This article originally appeared in the February 2001 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
How often have you had the following happen to you:
I've seen this one before, you say to yourself. A big 19 pip lead after the roll. Should be a piece of cake. All I have to do is avoid leaving a shot. I am running out of sixes to play, but I know how to handle that. By playing the number in my inner board, I will keep a spare checker on the eight point. That way if I roll a six next turn I won't be forced to break the eight point and then be squeezed off the midpoint prematurely. My doubles will come eventually, or my opponent may be the one who is squeezed first.
So, instead of playing the natural looking 8/1, you play 5/1, 4/1 -- reasonably smooth and it holds the spare on the eight point. Your opponent rolls 6-2, and plays 8/2, 7/5. Hmm -- he doesn't seem so concerned about saving sixes. Maybe he will pay for that by being squeezed off my bar point prematurely. That will serve him right.
You roll 6-4. You play 8/2, 5/1. Scrunch, scrunch. Ugly, but at least you didn't have to break the eight point. And another two pips for your racing lead. Shouldn't be much of a problem if you can avoid leaving a shot.
Suddenly your opponent rolls 5-5 and runs for it. Yikes! The race just got close. You are ahead in pips, but in crossovers it is another story. This could get scary.
The race goes on. You aren't missing, but you aren't rolling doubles either. Your opponent isn't outrolling you, but he is ripping checkers off every turn. You still have the lead in pips, but that lead may turn out to be phony.
Finally you come down to:
Still a 7 pip lead in the race and on roll, but that pip lead is looking meaningless. He is one checker ahead of you, and if he doesn't miss he will win. You roll 5-1. He rolls 5-3. Uh oh! You roll 6-3. Yep, here comes that damn 4-cube. You have to take. He rolls 5-2, and wins 4 points. A disaster. One more unlucky game down the drain.
But wait. Was it just bad luck? After all you were ahead in pips all the way. That indicates that had you placed your men better for the bearoff you might have been able to win. But what could you have done? When you brought your final checkers in and started bearing off you already had those checkers on the ace and two points. It wasn't your fault that you rolled so well that you took checkers off the higher points in the bearoff, was it?
Fortunately you happened to have the game recorded. Let's roll the cameras back to where you played that six-saving 4-3. Hmmm. A couple of checkers did go to the ace point on that roll, didn't they. And on the followup 6-4 you were forced to take two more checkers deep into your inner board. Maybe that six-saving wasn't such a good idea after all.
Now you are starting to get interested in this position. Let's suppose you had played 8/1 with the 4-3. On the next roll you would have been forced to play 8/4, 8/2, breaking the eight point but keeping a relatively smooth position. Diligently you play through all the moves as they would have been played with the same dice rolls. This time you are ahead, not behind, in the crossover department after he rolls the double-fives. The end position comes in differently. You have taken one more checker off, and instead of losing the race by a roll you win by a roll. That play of the 4-3 did make the difference, but not the difference you thought it would make.
Now you are getting more curious, so you go back and look at your opponent's 6-2 play right after your 4-3 roll. At the time you had snickered at him for taking two checkers in and not saving a six. Now you wonder -- maybe he knew something. You have him play it by saving a six with the same dice rolls, and sure enough -- he would have wound up wasting just a little bit and been a roll short in the end.
The above example may look contrived, but I have seen this type of scenario occur again and again. While saving sixes is often correct, it is often overdone by most players who are familiar with the theme, including experts. The reason is that when they don't save a six and are forced to leave a shot which is hit, the cost is immediately apparent and they won't forget it. However when they lose a race because they saved a six, it is not so obvious what has happened. They blame the loss on bad luck in the race rather than their failure to prepare adequately early.
Saving sixes does have its place. The most common situation occurs in a holding game where one is way ahead in the race. Avoiding getting squeezed off the anchor has the highest priority, and you can afford some wastage if the race lead is really big. For example:
Blue will be 32 pips ahead in the race after this roll. That's a lot -- so much that even if White rolls big doubles White will maintain contact as much as he can. Blue's goal is to make it a race. The only way Blue can clear the anchor safely is to roll doubles, and he needs as many turns as he can take to roll those doubles before facing the evil day. If Blue plays 7/2, 7/1 then his next six (except 6-1 or 6-6) squeezes him off the anchor and leaves White a double-shot. Blue can delay the evil day by saving a six and playing 7/1, 6/1. This may give him time to roll doubles, or at least force White to clear the eight point before Blue is squeezed off the anchor. It is the correct play.
It should be noted that there are several features of this position which make saving the six correct. One is that Blue is very far ahead in the race, so he can afford a bit of wastage for the bearoff. As we have seen, if the race is moderately close this may not be the case. Another feature is that Blue is saving his last six. That is important. However, it is not necessary to save a bunch of sixes. I have seen this sort of position mangled quite often.
This is similar to the previous position, but Blue has more checkers in the outer board while his inner board is starting to crunch. Trying to save as many sixes as possible with 9/3, 5/2 is not the right idea. Blue should play the natural 9/3, 8/5 or 8/5, 7/1. If Blue crunches his board in order to hoard sixes, there are several bad things which might happen.
1) Blue could find himself in trouble in the race. It is true that he is
way ahead now, and that is not likely to change. But if Blue piles all of
his inner board checkers onto the ace and two points and White suddenly
starts rolling doubles, Blue's racing lead won't be nearly as great as
the pip count indicates since there will be so much wastage involved.
That one extra six Blue saves by playing 9/3, 5/2 just isn't worth too much. Either Blue rolls doubles in the next few rolls or he will be forced to leave the anchor pretty much regardless of how many sixes Blue saves now. Given that, Blue should concentrate on putting his checkers where they belong.
When the race is close, wastage can be very costly. Even if there is some danger of being squeezed off an anchor prematurely, it is important to play smoothly rather than be too concerned about saving sixes. The following is a very typical type of position which comes up all the time.
I have seen many players in this type of position play 11/3, thinking that they are doing well by saving a six. This wrong. It is true that by playing 11/3 then Blue may be able to delay the evil day he is squeezed off the anchor by a turn, and that may give Blue one more chance to escape both checkers with two large numbers. However, the cost is too great. Right now the race is pretty close, but once Blue starts burying checkers he will be falling farther and farther behind in the race even if he rolls the same pips as White rolls.
In addition, what happens if and when Blue finally is squeezed off the anchor? If White rolls a joker which makes the five point on Blue's head it is all over -- nothing Blue can do about that. But what if all White can do is hit loose. Will he be willing to do so? Not clear. White has a small lead in the race, so he may not want to put it all on the line. He will be far less inclined to hit loose if he is staring at a closed board on Blue's side. If Blue has crunched his position, White will be freer to hit loose.
Thus, Blue's correct play is the beginner's play of 11/6, 8/5. From there Blue lets the dice decide. If Blue rolls a six he gets squeezed off, but it will then be up to White to roll a perfecta or risk losing everything with a loose hit. If Blue doesn't roll a six he can hold the fort, breaking from the six point if need be, and have a compact position. This way Blue both maximizes his racing chances and his winning chances if there is some blot-hitting.
When bearing in while waiting to escape a back checker, it is important to keep a flexible position. I have seen many players mishandle the following type of position.
Many players will play 6/1, thinking that by moving to the ace point they are saving as many pips as possible. This is very wrong. By going to the ace point they are cutting down on their flexibility for the future, which is very costly. In addition, in this position the idea isn't to save sixes; it is to kill sixes. Once Blue brings his outfield checker home he will no longer have to play sixes, which will help him maintain his board longer. It is far better to play 16/11.
When you are in very bad shape, it is necessary to think optimistically rather than pessimistically. You can't be worried about bad rolls. You have to assume that good things will happen, and play to make the most of them. The following type of position is often mishandled:
Blue is not going to get a shot next turn, and he may not have a chance the roll after that. I have often seen players play B/22, 6/1, in an attempt to save a six so they won't be forced to run. This is not correct. There are three important factors to consider:
1) If and when Blue gets a shot, White will have several men off. Blue will
have to be able to contain the hit checker, and if he doesn't have a closed
board his chances of containing the checker go down considerably. Blue must
keep the closed board and think optimistically. His ideal scenario is that
next roll White has to play a checker from the five point. Blue then doesn't
roll a six, holds his board, White leaves a shot, and Blue hits. This is what
Blue should be hoping for to win the game. If Blue rolls a six and can't
stay back, so be it. Blue isn't likely to win anyway, so he must make
the play which maximizes his winning chances when things to right.
If sixes can be saved without doing major damage to the board, it may be correct to save a six. For example:
Blue is well ahead in the race, so getting squeezed off the anchor prematurely is a concern. Since he can save an extra six and keep his board in one piece with 10/1, he should do so. 10/4, 8/5 is a more flexible play, but here it is probably better to save the extra six and see what the future brings.
However, this concept must not be overdone. Change the position slightly to:
Now Blue should play 10/4, 8/5. Holding the five point for future contact is more important than saving an extra six. As we have seen, it is vital to keep one's board intact even if it may mean getting squeezed prematurely.
Saving sixes does have its place. When one of the players is likely to be forced off a key anchor to leave a shot in the next roll or two, it is worth a little bit of wastage and board destruction in order to increase the chances that it is the other guy who is squeezed first. This is particularly true if you are ahead in the race, so getting hit is more costly than usual. For example:
In this position it is well worth saving a six and playing 6/1, 5/4 rather than holding the closed board with 7/1. Saving the six may make the difference as to who will have to leave the first shot. Blue isn't going to be getting a shot next roll, and after that he will be forced to crunch anyway if he doesn't roll doubles. Since there he is nothing he can do about the crunching, it is correct to save the six for now.
However, it is far to easy to overdo this concept. As a contrast, consider the following position.
This time, Blue should not save a six -- he should play 7/1. There are two major differences between this and the previous position:
1) White might leave a shot next turn. If that happens, Blue will be very
happy he kept his closed board.
The key is that, while Blue would rather not be squeezed off the anchor and be forced to leave that first shot, it might not turn out too badly. For example suppose White rolls something like 5-2 and closes his board, and Blue rolls 6-4 and is forced to play 18/8. This is terrible for Blue if White hits the shot, of course. But suppose White misses with something like another 5-2. White is forced to play safe and crunch his board. Now if Blue can get away, suddenly it is a whole new ball game. White still has the lead in pips, but it is Blue who is ahead in crossovers. By forcing White to crunch while not wasting himself, Blue will have essentially turned the game into an even race. This isn't saying that Blue wanted to be squeezed off the anchor -- he would have preferred to hang on. But when he is squeezed off first and White misses the shot, Blue is in surprisingly fine shape.
Saving sixes is an important concept which should be in every player's arsenol. But it is important not to overdo it. Smoothness and flexibility usually have a higher priority, and the sixes that are saved can come back to haunt you later.