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

In the early stages of the game, both players start with an anchor onthe enemy ace point. This is not an ideal anchor. The checkers aretoo far back, and in danger of being primed. In addition, they failto control the enemy outer board sufficiently. It is usually advisableto break this anchor and split the back checkers early, to try to makea more Advanced Anchor and to make it difficult for the opponent to bringbuilders down from the midpoint safely. In the early stages of the game,the dangers of being attacked are relatively small, since the opponentdoesn't have a strong board and he doesn't have ammunition in placeto carry out an attack.

It is in the later stages of the game where anchor-breaking decisionsbecome critical. The opponent will have started to build up his boardand 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 thesedangers is sometimes very difficult. Here are some criteria to look at.

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

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

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

4) Your structure on your side of the board. It is dangerous to be weakon both sides, since this gives your opponent too many good rolls and givesyou too much to do. If you have blots on your side of the board, breakingthe anchor is more dangerous than if you are solid there. Readers have nodoubt heard that it is usually unwise to slot and split. This is an exampleof 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 oftime and be forced to crunch your board or concede outfield control ifyou hang onto your anchor. In this case, it is often wise to break offthe anchor if it can be done conveniently. If it is your opponent who ismore advanced, then breaking off the anchor isn't so vital. Now you willprobably be able to play your rolls decently, while it is your opponentwho will have the timing problems. Note that if your opponent is moreadvanced 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 togive up his midpoint. The timing is likely to go against him, and hewill probably wind up with the two back checkers stuck on White's threepoint far away from the rest of his army. White will maintain dominanceof the outfield, as Blue is forced to play in his inner board. It isfar better for Blue to use this roll to break the anchor convenientlywith 22/13. White doesn't have too much attack material in place, soBlue isn't in too much danger of being blitzed. With any reasonableluck Blue will soon escape the other back checker and then then haveonly 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. Whitehas plenty of ammunition with which to attack. White has the strongerinner board. Blue has an outfield blot. Blue can play the rollcomfortably without sacrificing anything if he doesn't run. This timeit is clear for Blue to hold his anchor and simply play 11/2. Blue hasthe timing advantage, since White is ahead in the race. Blue's plan willbe to sit on the anchor, build up his board, and wait for White tocommit himself. 22/13 would be a serious blunder.

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

Back in 1992, I wrote an article for Inside Backgammon calledAnchors Aweigh, where I discussed this topic. At the time I was veryoriented towards holding onto anchors, playing a backgame or a holdinggame if need be but avoiding being blitzed. It should be noted thatthis was in pre-bot days, so we didn't have good computer rolloutsavailable to check things out. In the article, I examined 12 positionsfrom a world championship match between Paul Magriel and Michael Meyburg.Each of these positions involved anchor breaking plays. For each ofthem the player chose to break the anchor, and at the time I felt thatbreaking the anchor was incorrect for each position. The article caused quite a bit ofcontroversy, and it was felt that my conclusions were wrong on severalof the examples. Today my views have shifted somewhat, and guided frommy experience with the bots I am more inclined to break anchors thanI was 10 years ago. I thought it would be interesting to reexaminethese 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 besignificant, 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 bebreaking the anchor this prematurely since he isn't in position to winthe game and he still has to worry about the checker on White's twopoint. 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 checkeronto a bad place. Blue has evened up the race with this hit, but if hegets 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 goodtime to get off the anchor and try to bring the checkers around. White'sposition 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   +.08724/23*, 8/2     +.082

163 178

White money game Blue

Magrial played 24/22, 20/15. I argued that splitting was too dangerouswith White having the stronger board and a few builders, and Blue in noimmediate danger of being primed. Instead, I preferred 20/15, 8/6.My thinking at the time now looks very wrong to me. This is probablygoing to be a game about outfield control, and this is an ideal timeto activate the back checkers -- relatively safe, and quite productive.Blue would like to advance his anchor if he can. Keeping both menback 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 anybodyat the time. Make the ace point early in what figures to be a longpositional battle? Horrors! These days we have learned better. Whilemaking the ace point is no bargain, leaving the Blot on the ace pointwaiting to be hit at just the wrong time is even worse. The bots havetaught us this lesson quite well. Not only does 8/3*, 3/1 solve thisproblem, but it puts White on the bar and gives Blue a chance to getWhite'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       -.30024/22, 20/15    -.31420/15, 8/6      -.377

151 159

White money game Blue

Same game a few moves later -- this time it was Meyburg who had a potentialanchor-breaking play. There are several possibilities which weren'teven considered in the article. He could play 13/8, making an importantpoint. He could play safe with 22/20, 9/6. Even hitting loose on theace point isn't so dumb here. However, let's suppose that Blue will alwaysbe slotting the five point with the three, which was the style in those daysand 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 ifWhite hit, then Blue could fall back on his 5-3 "backgame" thing, whileif Blue gives up the 22 point now it is gone forever. Looking at thingsin the 21st century, I have changed my tune. The race is close, and Blueloses a lot of ground if he is hit. A 5-3 backgame simply isn't likelyto work. The overall timing is wrong -- White has too much stuff to play within the outfield. It is more important for Blue to get a spare on the 20 pointready to spring out into the outfield so Blue can play a decent holdinggame. This is a better game plan.

Rollout results:

22/20, 8/5      +.0469/7, 8/5        -.026

In the light of the new era, I'm not so sure my analysis was right. Surethe hit is dangerous, but not overly so. White is on the bar, so thebest he can do is enter and hit back. He might not do that -- all histwos don't hit. White's forces are pretty thin for an attack. All Bluehas 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 issuddenly 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 Whiteto double. Does this make hitting wrong? At the time I argued that thiswas another argument agaisnt hitting -- that White would cube if Blue hitbut White would be a long way from a cube if Blue played safe. This soundspersuasive, but proper reasoning leads to the opposite conclusion. Whatyou want to do is to avoid letting your opponent have efficient cubes, whereyou have a close pass/take decision. If Blue plays B/18* White has a gooddouble, but Blue's take is very easy -- it isn't a close decision. On theother hand if Blue plays B/23, 13/8 White doesn't have a double yet, buthe is likely to improve slowly to where he has an efficient double.Consequently, if the two plays are otherwise equal it is better for Blueto make the cube-provoking play, since this forces White to make aninefficient 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*           -.359B/23, 13/8      -.362

141 124

White money game Blue

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

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

Rollout results:

13/6            +.19918/11           +.183

125 151

White money game Blue

At this point Mayburg was well ahead in the match, which explains why thecube is remaining in the center for many of the following positions.Here, Magriel chose to play 24/23, 6/3, thinking that he should begoing 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 havean escape route if needed. The big danger is being attacked since Whitehas the stronger board. It is better to try to win the timing battle.

Rollout results:

6/5, 6/3        -.44524/23, 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 siton the ace point, his timing is going to run out and he won't be able tohold his board long enough to damage White when White is forcedoff the anchor. Blue still gets gammoned more by splitting, but theadditional wins are more than enough to compensate for these gammons.In the actual position Blue does have sufficient timing to sit andwait with those three checkers on the midpoint to play with.

The next four positions are all from the same game, and involve interestinganchor-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 togain too little. White has the stronger board, and there is seriousblitz danger. Blue doesn't like getting stuck on the 24 point, but after13/7, 6/5 Blue has good chances to build a five-prime and become a seriouscontender in the priming battle. The timing is close, with White'sslight racing lead (which is better for Blue's timing) compensated forby White's more advanced prime and White having more numbers which movehis back checkers. This analysis still seems correct to me.

Actually, if Blue wants to break off the anchor, he is better off runningall the way with 24/17 than making Magriel's play. This will solve histiming problems, and if he can survive the attack he will be in pretty goodshape. However, this play leads to a lot of gammons. I think thatholding the anchor and working on the offense has sufficient winning chanceswithout the increased gammon risks from the blitz.

Rollout results:

13/7, 6/5       -.19524/17           -.23824/23, 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 splittingplays: 24/22, 24/21 or 24/22, 10/7. Even 6/1* has it merits, althoughit is an entirely different kind of play. However, I argued for holdingthe anchor with 10/7, 6/4. My argument was that Blue needs to protect hisback men while bringing in ammunition for the blitz, and that once the attackgets going Blue should have no trouble escaping. This argument looks allwet 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 stillsitting with two checkers on White's ace point, he could be in real timingtrouble. 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 keyis that Blue has the stronger board, so he should not be worried aboutbeing attacked. His big danger is losing the priming battle.

Rollout results:

24/21, 6/4      +.09710/7, 6/4       -.021

Back to Magriel's side of the board. He played 23/17. I didn't like thisplay at all. Most of the same arguments apply -- White has the strongerboard, and Blue is in danger of being attacked. In addition, this playleaves 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 canescape from the 23 point with sixes. This puts Blue in pretty decent shapein the priming battle, and gives Blue a basis from which he can launchan attack of his own. The bad part is the blot on the ace point, but evenif White hits the checker Blue's position will be sound, and if Whitemisses 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*     -.34723/17           -.462

Magrial played B/22, 6/4*. I can only imagine that he got carried awaywith 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 doon both sides of the board, and if it blows up in his face thereis a very severe gammon danger. I recommended making the defensivethree point, and I stand by that recommendation -- I don't think itis close. The race is close, so Blue will have some winning chancesafter White escapes his back checker, and White might not be ableto 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     -.513B/22, 6/4*      -.674

Meyburg played 24/21, 13/7. I claimed that since Blue is in no dangerof being primed and that White has a bunch of checkers on the eight pointwhich 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 ofmaking a good advanced anchor, and since White has only a two-point board andnot 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 theanchor -- it is that it cleans up the blot on the 11 point by moving itto 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 mentionedthis point. Despite this, I think I now prefer Meyburg's play.

Rollout results:

24/21, 13/7     -.10113/7, 11/8      -.108

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

Rollout results:

24/21, 9/7      -.3307/4, 6/4        -.416