Problem of the Week #3: Solution

Here’s the position for Problem #3:




Things went badly for Black in the early part of the game, and after getting a couple of men hit, he wound up making his 20-point. White has made some progress, securing his own 10-point to make the start of a blockade. Now it’s Black’s turn. In Part (a) he needs to decide how to play a 3-3, and in Part (b), a 4-1.

We call these positions proto-backgames. A proto-backgame is a position where one side (Black in this case) has had several men hit and sent back, but the opponent (White) hasn’t yet been able to make a prime to contain the checkers.

These positions are very difficult to play because they can branch off in so many directions. One branch leads to a genuine backgame, in which White manages to build a real prime while Black maintains a couple of points in White’s board. Another branch leads to a standard holding game, where White gets hit a few times and builds an anchor in Black’s board, while Black keeps the 20-point and releases his rear checkers. Sometimes both sides build an assortment of holding points throughout the opponent’s position.

Proto-backgames are governed by two key strategic considerations.

Key idea #1: In these very long games, the value of key points rises. In typical holding/racing games, your 20-point is a good defensive anchor, but with the game moving along rapidly, you may be able to hold that point for only 10-15 moves. In a proto-backgame, however, you may be able to keep the 20-point for 30-40 moves. During that whole stretch, the 20-point is working hard to keep your opponent from building a prime, making the point even more valuable than usual. In this position, for example, Black will not yield the 20-point unless he’s forced to, or unless he’s managed to prime some White checkers and is now looking to disengage.

Key idea #2: As in true backgames, Black is currently so far behind in the race that he doesn’t really mind falling a little further behind, as long as he’s battling for key points. Right now Black has no board, so White can take chances with little risk. As soon as Black makes a board, White’s play becomes much more constrained. So Black will vigorously fight for his 4-point, 5-point, and bar-point, and he won’t mind slotting those points if he can.

With these ideas in mind, our two rolls play pretty easily.

Part (a). With a 3-3, just make two great inner points with 8/5(2) 6/3(2). Suddenly Black has an instant board, and White is under a lot of pressure. After this play Black has a lot going for him: the best anchor, a great inner board, and control of all quadrants. White now has to play very carefully.

Part (b). Since Black has no fear of being hit, 6/5 is the best play with an ace. Black unstacks and starts a great point. The four can be played in several ways. Some players suggested 11/7 or 13/9, which are both good. But if you’re happy leaving extra shots (which is perfectly OK in this position) just play 8/4*! Compared to 11/7 or 13/9, it has the merit of knocking out White’s point-making numbers like 4-2, 5-3, or 6-1.

Plays like 8/4* 6/5 are routine in positions where you’re way behind in the race, have at least two anchors, and your opponent has no board. However, you must have these conditions present for the ‘pure’ plays to work. (‘Pure’ was what we called these plays in the 1970s and 80s – it just means putting your checkers where you’d like them to go and ignoring the chance your opponent might hit.)


Solutions:

Part (a): Play 8/5(2) 6/3(2).

Part (b): Play 6/5 8/4*.

Now, some quick comments about other suggested plays.

In Part (a), a number of players tried 6/3(2) and 24/21(2), making the 21-point rather than the 5-point. This is obviously better for defense, but is defense really the issue here? Black has the 20-point already, which is the best defense possible, and 8/5(2) gives him good offensive chances as well. The real problem with putting two checkers on the 21-point at this stage is that Black ties down four checkers to defensive purposes, at a stage where the future character of the game is still very much in flux. By staying back on the 24-point, Black is holding that point, to be sure, but he’s also free to move those checkers if he needs them, since they’re not serving any vital function. Once the checkers move to the 21-point, they’re really fixed in place and much more difficult to move. That’s a big concession at this early stage.

We also had a vote for 24/18(2). That suffers from the same defect as moving to the 21-point, only more so, since Black doesn’t get any board at all.

In Part (b), we had votes for all sorts of plays, but 13/8 was the favorite, with six votes. However, it’s much too conservative a move. Black has fallen way behind in the race, but that racing deficit has bought him a lot of freedom in other areas. He doesn’t really care much if he’s 40 pips behind or 60 pips behind. But he cares a lot about unstacking and putting his checkers to work quickly, before White builds any more points in his board. Hence 13/8 really misses a good opportunity to get to work quickly.

Thanks. I really had no idea what black's gameplan was in the position but your analysis cleared it right up.

As usual i am 0 for 2 but at least I am learning from my mistakes.

Nice to find that solution offered was right.

I also was one of the more conservative guys. I guess we all suffered from the impression that we didn't see that heading for the backgame is actually the best chance.

I personally wanted to steer the game in the direction of a holding game. One point was to make second advanced anchor because then hitting an outfield blot from one of the advanced anchors still leaves the other one intact...

For me it really was a dislike for committing to the backgame, that governed my decision...

Mr Robertie,

I guess your Backgame Larry story caused all this. (-:

What also helped were the many times I got gammoned when I went all-out into a backgame after losing a blot hitting contest in the opening.

In part (B) what's wrong with playing 24-20 with the four roll (after slotting the 5 with the one roll)?

You could use the extra builder/hitter on the 20 point since you aren't breaking that point anytime soon. The lone blot you leave on the one point actually keeps pressure on your opponent and can get in easily if hit.

~ Rick

Another backgammon poster told me about this series of bg problems. This is great!

Mr. Robertie, I'm actually reading your 501 problems and learning a lot. But I often wished the analysis was deeper or more extensive. Of course that would have made the book way too long and impractical, but I will definitely add these more deeply analyzed positions to the 501 in the book.

In case the opponent has no homeboard, I am a proponent of hitting in my own homeboard as much as possible anyway. This aggressive behaviour is validated by Gnu supremo. It creates games which are much more interesting, like the above problem.

One well-played sequence that leads to the position of Problem #3 is this:

White 63: 24/18, 13/10
Black 21: 13/11, 8/7*

White 64: bar/21, 24/18*
Black 65: bar/20, 13/7*

White 61: bar/18*
Black 32: bar/20

White 53: 18/10
Black 41: ?

XGID=----a-E-B--AdC-b-c-eB---B-:0:0:1:41:0:0:3:0:10

Mike

Since some time i am playing all sixes 13/7 in order to create a dynamic game. As mentioned before, if you are the better player you could be able to make the loss in equity more than good by the increase in complexity. Particularly if you have made some defensive point you can venture a lot.

In the early game with a random 6 to play, 24/18 is almost always much better than 13/7. Backgammon is basically a race, and trying to lose ground in the opening for complexity's sake is a sure recipe for losing lots and lots of holding games.

Once you have four men back, you are pretty much free to play as purely as you want. But that's very different from playing an opening 6-2 13/7 13/11, or some such nonsense. Make normal moves and you'll get plenty of complex positions along the way.