This article originally appeared in the August 2000 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
In today's modern era of backgammon, most players play pretty well. It
not be sufficient to just make the theoretically correct play. If you
are unable to create problems for your opponent he will play well also, and
your edge will be small at best. It might be better to make slightly
inferior plays if these plays have a chance to induce your opponent to make
even greater errors.
One obvious way to achieve this goal is the complicate the position. But exactly what complicates a position? Certainly the longer the game is, the more chance your opponent has to make errors. Can we control the average length of the game by our choice of plays?
As a test, I had Snowie roll out a few of the opening plays. I wasn't interested in the rollout results as much as I was interested in the time it took to complete the rollouts. It seems like a reasonable statement that the longer it took to complete the rollouts, the longer the average length of the game was. Here are some results from 1296 trials, 1-ply, with no truncation (i.e. games played to completion).
24/23, 13/11: 1 minute, 46 seconds
24/20, 13/10: 1 minute, 47 seconds
24/14: 1 minute, 43 seconds
It can be seen that slotting plays or plays which leave blots which are likely to be hit lead to longer games than more conservative plays. This is what we would have expected, but it is interesting to see this confirmed by actual tests. So, even if you think that splitting is the theoretically correct play with an opening 2-1, it is probably the wrong play against a weaker opponent. You want to lengthen the game, since the longer the game the more chance he will have to make errors. Since the slotting and splitting plays are pretty close anyway, it is better to slot if you prefer the longer games.
In the middle game, this phenomenon can be even more striking. For example:
Blue's obvious choices are 24/20, 23/20 and 8/5* ,8/4*. Both plays are quite productive, and it is not particularly obvious which play is better. However the two plays lead to considerably different types of positions. After 24/20, 23/20 the game is likely to turn into a mutual holding game, which will often be a race. These games are not only relatively simple to play, but they tend to be shorter. After 8/5*, 8/4*, complications figure to develop. White is a favorite to hit back, and the the checkers start flying. This game is likely to take much longer to complete. An analysis of the time of the rollouts confirms this:
24/20, 23/20: 1 minute, 46 seconds
The double hit definitely leads into longer games, and probably more complicated games as well. Thus, if you believe you are the superior player you should definitely play 8/5*, 8/4*, even if you believe that making the 20 point is the better play.
Many experts believe that the best way to play against a weaker opponent is to try to complicate the position. While having a bunch of checkers back will tend to make the game last longer, that doesn't necessarily mean that it is a difficult position to play. Sometimes that sort of position is quite easy for the average player to handle, and his errors if any are not likely to be very costly. I have seen players who are generally quite weak suddenly start playing as though they are pros when the more complex positions are reached. For example:
This is a typical complex position where both sides have a lot of men back. Let's suppose Blue has a roll to play where the best play isn't obvious. 6-2 looks like a good example. A nice chance for a player to make a serious error, right? Not really. According to Snowie rollouts, the top ten plays were within .075 cubeless. This is the case for just about anything Blue might roll. An average player just can't misplay this sort of position too badly. Even though the games will tend to be long, your opponent doesn't figure to make many serious errors.
When you have a position type where your opponent is going to have a lot of difficult decisions, it is important to make sure the game will be played to the finish. This means sending over a cube which would ordinarily be uncalled for. For example:
Blue has the advantage, of course, but hardly a doubling advantage. White's position is solid, and the volatility is very low. Against a weaker player, however, this is a must double. It is vital to force him to play this game to conclusion. White is going to have a lot of difficult decisions to make in this game -- whether to go frontwards or backwards, which anchors to break, whether or not to hit, etc., as well as the possible necessity of employing good technique at verious stages of the game. This is very unlikely to turn into a simple race or holding game. Against an equal player doubling would be silly, but if your opponent is weaker then doubling is quite profitable. In fact, it isn't even clear that you are rooting for him to pass, even though in theory this is a trivial take.
When choosing between approximately equal plays, try to pick the play which is likely to give your opponent a difficult choice. This may induce him to make a serios error. If your opponent's play is virtually forced, he can't make an error. Often this is a decision of whether or not to hit. For example:
It isn't clear whether Blue should come out with 24/18 or make a slotting play such as 13/7 or 24/22, 13/9. These plays might be about equal in theory. The problem with the slotting plays is that White virtually cannot misplay his next roll. If he can hit, he will do so. If not, he will just bring builders down from the midpoint and try to develop some more.
Instead, suppose Blue plays 24/18. Now some of White's plays aren't so clear. Is it worth it for White to break a point and hit with a number such as 3-1 or 3-2? Not so obvious. And if White does the wrong thing (hitting when he shouldn't or not hitting when he should), there is a good chance that he will be making a serious error. This factor should lean us toward playing 24/18 unless we are convinced that one of the slotting plays is clearly superior.
Should Blue play 7/3 or 13/9? Both are reasonable. 13/9 leaves a better strucure, but there is some downside if the blot is hit. Or is there? Sure the hit will be easy with 5-3 or 5-5, but what about other rolls such as 5-2 or 4-1. Is White even supposed to hit? A wrong choice by White, whatever it is, could be a pretty serious error. Assuming the choice between 7/3 and 13/9 is close to begin with, Blue should play 13/9. This gives White the potential to make a big error.
Cube decisions should also be tailored to the possibility of an error by the opponent. In a simple and well-known position, it may be correct to refrain from making a marginally correct double.
On the other hand, it may be correct to make a premature double if there is a chance your opponent may incorrectly pass. He won't make that mistake in simple holding games such as the one above, but in tenser types of positions he may get it way wrong.
Priming battle are good examples of positions where players can lose their perspective. In the above position, it is very easy for the White player to see how Blue can make the bar point next turn and White's position will just crunch to dust. I have often seen players pass positions such as this. In reality, Blue doesn't even have a double in theory. Sure he will probably make the bar point next turn, but he might not. If he does, White still has plenty of chances. Blue has two men stuck on White's ace point, and White has a good offense with builders well distributed. White has some maneuvering room with the two checkers on the midpoint, and if Blue is unable to roll a six and escape White could easily win the priming battle. After all, it is White who has the more advanced anchor. If Blue does escape one checker, White may be able to attack the remaining checker and scramble over Blue's blockade while Blue is stuck on the bar. If all else fails White can play a two-point game -- no bargain, but it does generate some wins and is good gammon protection. There are so many good things which can happen for White that a double by Blue is premature, but against many players you will get a pass from this position.
End-game positions often lead to drastic mis-evaluations. In this position, Blue doesn't yet have a double. He needs to get some more ammunition in place first. However there are many players who will quickly pass, since they can see that they are likely to be contained. What they forget is that when they do get away it is often with a joker which leads to a gammon. In addition White can't be gammoned, and occasionally White will win after being closed out. These possibilities add up an easy take, and since the position is relatively involatile Blue should hold off on the redouble. Yet I have seen many players pass similar positions.
It is more dangerous to delay making a theoretically correct double with the hope that your opponent will err and take later when he should be passing. There is the chance that your position will get way to good and the pass will be obvious, so you will lose your market. In some positions such as the above, you might get away with it. White has a solid take, since his backgame chances are pretty decent. However Blue definitely should double in theory, because if White rolls one bad number his timing will collapse. Against certain backgame egomaniacs, it might be right to wait. Even if White's timing gets worse, they may still take, and that will be a serious error.
These examples illustrate how one can take advantage of the weaknesses of an opponent and induce more errors. This sort of thing must not be overdone. You still have to make the correct play most of the time. Since you can't predict what the dice will bring, you don't know if the positions you are after will develop. When the choices appear to be close, that is the time to take your opponent's weaknesses into consideration.