Prime Development

Prime Development
by Walter Trice – 18 July 2006

Five Problems, One Solution – In each case below, the best play has a common solution. The rollouts for the five positions appear at the end of the article.

 

 

Problem 1: Red to play 5-4.

The roll of 5-4 makes the 4 point. The resulting string of three home board points – 6-5-4 – looks threatening against White’s two back checkers, and in fact this is a very powerful formation. But there is a famous chess maxim that applies just as strongly to backgammon: When you spot a good move, look around for a better move. There is a better move here. Playing the 4 to 13/9 Red can make four out of six consecutive points, using only half his roll, and then use the 5 for a partial escape with 21/16.

Isn’t the 4 point better than the 9 point? Well of course it is, but that is not the whole of Red’s choice. In this position the 8 and 9 points together have more value than the 4 point, especially because they contribute to 4/6 of a full prime. Running a back checker out is added value.

The principles behind 13/9, 21/16 are not absolutes. Alter the circumstances slightly and Red might prefer to make the 4 point. For instance, if White’s back checkers were split, with one of them on White’s 21 point (Red’s 4), then Red would of course make the 4 point and hit the blot. At a match score where a gammon would be especially valuable to Red he would rather make the 4 than the 9 even without a hit. As with many decisions of this type, the stronger home board is best for winning a gammon, but the best prime-building play wins more games.

Problem 2: Red to play 6-4.

Here’s one that will take many players by surprise. First, let’s reject the running play 24/14. Running just doesn’t take Red very far towards where he wants to be. Even if the runner survives without getting hit, Red can’t uncork the champagne until the other straggler escapes too, and in the meantime White may be able to attack it. Moving 24/14 might be okay if Red had nothing else to do in the position, but here he has a couple of plays that make offensive points.

After rejecting the run, one quickly spots 11/5, 9/5, making what we have all been taught is “the best point on the board”. But the value of a particular parcel of real estate often depends on what has already been developed in its neighborhood. In this case Red should make the bar point (13/7, 11/7), even though he must give up his midpoint (13) and leave a blot exposed to a direct shot in the process!

With the bar point Red has five out of six consecutive points. Most players would realize that this makes 13/7, 11/7 a very strong play if they noticed it. But it is all too easy to see the choice as being just between two points. We have all faced this choice – make 7 point vs. 5 point – many times, and we have learned that it generally turns out that making the 5 is better. This is one of the exceptions.

Problem 3: Red to play 1-1.

Problem 3 tripped me up in a recent match. Red could play safely if he only had three aces, but with 1-1 he must decide where to leave a blot. I played 16/13, 3/2 without enough thought. It looked safest – obviously it minimizes shots – and the third checker on the 3 point is not very useful, so my play seemed natural.

What I was overlooking here was that Red has points six pips apart – the 9 and the 3. These points can never be part of the same prime, so they are redundant. Not only that, by playing 3/2, I was starting a second point six away from a made point. If I followed up covering with a 4 in my next roll, 6/2, I would have two pairs of redundant points and over all a position that would be using the checkers inefficiently.

The superior alternative is to play 9/7(2), switching points, to make four out of six consecutive points. The bar point does little to block White’s anchor, but it does help to hem in White’s blot on the 24. If White can’t move that blot he may be forced to give up his midpoint, which will make Red’s bear-in easier. The bar point also provides a base for a checker that may contribute to pointing on White’s blot. These advantages outweigh the additional shots.

It is even possible that White might have to give up his anchor and leave the blot stranded behind. Consecutive 6-6’s or 5-5’s, for instance, would do this right away.

Problem 4: Red to play 4-3.

Red’s main game plan is to attack. He will try to close out one or both of White’s blots. Obviously Red must hit with the 3, but then what? One might focus exclusively on providing builders for the two open home board points and play 10/6 or the wide-open 13/9, either of which aims four checkers at the slotted 5 point. But the best 4 makes the bar with 11/7. If White fails to roll 5-x or 4-1 then Red may make a full prime, and if White enters with an ace, his escaping sixes are blocked.

Here the focus on attacking may divert one’s attention from the value of blocking points and the possibility of trapping a checker behind a six-prime.

Problem 5: Red to play 3-3.

Originally I had intended for Problem 5 to serve as a curious counter-example to the general principle that in prime-vs.-prime games one should make priming plays. The results of the long Snowie rollout with rigorous parameter settings show that my instinct was wrong here, at least for a money game with a live cube.

Why is this even a problem? Wouldn’t anyone just make the six-prime, which turns out to be the correct play? It wasn’t obvious to me even that the priming approach was best for the win. Although you tend to have a timing advantage with fewer checkers primed, Red could lose his prime too soon if White managed to roll a deuce and anchor on the 22 point. There’s nothing fundamentally wrong with the idea of attacking and gaining the time needed to roll a 2 and a 6. Furthermore 9/3*(2) obviously is going to win more gammons than 13/7(2). One problem is that it also loses more gammons. Another is that a live cube reduces the relative value of a gammon somewhat. Even so there are match situations where gammon wins matter more and gammon losses less, where the attacking approach would be right.

I’m sure that most readers have caught on to the common solution to these problems by now, but just for the record here it is: In each case the best play is the one that makes the greatest number out of six consecutive points. Always look for such a play, even if it doesn’t seem like the position before you demands a priming game plan. The best-of-six play, if it exists, will not always be the best play, but it very often will be, and if you don’t go looking for it you may not spot it.

Here are the rollouts for the positions above:

Problem 1: Red to play 5-4.

Problem 2: Red to play 6-4.

Problem 3: Red to play 1-1.

Problem 4: Red to play 4-3.

Problem 5: Red to play 3-3.