This article originally appeared in the September 2003 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
Playing perfect backgammon is impossible. We can't do it. The bots can't
do it. Quite often, even the most extensive analysis or rollout won't
determine what the truly best move is. There are simply too many
variables involved, many of which may be beyond anybody's grasp, whether
you are carbon-based or silicon based.
Our goal is to play as nearly perfect as we can. This means avoiding the big blunders, or Whoppers as they are often referred to on GammOnLine. We can tolerate the small .01 or .02 errors -- in fact, quite often they turn out not to be errors. What we are trying to avoid is the .10 errors. Anybody who plays a match making no error greater than .02 or .03 in equity has played one very fine match.
In this article, I am going to discuss five common types of flawed thinking which are likely to lead to a big error. If you can avoid the errors discussed here, you will probably be playing as close to perfection as you can.
1) Missing a candidate move
A long time ago, Paul Magriel told me that the most common checker play errors didn't occur when a player made the wrong choice between two candidates -- they occurred when a player never even saw one of the candidates. He said this was true for players of every level, from novice to world class. At the time I found that hard to believe. Perhaps it is true for novices, but for world class players? Yet, experience has taught me that Paul was 100% correct. When I analyze matches I have played over the board and look at my big errors, in the majority of cases I never even considered the correct play. Everybody has this problem, and everybody will fall prey to this error.
How can we reduce the times we overlook the best move. Here are some suggestions:
Don't play too quickly. I'm not suggesting stewing over every play for 5 minutes -- in fact, I believe that can be detrimental to one's game. What I am suggesting is to not make the first reasonable-looking move you see without examining all the plausible alternatives. How are these alternatives found? If you roll a 5-4, scan the entire board and see where each checker moves 5 and each checker moves 4. Don't forget the possibility of taking the entire move with one checker. Many of the plays will be obviously absurd, but make sure you have at least scanned them before you eliminate them. In fact, even before you roll the dice you should be having a good idea of where you will be wanting your pieces to move. While your opponent is thinking about his play or while you are shaking your dice, you should be looking over the board and seeing what pieces you are likely to want to move and where you would like to move them. No doubt you have seen some experts play most of their rolls almost instaneously. You wonder how they could possibly have analyzed all the possible plays and come to a conclusion so quickly. The secret is that they have done a lot of their analysis before they have rolled. For example:
Suppose you are Blue, on roll, in the above position. Your offensive structure is fine, and you don't figure to be able to improve it any this roll. It is the three checkers stuck on White's ace point which are the sore spot in your position. As you are shaking the dice, you are mentally reaching for that checker on top of that pile to move it. You know that is what you want to do almost whatever you roll. If a 6-4 pops out, you don't have to think -- you can just automatically play 24/14. If you roll 5-2, 24/22, 13/8 will just play itself. And so on. Of course you would find these plays anyway, but the expert can make them instantly because he knows what he is trying to do with the position and where various numbers will take the checkers he wants to move.
It may seem contradictory that I am suggesting that you don't play too quickly, while at the same time showing how the expert plays quickly. This is not the case. What I am trying to illustrate is how by looking ahead the expert can increase his efficiency scanning the board for plausible candidates.
Don't play half a move until you are 100% sure that it will be part of your play.
We have all seen experts roll a 5-2, play the 5, and then look around for the best 2. We all do it ourselves. In fact, this is a good way to help visualize the resulting positions and analyze to possible 2's -- provided that you have first determined with 100% certainty that the half of the roll you are playing is going to be part of every reasonable candidate play. If you don't do this first and play a reflex half of a roll, you may very easily never see the best play as a candidate. For example:
Your opponent opens with a 6-3, playing 24/18, 13/10. As you are shaking your dice, you are thinking -- come on, baby -- give me an ace or a six -- particularly a six -- I will be hitting. In fact, this thinking is quite proper as far as it goes. Out comes a 6-3. Bang! 13/7* is obvious with the six, so you play it. Then you examine the position after that six has been played, see that 24/21 and 13/10 are the logical possibilities for the three, play one of them, and scoop up your dice.
As I'm sure all GammOnLine readers know, either of these plays would be a good-sized blunder. The clearly correct play is 24/15*. This also hits, but it rips away a key builder, gains more in the race, starts to escape a back checker, and leaves far fewer return shots. Yet, if you play 13/7* first and then look around for the best three, you are quite likely to completely overlook the best play. I'll grant that since this is a response to an opening roll the position is so well known that most players aren't likely to make this error -- although I have seen it happen. However, in more complex positions it is quite easy to believe that a part of one's play is forced when, in fact, an entirely different use of the number is considerably superior.
It should be noted that if Blue had instead rolled 6-2 in the above position, then it would be quite proper technique to play 13/7* and look around for the best two. The reason is that as Blue scans the position for his candidate plays, he will soon see that the only two reasonable candidates are 24/22, 13/7* and 13/11, 13/7*. Once Blue comes to that conclusion then he is quite correct to play 13/7* and look for the best two. The reason is that 13/7* is part of both of his candidate plays, so he should play that part of the roll. However, if Blue plays 13/7* before making the determination that this is going to be part of all of his candidate plays, he risks falling into the trap.
Keep an open mind:
When examining the candidate plays, be sure not to prematurely eliminate a candidate because of some general principle which is usually correct. Each position is unique, and unexpected plays may turn out to be correct. Quite often a player will be able to analyze the position and come to the proper conclusion -- provided that he considers the play in the first place. However, if the play doesn't pass his first screening because he is applying some general principle mistakenly for the position, then he has no chance to analyze the play. For example:
There are a lot of possibilities. Perhaps 13/9 with the 4, followed by 13/12 or 6/5 with the ace -- either of these aces has its pros and cons. Perhaps it is right to pay off to a 6-1 joker in order to get more ammunition aimed at White's blot and play 9/5 with the 4. If Blue does that, should he play 13/12 with the ace, giving diversification but losing a huge swing if White rolls 6-5? Or should he guard against this and play 5/4 with the ace? Or maybe Blue should hit loose with the 4, following the good general principle of not giving the opponent one roll which escapes the back checker. If Blue does hit loose, does he follow with the very big 9/8, or the more conservative 13/12? So many possibilities to choose from.
The fact of the matter is that I haven't even mentioned the best play. It is 13/8!. This may seem very unintuitive to many players. We have all been taught how dangerous it is to slot the back edge of a prime into a direct shot, particularly when the opponent has a strong board. It this position, however, it is a standout play. The key is that Blue's entire focus has to be on containing White's back checker. White is way ahead in the race, but if Blue can contain this checker he has a good chance of forcing White's position to crack after which Blue will be in great shape. If White is rolling a six, Blue is likely to be in trouble anyway. Furthermore, if White doesn't hit Blue will be threatening to make either a five-prime or a solid six-prime, and he will probably be able to send over a cube which White will not enjoy seeing. I'm sure that most readers can understand why 13/8 is the best play by far, and if they considered the play as a candidate they would probably come to the right conclusion over the board. However, if they immediately eliminate it from the list of candidates because it leaves a direct shot which allows White to flee at the same time, they will never have the opportunity to appreciate the full merits of the play.
2) Losing the forest through the trees
Playing expert backgammon requires looking at the whole board, not just bits and pieces. Quite often players are unable or unwilling to do this, and focus on small details which may be of very minor importance. For example:
What is the best play? I haven't the foggiest idea. What I do know it that the equity difference between any of the reasonsble plays is going to be tiny. I guess I would play 16/15, 14/12, but some other play might be a bit better. I would not spend any time on the play at all -- I would just grab a couple of checkers and put them on what seems to be good places. However, I have seen players study this sort of position for a couple of minutes. They are trying to work out what will happen if they roll 5-5 followed by 6-6 or something like that. It isn't worth it. First of all, these are very low probabality events. Secondly, keeping diversified and bearing in smoothly is more important than guarding against specific sequences. It is often correct to pay off to boxes leaving an immediate shot if the alternative involves an ugly structure. In this sort of position, spending time trying to work out the best play is simply a waste of mental energy, and it is quite likely to lead to the wrong play anyway. These same players might make a snap judgment on a really critical decision because they can't mathematically analyze it. Note that I wouldn't be playing my 2-1 randomly. Any play I would choose would wind up with the outfield checkers on three different points since I know from general principles that a high priority is to diversify as much as possible.
Blue can either play safe with 13/8, 6/2 or he can make the big play and hit loose with 13/4*. Obviously 13/4* will win more gammons, but getting hit back would be bad and Blue is well ahead in the race. Which play is best is not immediately obvious. This is potentially a critical decision, and while the two plays might turn out to be close it is also possible that one play is way better than the other play. There are a ton of factors to weigh -- White's board strength, Blue's lead in the race, Blue's potential awkardness if he doesn't hit loose, Blue's ability to cover if he survives the loose hit, Blue's improved gammon chances after hitting, White's timing problems, White's potential recube if Blue hits and White hits back, the match score if playing a match, and so on and so on. The point is that this sort of play can't be calculated. Yes, it is easy to see that if Blue hits White has 13 return shots, 7 rolls which enter without hitting, and 16 flunks, but what does one do with this information? Hitting is great when White doesn't hit back (particularly when White flunks), but terrible when White does hit back. Equating the great and the terrible in the proper weighings is very difficult, even for the best players and bots in the world. The important thing to realize is that this is likely to be a critical decision, and this is the type of position which it is worth taking your time on. Yet, the same players who will ponder over the 2-1 for 2 minutes in the previous position will make a snap judgment in this sort of position because they know that they won't be able to calculate it out. Granted one will have to go by feel to some extent, but this position deserves a lot of thought.
When faced with a murky play problem, many players will try to find something solid upon which they can base their decision. They may count shots, count pips, look at duplication, anything which gives them a quantitative basis for their choice. While all of these factors matter, quite often they are relatively unimportant. Usually the overall position is the most important thing, and that can be judged only by experience and feel. If a player focuses on one little aspect of the position, he is likely to wander astray. For example:
The shot counter sees that B/18, 13/7 leaves only 11 shot numbers, while B/18 exposes the blot to a triple shot which is at least 27 shot numbers (29 to be exact if my count is correct). That could easily persuade him to play B/24, 13/7. In fact, B/18 is considerably superior. The position is better balanced -- B/24, 13/7 strips the midpoint. White has to break an important point to hit on his bar point, while White would love to hit with the spare checker on Blue's two point. Blue loses much more ground if he is hit on his side of the board than on the other side of the board. In addition this position is about outfield control, and B/18 brings another Blue checker to bear on the outfield while B/24, 13/7 takes a checker away. The quality of the hit combined with the overall position makes B/18 much better, but a player who concentrates on the little stuff can easily count the shots, lose the forest through the trees, and play B/24, 13/7.
3) Mis-evaluating priorities:
Choosing a play is easy if there is only one play which does everything you want to do. With the difficult play decisions, there are often several plays which each have their plusses and minuses. Weighing these plusses and minuses correctly is the key to finding the best play.
Have a game plan:
With every play you make you should have some idea in mind what you are trying to accomplish. Of course there are often several intertwining game plans, and the one which should be emphasized may be determined by the dice roll you get. Still, it is worth a lot to know what your main objective and secondary objectives are going\ into the dice roll, so when the roll comes you can choose wisely. For example:
Before the dice roll, what does Blue want to do most? His big problem is his back checker. It is stuck by itself behind a growing prime and facing a strong board. If Blue can just escape that back checker, he will be in fine shape. If you asked him what his best roll is, he would say 6-5 without hesitating. Sure building up the board would be nice, but with White anchored on Blue's three point Blue can't attack and he is unlikely to be able to prime White successfully. Running that back checker to safety clearly should be Blue's number one priority.
In order to run that back checker, Blue needs a six other than 6-1 or 6-6. As he is shaking his dice, he is mentally reaching for that back checker, hoping he rolls that six. And so he did! If Blue concentrates on sticking to his main game plan, he will play 24/15 and not be led off his path with the prospect of making his five point. Not only does 11/5, 8/5 not really accomplish what Blue is trying to do -- the play strips the eight point, loses the 11 point, leaves a dangerous blot in Blue's outer board, and cramps Blue's position. Yet, without a focus on the main game plan, which is to escape the back checker, Blue might well get this play wrong. In fact, a world class player did make this error in a late round of a big tournament.
Play the position:
There are plenty of examples of this. If you are ahead in the race, try to disentangle and go for a straight race. If you are behind in the race, attempt to maintain contact. If your opponent has only one man back, put extra effort into preventing that checker from escaping. If your opponent has a four or five-prime containing one checker, getting that checker to the edge is important. If your opponent has an attack force, making an anchor is vital. When there are conflicting priorities, a little common sense will often lead you to what is best for the position:
Blue can hit the second checker, or he can escape the back man. Running is the better play to win the game. If Blue hits and is hit back, he will have two checkers which have to escape and White will be back in action. However, hitting loose will win more gammons, and if Blue can win the fight for his three point he will have a great position. Is it worth the risk? Blue has the stronger board and has made a deep point. If White anchors on Blue's three point, Blue is going to have plenty of problems even if he escapes. White's blockade isn't insurmountable. Blue has enough checkers on the midpoint so crunching isn't an immediate danger. The point is that Blue's position is more blitz oriented than anything else, so that should be what Blue is concentrating on. Changes in the position such as strengthening White's board or blockade could change this quickly, but the actual position screams attack and Blue should play 13/10, 9/3*.
Do what the dice tell you:
You aren't always going to get the rolls you want. You have to play what you roll. The expert will make the most of his dice rolls, even though the roll may not correspond to the preferred game plan. In particular, if there is something which needs to be done and you roll the number to do it, think twice before using the roll for something else even though that something else may be more in line with what you would like to accomplish.
Blue would sure like to lock up the bar point, and that is one of his major goals. However, making the bar point involves releasing both the nine point and the midpoint, and leaving that direct shot on the midpoint. In addition, Blue can use the roll very profitably to run the back checker. That is what the dice are telling him to do, even though making the bar point is such a great improvement.
4) Making awkward plays:
We don't control the dice when we play backgammon. The dice control us. They tell us the limitations of what moves we can make, and often these moves aren't the moves we would like to make. The secret to success is to position your checkers in such a way so as many rolls as possible are good rolls. This is sometimes called flexibility, although it is really more a matter of being prepared. If you watch an expert play, it will appear that he gets less than his share of bad rolls. This isn't luck or accident. The reason he seems to get less than his share of bad rolls is that he positions his checkers so as to minimize the number of bad rolls in the future.
Keep checkers in play:
We all know that burying checkers is bad. What is often not realized is just how bad. Of course sometimes you will have to bury checkers. When you are bearing in against an anchor and your opponent has a strong board, safety is the absolute number one priority and it is very rarely correct to volunteer a shot. This is not true earlier in the game.
We have all been taught the importance of the race in mutual holding games, so it may seem worthwhile to make the awkward play of 8/2, 6/4. It isn't. Taking a checker out of play on the two point and stripping the eight point is quite damaging to Blue's position. If he makes this play, he is likely to find that every play after this will play equally awkwardly unless he rolls perfectly. Blue should play 13/7, 6/4, the natural developing play which gives him nothing but good numbers next turn if White doesn't hit. Blue won't like it if White hits, but the hit is far from fatal. Interestingly enough, in the old days nobody would even consider anything but 13/7, 6/4, since going to the two point is so anti-positional. Today we realize the importance of the race, but it is still necessary to make comfortable plays.
Leave future plays:
The idea behind avoiding awkwardness is to give yourself ways to handle less than ideal rolls comfortably while waiting for the good rolls. This doesn't always lead to the prettiest position. For example:
8/5, 6/4 may look like the obvious play, but actually it is quite wrong. The proper play is the seemingly ugly 13/8. Beauty is in the eyes of the beholder, and the expert sees that the big pile of checkers on the eight point, usually, an eyesore, is a beautiful thing. Blue is trying to clear his midpoint against White's bar point holding game, and Blue will need as much time as possible if he doesn't roll his eventual doubles for quite a while. The more checkers Blue has on his eight point, the longer he can stave off the evil day when he is forced to break his eight point and then get squeezed off the midpoint. In addition, 13/8 prepares to clear the midpoint next roll if Blue rolls doubles. Those spares on the eight point permit Blue to swallow a bunch of poor rolls, and thus create extra flexibility in this position.
Avoid ugly structures:
We all know instinctively what is ugly in backgammon. Three or more checkers piled on a deep point. A stripped six point or some other key point. These defects in a position lead to lack of flexibility, which in turn leads to more rolls which destroy the position. Any time you see yourself making a play which creates an ugly structure, stop. Put the pieces back, and look around to see if you can do better. Sometimes there is no choice, but quite often a little thought will reveal a more comfortable play.
6/2 may look like the obvious play. Wait! Three checkers on the two point? Maybe more in the future, since Blue may eventually have to play a six from the eight point to the two point. Ugly play! Put it back and look to see if there is something else. Once you realize that Blue doesn't need to keep his board right now since White isn't going to be leaving a shot, it becomes clear that there are other possibilities. 4/1, 2/1 is more flexible, and spreads the checkers out better, but this play does cost Blue the four point and he may not be able to get it back. 6/3, 2/1 holds the four point and avoids the ugly mess on the two point. Three checkers on the three point isn't nearly as bad as three checkers on the two point, since the spare can be moved with either an ace or a two. The downside to this play (as compared to 4/1, 2/1) is that it loses one of the critical spares on the six point. I don't know which of these plays is better, but they both look a lot better to my eye than 6/2. Three men on the two point? Ugly play!
Let all numbers play
Any time you make a play, it is worthwhile to check that all of your numbers, particularly 4's, 5's, and 6's can play decently next turn. You would hate to have a simple 4 or 5 on one of your dice destroy your position. Sometimes there is no choice, but often a little thought can save a lot of grief.
Making the bar point with 11/7, 9/7 may look like an automatic play to some players, but it is actually a very poor play. The problem is: How does Blue play his fives? 6-5 and 5-4 leave an immediate shot, and other fives except 5-1 force Blue to break his six point with the bar point still uncleared. Since Blue has three checkers on the bar point it will take him two rolls to clear it, and if he rolls a five on either of his next two rolls it won't be pretty. If Blue looks at how future numbers will play, it will be apparent that 11/7, 9/7 leads to a very awkward position. Much better is 11/9, 7/3. Now Blue can play anything decently, and at worst he will have to leave an indirect shot clearing the nine point.
5) Failure to cube:
There are several different kinds of cube errors, but this is by far the most common and most costly. Let's see what can be done about it:
Every roll is a new cube decision:
If a player learns and acts on the above sentence, that will improve his game more than any other possible advice. If the cube is in the center or on your side, the first thing you should think about before rolling the dice is whether or not to double. I mean every roll! It is true that for the large majority of your rolls the decision to not double is trivial, but by training yourself to do this you will not be making the big mistake of not doubling because you forgot to think about it. How often have we all seen the following sort of scenario:
Blue opens with 4/2 (8/4, 6/4), and White responds with 5-4 (24/20, 13/8). This leaves:
Obviously nothing special has happened yet. Now Blue rolls 4-4(13/5(2)*, and White rolls 5-3 (B/22, 13/8) leaving us:
Blue now rolls 5-5, a crusher (8/3(2)*, 6/1(2)*). White flunks, leaving:
Playing for money, Blue would have to cash. In a match, Blue can play on for a gammon. He does so, and gets his gammon. After the game is over, he asks me if he was correct to play for a gammon. How should I answer?
The answer is that there is no answer, because the question is incomplete. I would have to know which turn Blue was talking about. If he were to ask me if it was correct for him to play for the gammon after rolling the 5-5, I could say yes. But what about after the 4-4? Why didn't Blue double? Did he think he wasn't good enough? Did he think he was too good? Or, as I'm sure was the case, did he simply forget about the cube? In fact Blue has a very strong double at that point, and White has a proper take. Blue's failure to double after rolling the 4-4 was a huge blunder. He simply rolled without thinking about the cube. It happens all the time, and it is the single most common and most costly error backgammon players make.
Don't wait and see:
It is common to reach a position where if things go well on the next exchange you will be crushing your opponent with good gammon chances, but if things go badly you could be in trouble quickly. Many players take the wait and see what happens approach. They figure that if they get a good roll they can play on for a gammon, while if they get a bad roll they will be happy they didn't double. This approach is sometimes correct near the end of a match when the player needs fewer than 4 points to win the match, but for money or at an even match score it is a terrible blunder -- one of the biggest. Here is a typical such position:
Blue can see that if he rolls a four he is going to have a very powerful position -- one which he could almost surely cash if necessary and a good shot at a gammon if White rolls badly from the bar. On the other hand, if Blue flunks White will be a favorite to make his four point and then it is anybody's game. It may be tempting to wait and see, but that is exactly the wrong thing to do. Turn the cube, roll that four, and win 4 points instead of 2 points. If the game turns around, so be it. The odds are heavily weighted in favor of doubling.
Don't let the big ones get away
The more volatile the position, the more correct it is to turn the cube provided you have some kind of overall advantage. The reason is that if you win the next exchange, you could lose your market by a country mile. The previous position is a good example of this. Contrast with turning the cube when your opponent has a solid holding game. Assuming he has a take, you aren't likely to lose your market by much on the next exchange whatever happens. Thus, failing to double isn't going to be very costly. With volatile positions such as blitzes, it is another story. If you roll well and he rolls badly, your equity could shoot up into the stratosphere. You can't risk having this happen without the cube being turned first. That is why it is often correct to double a blitz with a cubeless equity of around .380, while it might not be correct to double a holding game with a cubeless equity of .480.
Follow Woolsey's law
I have written enough on this in the past, but it bears repeating. When you can't say for sure whether or not your opponent has a take, then it is always correct to double. There are many examples of this. In fact, most proper cube turns will probably fit into this category. Maybe it actually is a pass, if you aren't sure. Maybe he will pass. Mabye the double is correct anyway. Unless your assessment of the position is way off, if you think there is even the slightest chance that it might be a pass then you can never be far wrong doubling, and you may be very right.
Watch for the turnaround
Once you have decided to play on for a gammon, the decision is not etched in stone. Every roll is a new cube decision. Before every turn, you must reconsider the decision to play on for the gammon. If your opponent starts to make some progress, it may be correct to cash before he gets to the point where he has a clear take. The window of opportunity may be very small -- possibly just one roll. If you miss that window and he rolls another good number, you will find yourself in danger of losing a game which should have been yours for the taking.
Let's say that you rolled some joker, and arrived at the above position. Clearly you have a good play-on for a gammon. The gammon chances are very good, with the potential to close out three White checkers, and your advantage is so great that you will probably be able to cash later if necessary. But things don't go that way. You roll a poor 3-2 (13/8), and your opponent rolls 6-2 and enters a checker. Now we have:
Hold it! Every roll is a new cube decision. Last turn you were playing on for a gammon, but this is a different position. White has his anchor, so the gammon chances have decreased considerably. In addition, the losing chances have gone up. You may not escape White's blockade in time, or White may win from the two point anyway. This re-evaluation makes it clear that it is no longer correct to play for the gammon. It is vital to double NOW. White probably has a pass -- if he chooses to take that is his business and you won't care much either way. If you wait just one more roll, it could be costly. If you fail to escape and White enters his last checker, now White will have a huge take if you should dare to turn the cube (which you shouldn't). The window of opportunity would have slipped by if you failed to double when you should.
The above types of errors are perhaps the five most common and most expensive errors made by players at all levels. If you can avoid these errors, you will be playing backgammon as well as humanly possible.