. It is necessary to look ahead, see what course the game is likely to follow, and prepare accordingly. For example:
Blue has a difficult 5-1 to play. The four obvious choices are:
a) 6/1, 3/2
Blue won't like it if he is hit, although it is far from the end of the world since White has an inner board blot and Blue has the stronger board. More important is what happens when White doesn't hit. Instead of worrying about minor details such as duplication, let's look at the big picture and see what course the game is likely to take.
Blue is well ahead in the race. Therefore his main game plan should be to bring all his checkers around safely. While waiting for the fortunate doubles necessary to do this, he must position his checkers so he can handle awkward rolls. In the meantime, what about White? White will try to sit on the position as long as he can, but he also has a limited number of spare checkers to play with before something has to give.
Now that we understand the fundamental elements of the position, let's examine our four candidate plays:
a) 6/1, 3/2. This play has the obvious plus of not leaving an immediate shot, which is not insignificant. But what does Blue do for an encore? Every point is stripped, including the vital six point. This play leaves Blue no flexibility at all, and if he doesn't roll doubles immediately he will probably be forced to leave a shot when White's board is stronger. Since White's position is currently improving rather than deteriorating, playing safe now is not a high priority. This safe play leaves Blue in a bad position for his next roll.
b) 8/2 is the safest of the shot-leaving plays. In fact White will be reluctant to hit unless he can also cover the blot on the four point, since hitting involves breaking the anchor. But what does the future look like? Blue will be able to move the blot on the eight point next roll, and he will have one spare on the six point to play with. After that, he is out of time, and will probably be forced to leave a potentially fatal shot. White has four spare checkers to play with (one on each of the midpoint, eight point, six point, and five point), so it looks like White will be able to play comfortably longer than Blue can. The cue ball is positioned better than after the super-safe 6/1, 3/2, but not much better.
c) 13/8, 2/1 leaves a different sort of position. If White misses the shot, Blue can probably bring the checker on the midpoint to safety next turn. Now the timing is considerably different. Blue has plenty of pips to play with, counting the checker on the midpoint and the spare on the six point. If things start to get tight Blue can break the eight point in a pinch, leaving him even more timing. This means that Blue will probably be able to last for several rolls while waiting to roll those doubles which see the back men home. In addition White's spares are limited, so White may run out of time before Blue does and be forced to make a vital concession. This plan makes more sense. After 13/8, 2/1, Blue is better prepared to handle most awkward rolls for the next few turns. The cue ball is placed where Blue wants it.
d) 18/13, 2/1. This play has the obvious detraction of leaving a double shot, as well as giving White several hit and cover numbers. In addition, if the blot is hit that blot will have to survive on its own, while the other plays kept the anchor on the bar point so a hit blot would have a potential place to land. Even so this play is most consistent with Blue's game plan of bringing them in and winning, so it is a definite candidate if Blue will have an easy road home when the shot is missed. However, that is not the case. First of all the outfield blot will have to find a home, which may not be easy. Even assuming Blue gets this checker safe, he will still have to clear the midpoint against White's five-point holding game. Once Blue releases the enemy bar point White will have a lot of free checkers to play with, so the timing will go in White's favor. Thus it doesn't appear that Blue's gains when he gets away with the play are great enough to justify the risks involved.
Looking at the big picture, 13/8, 2/1 stands out as the best play. Top experts will find this play because it "feels" right, even if they can't exactly quantify why. What they are feeling is the comfort of being able to play future rolls conveniently. They know the cue ball is positioned properly.
Blue has three possible plays, each leading to a different type of position.
23/16 might be the best play to win, but it just asks to get gammoned. White has plenty of firepower with which to attack, and Blue would be a sitting duck. Blue should not plan on playing the rest of the game on the bar. He needs that anchor. This is not the right game plan.
Advancing the anchor with 23/22, 7/1 is consistent with the overall position, since Blue is actually a bit ahead in the race. But what does Blue do for an encore? If he doesn't roll an ace followed by a six very quickly, his whole game will collapse. Meanwhile White will calmly bring his back checkers out into the outfield. If Blue could call his next rolls this is what he would do, but he can't do that. This play leaves him badly positioned for most followup numbers.
22/16, 7/6 is the play which prepares Blue for the future. He springs a back checker, which gives him some room to handle awkward rolls as well as staking a claim in the outfield. In addition he hangs onto an anchor in case of disaster. Now if White breaks off the anchor (which he will almost certainly have to do in a roll or two), Blue will be in position to attack. True Blue will then need some luck to win frontwards, since his back men are stuck, but he could get lucky. This is a sensible game plan which lets Blue play most of his next rolls comfortably, vital in this sort of position.
A common sort of problem in a holding game. Blue can save two sixes with 6/1, 6/3; one six with 7/2, 6/3, or no sixes with 7/2, 7/4.
Blue is ahead in the race, but not substantially so. Since a lot of holding games turn into races, it is moderately important for Blue to take some steps to avoid being squeezed off the 18 point. On the other hand Blue doesn't want to trash his board, since this will hurt him both in a race and if he hits a shot.
Bringing both checkers home with 7/2, 7/4 is shortsighted. White will probably be able to hold his eight point for a roll or two, and if Blue gets squeezed off the defensive bar point by rolling a six White will have a game-winning double shot. This play would show a lack of preparation for some awkward rolls.
Is it correct to save two sixes? This involves trashing Blue's board pretty badly. Let's see what is likely to happen to White's position. He can probably hold his eight point for a roll or two, but will then have to release it in order to keep his board intact. If nobody rolls doubles Blue will probably be squeezed first since his anchor is deeper and he is ahead in the race, but if Blue hangs on for a couple of rolls then at least he won't be leaving a double shot. If he leaves a single shot, that may not be so bad. It is curtains if White hits, but what if White misses? White will be frozen on the midpoint provided Blue maintains a strong board, so if Blue can get the other checker by on the next roll he will have a lead in crossovers which will be helpful in the race.
The bottom line is that Blue must prepare for the future. If somebody rolls doubles the game turns into a race, and Blue doesn't want to have wasted too much. If nobody rolls doubles, it is important for Blue to keep a smooth board even if he is squeezed off the enemy bar point. Thus, Blue cannot afford to trash his board in order to save a second six. His correct play is 7/2, 6/3.
It should be noted that this decision is very dependent upon White's structure. If White had another checker on the midpoint then it would be more important for Blue to save a second six, since White would be able to hold the eight point longer. Also this would mean that Blue's lead in the race was greater, so Blue could afford to waste a little.
What could be simpler than making the three point with 9/3, right? That would certainly be the right play if Blue might be getting a shot in the next roll or two. However the true expert sees that Blue won't be getting a shot for several rolls, so making the three point immediately may not be essential. He looks ahead at what is likely to happen a few rolls down the road and attempts to prepare as best as possible.
What is likely to happen? White will not be leaving a shot for several rolls, and Blue will have to keep moving. This means that Blue will not be able to hold the five-prime from the three point to the seven point for long. He will have to aim for deeper points as well. So, how can making the three point now and slotting the two point later be wrong? Sounds fine provided Blue can conveniently slot the two point, and most of the time he will be able to do so next roll. However he might not roll a five or a four, and then things could get awkward. For example, if Blue plays 9/3 and then rolls 6-1 next turn he will be forced to dive to the ace point prematurely with the two point remaining bare.
Let's try another approach. Suppose Blue plays the unnatural looking 7/2, 6/5. The inner board blots won't matter, since White isn't leaving a shot next turn. Now Blue has 2's, 3's, 4's, 5's, and 6's to cover one of the blots, so he is guaranteed at least a 4 1/2 point board after his next roll. Furthermore, every roll will now play comfortably. This might seem like a small thing, but it is little things which make the difference between winners an losers in backgammon over the long run. A thoughtful player who looks ahead and sees where he wants to position his checkers will find such a play.
Back games probably require more planning ahead than any other types of positions. Here it looks natural for Blue to move a checker to the springboard on the 22 point, so if and when he rolls a six he can leap that checker out into the fresh air and gain some timing for the back game. This would clearly be necessary if Blue were in immediate danger of crunching.
In the actual position Blue is not in immediate danger of crunching; he has several checkers to play with. The problem is that White also has plenty of time. Those three checkers on White's midpoint represent several rolls of timing for White, during which Blue may be forced to crunch. If Blue plays 23/22, 8/4, White's timing figures to be quite good. White can throw a checker onto the two point when he needs to do so, and obviously Blue will not be ready to hit it. Also, once White starts bringing his men in and clears the eight point, he will not have to play sixes. This stalling effect may cause Blue to crunch.
Suppose Blue instead plays 24/23, 8/4. Now he needs a two and a six to escape, but he will have a few rolls to roll the two and the six before he starts to crunch. The difference between a 2-3 backgame and a 1-3 backgame is huge when the timing is tenuous as it is here. No longer will White have a convenient two point to land with his awkward large numbers; now he will be forced to dive to the ace point. White will not be able to do any stalling, since all of his numbers will always play. Also, and very important, Blue's shot figures to come much quicker against the 2-3 back game, since White has to clear both the eight point and the bar point with two of the landing places blocked. The expert who looks down the road a few rolls rather than just at the immediate position sees these things, and prepares accordingly by shifting to the 23 point.
The above examples illustrate how the backgammon expert, like the pool shark, looks beyond the immediate roll and anticipates future problems. While the dice will often destroy the best of plans, careful planning will make your game less dependent upon getting consistently good rolls.