**Lots of Action in September**

The new location and the fact that we're now running two levels of tournaments attracted the biggest crowd at the NEBC that I can remember -- 39 players. It was great to so many enthusiastic backgammon players, including some regular players from way back (Hi John, Michael and Bill).

We're very optimistic that we can continue running two tournaments as well as play at Frank's for years to come.

**Director Fight! Zamanian over Steg **

In the Open division, 23 players competed in the inaugural tournament of the 2017/2018 season. Not distracted by the duties of the running the tournaments (not distracted* too much*, anyways), **Alex Zamanian** was the last man standing when he beat Albert Steg in the finals. David Kornwitz and Paul A. Caracciolo, both of whom seem to be hitting the winner's circle more and more frequently lately, were the semi-finalists. Down in the consolation round, it was Daniel Bluestone over Joseph Ithier.

**Rigel Makes His Mark**

In our first intermediate tournament in many years, 16 players competed.** ****Mark Rigel** took the top spot over 2nd place Dale Libkin. Semi-finalists were Robert Brennan and Steve Hassman, while Pedro Calmell beat Anne Bidner in the finals of the consolation round.

**October Tournament**

Our next tournament is **SUNDAY**, **October 15th **at **12:00** at **Frank's Steakhouse **2310 Massachusetts Ave, Cambridge.

Entry fees are $60 for the Open division and $30 for the Intermediate/Novice division.

Please show up around noon to register. We like to do the draw promptly at 12:15. If you're going to be a little later than 12:15, you can call or text (text preferred) my mobile, 781-354-6466, to reserve a spot. And let me know what division you want to play in. If for some reason I don't pick up, leave a message. I'll be sure to check my messages before we begin the draw.

A $5 food credit is given with tournament entry. Before you leave, pay the tournament director for any food you ordered less $5.

A Week Later -- Connecticut!

Don't forget, the weekend after our tournament is the Connecticut State Backgammon Championships. I've been down every year, and it's always been a great time. It's not too late to plan to go. I'm not sure of the discounted hotel room situation, but there are lots of places to stay in the area. One year I stayed at the La Quinta Inn, and it was really inexpensive and convenient.

For full details see: http://connecticutbackgammon.com/tournament

Direct link to brochure: http://connecticutbackgammon.com/CT17flyer.pdf

**2017/2018 Points Race**

Throughout the season, we run a points race where players earn points for winning matches and making it deep into tournaments. After our May tournament, the top 7 points earners play in a playoff tournament for the coveted title of NEBC Champion and prize money provided by the club. The top points earner get a very valuable bye in this tournament. For current standings, see our website www.nebackgammon.org . There's also a link there now to explain exactly how points are awarded.

**Follow NEBC on Facebook**

We’ve had a Facebook page up for years but haven’t made much use of it until now. While we of course will continue to use emails for our official ‘newsletter’ announcements of tournament results and upcoming events, We’ll also be posting this information on Facebook, along with occasional pictures, backgammon positions, and other news about backgammon books, products, and events outside of town. The more people who view and participate in the NEBC page, the more useful this resource will be, so please head over there and ‘Like’ us today!

**September Article**

This month's article comes from Marty Storer. Thanks Marty!

If anyone wants to write something for the newsletter, let me know. It can be anything backgammon related -- analysis of a position, trip report to an out-of-town tournament, a funny chouette story, or really, anything else you can think of.

Saving the Gammon on the Last Roll

Copyright © 2017 by Marty Storer

The 6 is 16/10. Many players would automatically keep the outside checker going, but Black should at least consider stopping on the 10 point and filling the gap on his 1. He must maximize gammon-saving rolls for his next turn, should there be one, and it won’t take too long to count the misses after each play. Note that it’s much easier to count misses than to count gammon-savers: far fewer rolls miss than save.

After 16/8, Black misses with any 1 except double 1: ten rolls total. But after 16/10 3/1, only five aces miss: 31 21 11. The only other missing number is 32. The total is seven misses after 16/10 3/1, making that the best play by far.

All right, that counting exercise is not too difficult. The answer is not remotely astounding. But counting can be tedious, boring, and error-prone. Short of memorizing last-roll gammon-saving positions, are there any counting shortcuts available?

Jeff Ward published one of his tricks in the magazine Backgammon Times in 1982. He calls it the Rule of the Sevens. It says that in general you should not put your outside checker seven pips away from a gap in your inner board. In this problem, 16/8 does just that, so it violates the Rule.

The Rule of the Sevens is O.K. as far as it goes, but it doesn’t go very far. Here’s an exception (an equivalent position was given by Ward in a 1982 follow-up to his original article):

The 6 is 18/12; then 12/11 violates the Rule of the Sevens. But should Black fill the higher gap with 5/4, or the lower gap with 2/1? The Rule is silent on that point. It turns out that the Rule-violating 18/11 is best in this position, giving 14 ways to bear off next turn. The gap-filling plays give only 13 gammon-saving numbers each.

This counting exercise is much more difficult than Black’s task in our first position. Do we count misses or gammon-savers? Either way it looks easy to make a mistake.

Here’s another position where the Rule of the Sevens makes no clear prediction:

After 17/11, should Black play 11/10, 5/4, or 3/2? Using only the Rule of the Sevens, Black must choose between 5/4 and 11/10. The only way to find out which is best is to count. And since we know the Rule has at least one exception, we might as well count for all three alternatives. What a pain!

It turns out that 17/10 is best, giving 21 gammon-savers, versus 18 after either gap-filling play. But wouldn’t it be nice if we had better rules of thumb than Ward’s?

There is an extremely useful counting trick, which I discovered in 1982 after reading Ward’s articles, and which I’ll share now. To use this trick takes a little up-front work: you have to memorize the one-sided two-checker bearoffs. That is, you have to know how many rolls bear off the last two checkers in the inner board, no matter what points they occupy.

Here’s the table:

Select the points occupied by the last two checkers using the numbers in the first row and the first column (Points). Suppose your last two checkers are on the 3 and 2 points. Select row 3, column 2 (or row 2, column 3 if you want): the number in that table cell is 25, which is the number of rolls that bear off the last two checkers if they’re on the 3 and 2 points. If both checkers are on the 6 point, go to the [6,6] table cell and read 4: that’s how many numbers bear off the last two checkers if they’re both on the 6 point (you need double 3s, 4s, 5s, or 6s).

Note that you only have to memorize a bit more than half of the table, because there are duplicated entries: for example, the number in the [3,2] cell is the same as the one in the [2,3], because the information in one of those cells means the same thing as the information in the other. Therefore there are only 21 distinct entries to memorize (the unshaded ones), not 36.

Once you’ve memorized the table, you can put your knowledge to work for a whole class of last-roll gammon-saving problems. You can also use the knowledge in a similar kind of gammon-saving position.

This counting trick is most useful for what I call standard gammon-saving positions. For a gammon-saving position to be standard, you must have fourteen checkers inside and one in your outfield. Also, you need to have either no inner-board gaps, or else one or more consecutive gaps starting with the 1 point.

The problem position, with Black to play 62, is an example of a standard gammon-saving position: Black moves to his outfield with the 6, but can’t bear in with the 2. And he has a gap on his 1 point.

What does this problem have to do with the table? Everything.

Consider two numbers: the minimum number needed to bear the last checker in, and the minimum needed to bear off once the last checker is in. In this example there are two such number-pairs to look at: the first is [4,1] (the minimum to bear in and the minimum to bear off, respectively, after Black plays 16/10 3/1), and the second is [2,2] (minimum bearin and bearoff numbers after Black’s 16/8).

Use those two pairs of numbers to index the table. The entry for the [4,1] table cell is 29, and the entry for [2,2] is 26. This tells us that after 16/10 3/1, Black has 29 ways to save the gammon on the next turn. After 16/8, he has only 26. So 16/10 3/1 is Black’s best play.

Why does this trick work? I’ll tell you. In a two-checker bearoff, two numbers are key: the minimum to bear off one checker, and the minimum to bear off the other. In a standard gammon-saving problem, a pair of minimum crossover numbers is again critical, except that one of them is the minimum number to bear in. It’s just that simple.

Here’s another example of a standard gammon-saving problem.

Obviously, Black plays 16/11 with the 5, and now we have a standard gammon-saving problem: Black has one checker in his outer board, and consecutive inner-board gaps starting with his ace point. He has a 1 to play and must decide between 11/10 and 3/2. Note that the Rule of the Sevens is no help here.

After 3/2, the minimum bearin number is 5 and the minimum to bear off is 2. After 11/10, those numbers are 4 and 3. So, index the table accordingly: the [5,2] value is 19, and the [4,3] value is 17. Therefore Black plays 16/11 3/2, for 19 ways to bear off, versus 16/10 giving only 17 ways to save the gammon.

Consider the same position, but this time with Black to play 52. Now there are three choices to consider: 16/11 4/2 giving [5,2]; 16/9 giving [3,3]; and 16/11 3/1 giving—what?

Since Black reaches a standard gammon-saving position with 16/11 4/2 or with 16/9, we can look up the corresponding numbers in the table: [5,2] is 19 and [3,3] is 17, so we know that 16/11 4/2 beats 16/9. But what about 16/11 3/1? After that play Black has one gap, but it’s not on the ace point, so the gammon-saving position is non-standard. How do we handle non-standard gammon-saving positions, i.e. those having one or more inner-board gaps that do not start with the 1 point or are not consecutive?

The general method isn’t too hard. First, pretend that you do have a standard gammon-saving position, and index your table accordingly. Take the minimum bearin number, and also the number of the lowest point in your inner board: here, you get [5,1], and the corresponding table entry is 23.

Now, look at your inner-board gaps: here, Black’s only gap is on the 2 point. The only extra misses, over and above the misses in a standard [5,1] gammon-saving position, will be with numbers corresponding to the gap. The gap is on the 2 point, so the only extra missing numbers will include a 2.

If Black did not have a gap on his 2 point, he would have a standard [5,1] position, and rolls of 62, 52, and 22 would bear off a checker. But because of the interior gap, those rolls (five numbers out of 36) do not bear off. So, subtract 5 from 23, and you have the number of rolls to save the gammon after 16/11 3/1: 18 total. (Note that 42, 32, and 12 do not bear off in the standard [5,1] position, so you don’t subtract those.)

We’ve already determined that 16/11 4/2 gives us 19 gammon-savers and 16/9 gives 17. Since 16/11 3/1 gives 18,we choose 16/11 4/2.

Let’s consider another non-standard position.

After 18/12, Black can play 12/11, 5/4, or 3/2. None of the resulting positions is standard; for each of them we start with a number-pair for a standard position and then subtract numbers corresponding to Black’s interior gaps.

After 12/11, our standard number-pair is [5,1] giving 23 gammon-savers. Black has gaps on his 4 and 2 point, so we subtract numbers including 4 or 2 that miss in the non-standard position but do not miss in the standard. Those missing numbers are 64, 54, 44, 62, 52, and 22: ten total, which subtracted from 23 gives us 13 ways to save the gammon.

After 5/4, our standard number-pair is [6,1] giving 15 ways to save the gammon. From 15 we subtract 62 and 22: three numbers, for a result of 12 gammon-savers.

After 3/2 we again have a standard number-pair of [6,1] for 15 gammon-savers. We subtract 64 (but not 44 because that number bears off from the 12 point): two dice combinations, for a total of 13 ways to save the gammon. Since 18/11 gives us 13 saving rolls and 18/12 5/4 gives only 12, we choose either 18/11 or 18/12 3/2. I would play 18/11 in order to thumb my nose at the Rule of the Sevens.

A useful exercise is to try to solve the second position using my method. Feel free to use the table if you haven’t already memorized it.

This process becomes rather easy with practice. I have been using it since 1982 and my last-roll gammon-saving technique has been virtually error-free since then. I never make mistakes in standard gammon-saving positions, and I doubt I’ll goof up a non-standard problem more than once every year or two.