He’s Got Your Back

 

In the mid-seventies, backgammon swept the USA. Some of the dust settled north of the border, and inspired an entrepreneur there to launch a backgammon magazine. Its trajectory must have been shallow, as there seems to have been only one issue, but its short flight was impressive. One of its intrepid reporters was dispatched to the Mayfair Club in New York City. If the scientists at Los Alamos ushered in the Nuclear Age, the scientific players at the Mayfair Club helped usher in the Backgammon Age. The man from the Great White North cornered a few Tellers, Oppenheimers, and Feynmen, to see what they might tell, or opine, as they were fine men and women. To each there was one question he could not resist asking, almost before they had given their names and their achievements: “What about the backgame?” To which most replied: “What about the backgame?” It was clear that he expected the equivalent of the lore Hermione found in the restricted section of Hogwarts Library, and soon would know how to brew the backgammon equivalent of Polyjuice Potion. The experts all tried to let him down gently, essentially saying that the most special thing about backgames is that you should avoid them.

Still, I understand how he felt. A few years later, when I took up the game, backgames held the same fascination for me. The books of the era couldn’t resist describing them in terms that would naturally lead beginners to think backgames were a secret weapon of the experts, and that mastering backgames would show that, you, too, had joined the expert ranks.

If only someone would write a book? Around the time Mr. Canada was in the Mayfair, a Mayfair player, Paul Magriel, wrote his magnum opus, and said he would be writing many more books, with one on backgames being among the first he planned to tackle. It was never forthcoming. Over the years others would promise they would tackle it. I was among them, but backgames slipped all tackles.

Finally, someone wrote the book! Partial credit goes to Mochy, who wrote a quarter of a book, Backgammon Masterclass, on backgames. But full marks go to Encino dermatologist, Dr. Alex Eshaghian, who got the itch and scratched out Backgammon Backgame Strategies. Heft the book, peek inside, and you will see and feel why it took so long: doing the job properly took an immense amount of work. It’s 8.5 x 11, three hundred pages, nearly a kilogram in weight, and that hardly hints at the contents. There are hundreds of diagrams. I haven’t counted, and guess it is hundreds, but there could be over one thousand. Where there aren’t diagrams, there are tables, dozens at least, probably at least one hundred. The positions had to be conceived, rolled out, transcribed: that’s a tremendous amount of labor, even if it is a labor of love.

My one complaint is that I wish there were less of the first three-quarters of the book, and more of the last third. When I started playing, the books of the era decreed that the best three backgames, in order, were the 2-3, the 1-3, and the 1-2. That the higher the anchors, the less like a backgame it was. That if the gap between anchors was more than one pip, e.g. a 1-4, it weakened the backgame, etc. As I progressed a bit, and discussed backgame theory with my friend, Tim Wisecarver, he confirmed the received wisdom, and offered insight into the whys and wherefores. One of Alex’s achievements is to confirm what everyone took for granted. The received wisdom is correct, but he has the numbers to prove it, and the explanations was to why.

 

I am not sure if the terms Hintrose and Suhise are Alex’s coinages, or if he borrowed them from elsewhere, but they are crucial in understanding many of the explanations in the book. Hintrose is: Hits In the Next Two Roll Sequence. Suhise is: Subsequent Hitting Sequences. For example:

 

 

 

The defender (Black) has 35 Hintrose. That is derived this way: 65 (two numbers) times any 6 (eleven numbers) equals 22; plus 44 (one number) times 6 or 51 (thirteen numbers) totals 35 numbers out of 1296 where Black gets and hits a shot. Alex notes that calculating Suhise is more complicated, and seldom does so, but notes that the lower the blot left, and missed, the harder it will be to clean up, so the more Suhise will occur.

 

 

 

The checker play problem above is the first of a set of three, shown in diagrams 4.15 through 4.17 in his chapter on bearing in against backgames. The next two diagrams move Black’s man on his 8pt back to the 23pt and 22pt respectively. How should White play her 31 in each case? (The diagram wrongly shows 33 as the roll, instead of 31. Updating the images is such an enormous pain in the ass on Blogger that I hope this note of explanation suffices.)

In the position about White should not make her 8pt. Black’s timing is such that playing 11/7, leaving no Hintrose, is best. Move the checker back to the 23pt, and now making the 8pt is best. It blocks sixes, forcing Black to dump to his acepoint should he roll one. If the spare is on the 22pt, safety is once again preferred, since fives play to Black’s deuce, the next point he wants to make, and sixes are a problem for Black, whether or not the 8pt is made.

Here is another example of the thoroughness of his comparisons.

 

 

The above is position 8.40, in a section called “Comparison of Single Gap Backgames During the Attacker’s Bear In.” He notates the position as 1-3 (3), which means it is a 1-3 backgame, and the defender’s prime is from the 3pt out. The spare on the defender’s 6pt will always sit there, no matter whether the five-prime is from the 7pt through 3pt, the 8pt through 4pt (1-3 (4)), etc. Suppose the attacker is on roll in each case, what are the equities?

	CL E	SW	GW	BGW	SL	GL	BGL	GAW	E ND	E D/T
1-3 (3)	0.491	62%	26%	2%	38%	3%	0%	75%	0.701	0.676
1-3 (4)	0.388	56%	27%	3%	44%	3%	0%	70%	0.518	0.380
1-3 (5)	0.321	51%	29%	4%	49%	3%	0%	66%	0.390	0.201
1-3 (6)	0.293	49%	29%	5%	51%	3%	0%	65%	0.306	0.105

 

That is his table 8.13. I trust you can decipher everything, except possibly “GAW,” which stands for “Gammon Adjusted Wins.” He also has tables 8.14 and 8.15, which give similar information for an additional eight positions, for the 2-4 and 3-5 backgames. For those White’s formation is shifted back one or two places as appropriate.

 

The two most important columns are the SW and E D/T. The defender’s gammon and backgammon losses increase as his prime is moved further back, but his overall losses drop dramatically thanks to his improved timing. Even the position pictured above is not a double. I won’t reproduce table 8.14, but only 2-4 (3) is a double, the E ND being 0.869 and the E D/T 0.905. Nor will I reproduce table 8.15, but there 3-5 (3) and 3-5 (4) are passes (the first with a no double equity of 0.984 is nearly too good), and the others are borderline D or ND. Oddly, 3-5 (5) is barely no double, while 3-5 (6) is barely a double, 0.870 versus 0.874.

 

On the next page, tables 816 through 8.19 compare apples to apples, i.e., the first compares 1-3 (3), 2/4 (3), and 3-5 (3), the others the (4)’s, (5)’s, and (6)’s. This is all excellent, and useful information, but it reads more like a reference book than a textbook.

 

Which is why I was happy to reach page 233, and Chapter 13: Unorthodox Backgame Tactics. Chapters 13 through 15 are devoted to checker plays. This is the section I wish was much longer, because there is a tremendous amount of material covered in fewer than seventy pages. As the author admits, it would take several volumes to do these concepts justice, and I hope he is the one to expand on what he has done so far. Here are some examples.

 

 

A few years ago I think most people would have played 17/9 without hitting. Now I expect many open players would get this right: 17/11*, 4/2*.

 

 

 

This is position 14.8. In positions 14.9 and 14.10 White’s blot on the 21pt is shifted to the 22pt and 23pt. In each case, how should Black play 44?

 

In the position shown, Black should play 22/18(2), 8/4(2)*. Black does not have ideal timing for a backgame. With the recommended play he trails by only 13 pips, 166 – 153. He equalizes the board strength, and has the flexibility to continue priming, or otherwise shift game plans as things develop.

Move White’s man back a pip to the 22pt, and making a five-prime from the 4pt out is best. He has 4s, 5s, and 6s to run of one of his anchors, while keeping his prime intact.

Move the man back to the 23pt, and now Black should make both barpoints. White’s 66 and 65 are blocked, and 64 slots her 3pt, but leaves a direct shot.

 

 

 

 

I imagine that seeing these two side-by-side you know how to play them both? When White has the blot on her ace, Black should hit; when the ace is made, Black should make his 4pt.

 

Alex Eshaghian has written a book that belongs on every serious player’s shelf. No one will ever write the definitive book on backgames. The topic is too broad and complex for anyone to do that. But for now, Backgammon Backgame Strategies is as close as we have come, and will probably remain so far into the future.