On the other hand, any anchor must be broken at some time if the game is to be won. The object of the game is to bring all 15 checkers around and off, and this can't be done if two checkers remain on the opponent's side of the board. The problem is choosing exactly when to break that anchor. Break it too early, and you may be attacked or lose your chance for a last ditch defense. Break it too late, and you may be stuck there and forced to crunch your board. It is a difficult problem.

In the early stages of the game, both players start with an anchor on the enemy ace point. This is not an ideal anchor. The checkers are too far back, and in danger of being primed. In addition, they fail to control the enemy outer board sufficiently. It is usually advisable to break this anchor and split the back checkers early, to try to make a more advanced anchor and to make it difficult for the opponent to bring builders down from the midpoint safely. In the early stages of the game, the dangers of being attacked are relatively small, since the opponent doesn't have a strong board and he doesn't have ammunition in place to carry out an attack.

It is in the later stages of the game where anchor-breaking decisions become critical. The opponent will have started to build up his board and bring some ammunition down, so leaving the anchor can be dangerous. We will also have been building up our board, If we stick around too long, we may find ourselves in some serious timing problems. Balancing these dangers is sometimes very difficult. Here are some criteria to look at.

1) The strength of the enemy board. This is vital. The stronger the enemy board is, the greater the danger of being attacked.

2) Enemy ammunition. The more checkers your opponent has in the attacking zone, the better his chances of carrying out a blitz.

3) Diversion. If your opponent is on the bar or scrambling to put his defense together on the other side of the board, it is relatively safe to break an anchor. He can't do everything at once. If your opponent is solid on your side of the board, he can concentrate on attacking, which makes leaving the anchor more dangerous.

4) Your structure on your side of the board. It is dangerous to be weak on both sides, since this gives your opponent too many good rolls and gives you too much to do. If you have blots on your side of the board, breaking the anchor is more dangerous than if you are solid there. Readers have no doubt heard that it is usually unwise to slot and split. This is an example of being weak on both sides of the board at the same time.

5) Timing. This is a major consideration, and one which is quite tricky. If you are more advanced than your opponent, you are likely to run out of time and be forced to crunch your board or concede outfield control if you hang onto your anchor. In this case, it is often wise to break off the anchor if it can be done conveniently. If it is your opponent who is more advanced, then breaking off the anchor isn't so vital. Now you will probably be able to play your rolls decently, while it is your opponent who will have the timing problems. Note that if your opponent is more advanced that generally means he has more material in attacking range, which makes leaving the anchor doubly dangerous.

A couple of simple examples:

146 139

White money game Blue

Blue is ahead in the race. If he holds the anchor, he will have to give up his midpoint. The timing is likely to go against him, and he will probably wind up with the two back checkers stuck on White's three point far away from the rest of his army. White will maintain dominance of the outfield, as Blue is forced to play in his inner board. It is far better for Blue to use this roll to break the anchor conveniently with 22/13. White doesn't have too much attack material in place, so Blue isn't in too much danger of being blitzed. With any reasonable luck Blue will soon escape the other back checker and then then have only to deal with coming in against White's holding game.

Contrast with the following:

133 151

White money game Blue

All the factors are the other way. White is ahead in the race. White has plenty of ammunition with which to attack. White has the stronger inner board. Blue has an outfield blot. Blue can play the roll comfortably without sacrificing anything if he doesn't run. This time it is clear for Blue to hold his anchor and simply play 11/2. Blue has the timing advantage, since White is ahead in the race. Blue's plan will be to sit on the anchor, build up his board, and wait for White to commit himself. 22/13 would be a serious blunder.

These were easy examples, where all the relevant factors pointed in the same direction. What about positions where there are conflicting features? These are the difficult positions. It can be hard to weigh the various pros and cons for breaking the anchor, yet it must be done if one is to come up with the right play.

Back in 1992, I wrote an article for Inside Backgammon called Anchors Aweigh, where I discussed this topic. At the time I was very oriented towards holding onto anchors, playing a backgame or a holding game if need be but avoiding being blitzed. It should be noted that this was in pre-bot days, so we didn't have good computer rollouts available to check things out. In the article, I examined 12 positions from a world championship match between Paul Magriel and Michael Meyburg. Each of these positions involved anchor breaking plays. For each of them the player chose to break the anchor, and at the time I felt that breaking the anchor was incorrect for each position. The article caused quite a bit of controversy, and it was felt that my conclusions were wrong on several of the examples. Today my views have shifted somewhat, and guided from my experience with the bots I am more inclined to break anchors than I was 10 years ago. I thought it would be interesting to reexamine these positions today and see how the thinking has changed.

For each of these positions I have done a short Snowie rollout (144 trials, 2-ply). This is not necessarily large enough to be significant, but it gives us some idea of what is going on.

130 157

White money game Blue

Magriel played 24/23*, 20/14. In my article, I argued that he shouldn't be breaking the anchor this prematurely since he isn't in position to win the game and he still has to worry about the checker on White's two point. My feeling was that it is no disaster if White hits on the two point. Blue merely reenters and plays from there. I no longer agree with this. Playing 24/23*, 8/2 dumps a checker onto a bad place. Blue has evened up the race with this hit, but if he gets sent back from his two point he lose all the ground he has won. Blue has the stronger board, and White is on the bar, so this is a good time to get off the anchor and try to bring the checkers around. White's position is stripped, so White is unlikely to be able to do much damage.

Rollout results: (these will all be cubeless equities).

24/23*, 20/14   +.087
24/23*, 8/2     +.082

163 178

White money game Blue

Magrial played 24/22, 20/15. I argued that splitting was too dangerous with White having the stronger board and a few builders, and Blue in no immediate danger of being primed. Instead, I preferred 20/15, 8/6. My thinking at the time now looks very wrong to me. This is probably going to be a game about outfield control, and this is an ideal time to activate the back checkers -- relatively safe, and quite productive. Blue would like to advance his anchor if he can. Keeping both men back on the 24 point is going to leave him with problems later on.

Of course, the proper play of 8/3*, 3/1 wasn't even considered by anybody at the time. Make the ace point early in what figures to be a long positional battle? Horrors! These days we have learned better. While making the ace point is no bargain, leaving the blot on the ace point waiting to be hit at just the wrong time is even worse. The bots have taught us this lesson quite well. Not only does 8/3*, 3/1 solve this problem, but it puts White on the bar and gives Blue a chance to get White's five point which is the anchor Blue would really like to make. Today I would play 8/3*, 3/1 without giving it a second thought.

Rollout results:

8/3*, 3/1       -.300
24/22, 20/15    -.314
20/15, 8/6      -.377

151 159

White money game Blue

Same game a few moves later -- this time it was Meyburg who had a potential anchor-breaking play. There are several possibilities which weren't even considered in the article. He could play 13/8, making an important point. He could play safe with 22/20, 9/6. Even hitting loose on the ace point isn't so dumb here. However, let's suppose that Blue will always be slotting the five point with the three, which was the style in those days and might well be the right idea anyway. Which two should Blue play -- 22/20, or 9/7.

Meyburg played 22/20, 8/5. I argued for 9/7, 8/5. My feeling was that if White hit, then Blue could fall back on his 5-3 "backgame" thing, while if Blue gives up the 22 point now it is gone forever. Looking at things in the 21st century, I have changed my tune. The race is close, and Blue loses a lot of ground if he is hit. A 5-3 backgame simply isn't likely to work. The overall timing is wrong -- White has too much stuff to play with in the outfield. It is more important for Blue to get a spare on the 20 point ready to spring out into the outfield so Blue can play a decent holding game. This is a better game plan.

Rollout results:

22/20, 8/5      +.046
9/7, 8/5        -.026

In the light of the new era, I'm not so sure my analysis was right. Sure the hit is dangerous, but not overly so. White is on the bar, so the best he can do is enter and hit back. He might not do that -- all his twos don't hit. White's forces are pretty thin for an attack. All Blue has to do is enter if he is hit, and White will be doing a lot of scrambling. If Blue doesn't hit, he is resigning himself to an inferior position, well down in the race and very undeveloped compared to his opponent.

What about cube considerations? If Blue plays B/18*, the volatility is suddenly in the sky and White has a clear double. If Blue plays B/23, 13/8, then the volatility is low, and it would be incorrect for White to double. Does this make hitting wrong? At the time I argued that this was another argument agaisnt hitting -- that White would cube if Blue hit but White would be a long way from a cube if Blue played safe. This sounds persuasive, but proper reasoning leads to the opposite conclusion. What you want to do is to avoid letting your opponent have efficient cubes, where you have a close pass/take decision. If Blue plays B/18* White has a good double, but Blue's take is very easy -- it isn't a close decision. On the other hand if Blue plays B/23, 13/8 White doesn't have a double yet, but he is likely to improve slowly to where he has an efficient double. Consequently, if the two plays are otherwise equal it is better for Blue to make the cube-provoking play, since this forces White to make an inefficient double. This may seem contrary to what one's intuition says, and I had never heard of the concept ten years ago.

Rollout results:

B/18*           -.359
B/23, 13/8      -.362

141 124

White money game Blue

Magriel played 18/11. There are various possible plays such as 7/4, 7/3 and 8/1 which hold both the midpoint and the 18 point, but let's suppose that Blue is going to break one of the points and the issue is which one to break. Magriel's theme is that he is ahead in the race and White's board is a mess, so why not make a run for it now? I argued that this approach exposes Magriel to some bad variations, and that even if it works he still has a lot of work to do.

I have since seen this theme come up often, and the rollouts almost always favor breaking the midpoint. The idea is that you are going to have the problem of clearing the midpoint anyway if you break off the defensive bar point, and you will probably need doubles to do that. Meanwhile, by making a play such as 18/11 you expose yourself to an immediate catastrophe. The better game plan is to break off the midpoint, so if you are hit nothing bad will happen. If you aren't hit you bring the other checker home, and that gives you plenty of time to sit and wait for the eventual doubles. I would make the same 13/6 play that I made 10 years ago.

Rollout results:

13/6            +.199
18/11           +.183

125 151

White money game Blue

At this point Mayburg was well ahead in the match, which explains why the cube is remaining in the center for many of the following positions. Here, Magriel chose to play 24/23, 6/3, thinking that he should be going after a better anchor before Meyburg brought more ammunition into play. I argued that Magriel should hold the anchor. He is behind in the race, therefore the timing will probably go his way, and the back checkers have an escape route if needed. The big danger is being attacked since White has the stronger board. It is better to try to win the timing battle.

Rollout results:

6/5, 6/3        -.445
24/23, 6/3      -.595

It should be noted just how important the timing considerations are here. For example, moify the position to:

125 132

White money game Blue

Here it is correct for Blue to split the back checkers. If he tries to sit on the ace point, his timing is going to run out and he won't be able to hold his board long enough to damage White when White is forced off the anchor. Blue still gets gammoned more by splitting, but the additional wins are more than enough to compensate for these gammons. In the actual position Blue does have sufficient timing to sit and wait with those three checkers on the midpoint to play with.

The next four positions are all from the same game, and involve interesting anchor-breaking decisions for both sides in a priming battle.

132 139

White money game Blue

Magriel played 24/23, 13/7. I had felt that this risked too much to gain too little. White has the stronger board, and there is serious blitz danger. Blue doesn't like getting stuck on the 24 point, but after 13/7, 6/5 Blue has good chances to build a five-prime and become a serious contender in the priming battle. The timing is close, with White's slight racing lead (which is better for Blue's timing) compensated for by White's more advanced prime and White having more numbers which move his back checkers. This analysis still seems correct to me.

Actually, if Blue wants to break off the anchor, he is better off running all the way with 24/17 than making Magriel's play. This will solve his timing problems, and if he can survive the attack he will be in pretty good shape. However, this play leads to a lot of gammons. I think that holding the anchor and working on the offense has sufficient winning chances without the increased gammon risks from the blitz.

Rollout results:

13/7, 6/5       -.195
24/17           -.238
24/23, 13/7     -.286

Now we shift over to Meyburg's side of the table, with a 3-2 to play. Meyburg played 24/21, 6/4. There are other possible splitting plays: 24/22, 24/21 or 24/22, 10/7. Even 6/1* has it merits, although it is an entirely different kind of play. However, I argued for holding the anchor with 10/7, 6/4. My argument was that Blue needs to protect his back men while bringing in ammunition for the blitz, and that once the attack gets going Blue should have no trouble escaping. This argument looks all wet to me now. Blue is in definite danger of losing the priming battle. If White escapes his back checker or make the four point and Blue is still sitting with two checkers on White's ace point, he could be in real timing trouble. Blue has to do something -- he can't just sit on the position. I was overly optimistic about Blue's chances to eventually escape. The key is that Blue has the stronger board, so he should not be worried about being attacked. His big danger is losing the priming battle.

Rollout results:

24/21, 6/4      +.097
10/7, 6/4       -.021

Back to Magriel's side of the board. He played 23/17. I didn't like this play at all. Most of the same arguments apply -- White has the stronger board, and Blue is in danger of being attacked. In addition, this play leaves Blue's back checker stranded. I much preferred 24/23, 6/1*. Not only does this lock up the anchor, but it is a great anchor -- Blue can escape from the 23 point with sixes. This puts Blue in pretty decent shape in the priming battle, and gives Blue a basis from which he can launch an attack of his own. The bad part is the blot on the ace point, but even if White hits the checker Blue's position will be sound, and if White misses Blue can play along priming or blitz lines depending upon the dice. This analysis still looks pretty sound to me.

Rollout results:

24/23, 6/1*     -.347
23/17           -.462

Magrial played B/22, 6/4*. I can only imagine that he got carried away with the slugfest which had occurred. This play is far too risky. Even if he gets away with it, Magriel still has a lot of work to do on both sides of the board, and if it blows up in his face there is a very severe gammon danger. I recommended making the defensive three point, and I stand by that recommendation -- I don't think it is close. The race is close, so Blue will have some winning chances after White escapes his back checker, and White might not be able to escape that checker. The anchor cuts the gammon danger way down. Magriel was simply trying too hard to win.

Rollout results:

B/22, 24/22     -.513
B/22, 6/4*      -.674

Meyburg played 24/21, 13/7. I claimed that since Blue is in no danger of being primed and that White has a bunch of checkers on the eight point which are looking for a home that Blue should play 13/7, 11/8. Today, I'm not so sure. Splitting the back checker considerably improves Blue's chances of making a good advanced anchor, and since White has only a two-point board and not much ammunition there really isn't much danger of being blitzed. Actually, the strongest argument for 13/7, 11/8 isn't that it holds the anchor -- it is that it cleans up the blot on the 11 point by moving it to a valuable place so Blue won't have to worry about it in the future. Of course, in those days of carefree blot leaving, I never even mentioned this point. Despite this, I think I now prefer Meyburg's play.

Rollout results:

24/21, 13/7     -.101
13/7, 11/8      -.108

Meyburg played 24/21, 9/7. I criticized this play as splitting into the jaws of death when it wasn't necessary to take such risks. I recommeneded making the four point, which leaves a nice safe and solid position. I now see that I hadn't taken into account the timing issues. Blue is ahead in the race, White's anchor is more advanced than Blue's, and if Blue makes his four point White has an escape route via the bar point while Blue does not. The timing is very likely to go against Blue, and he will be forced to crunch his board in the future. It is vital for him to make his move to escape one checker or make an advanced anchor now before White can bring any more ammunition to bear. If Blue waits, splitting in the future will be far more dangerous. I now like Meyburg's play better.

Rollout results:

24/21, 9/7      -.330
7/4, 6/4        -.416