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Modern Backgammon Reviewed

There is a journalistic imperative that the lead should not be buried. So I will state forthwith: You must own a copy of Bill Robertie’s MODERN BACKGAMMON!

Two-Time World Champion Bill Robertie (That’s his full title, much as Tony Hopkins, actor, is now, Sir Anthony Hopkins, icon. Bill’s friends are permitted to shorten it to “Two-Time.”) (And Patrice reportedly calls him “Three-Time,” but that may refer to some skill other than backgammon.) has been writing about backgammon for a long time. In fact, he is now, having started with a newspaper column in the seventies, in his fourth decade. As Bill’s head start in life is not sufficiently longer than my own, I will refrain from adding that he is writing in his second century. During the 1980’s Bill, in between winning his two World Championships, produced three of, I believe, the ten best books on the game. In the nineties, while doing excellent work in Inside Backgammon, his books were not of the standard we had come to expect.

Come to think of it, whose books were? Once upon a time authors attempted to formulate principles to guide their readers toward correct play. Since the advent of the bots most books have been either annotated matches – “Look, here’s how Snowie would have played this match!” – Or collections of problems – “Most people would bring down the five, but it is correct to hit on the acepoint because it wins 4.8% more gammons…” How dreary! Mind you, the authors mostly gave us their best effort, and some of those efforts were very good, but in the end, the problems assembled were collections of exceptions, and the only way to learn from them seemed to be brute memory.

In MODERN BACKGAMMON Bill is trying to do something far more ambitious. He has looked at hundreds of positions, and tried to divine what sort of principles might underlie and unify the sometimes unique approach that the bots have taken to the game. It is (relatively) easy to look at two similar positions that have different answers, and find an ex post facto analysis that accounts for their differences. It is quite another to look at a hundred positions with a variety of answers, and try to isolate one principle that governs them all.

Bill claims to have identified four such principles. They are: Efficiency (put your checkers where they’ll do the most good); Connectivity (what we used to call Communication); Non-Commitment (keep your game plans flexible); and Robustness (have spares to play with). If I have skimped on my definitions it is because I am confined to a single review, while Bill has an entire book in which to develop his theses. Quite a long book it is. There is an introductory chapter, then chapters covering each of the four principles. Chapter Six is a set of problems, with solutions and explanations provided after you have worked them. Finally, there is a 25-point match (between Nack Ballard and Jerry Grandell from the 1998 Istanbul Super Jackpot Semifinals) annotated with a view toward showing the four principles in action. Altogether the book is 361 pages, and there are 364 positions to study. The match alone would make a decent book.

Given the scope and ambition of this book, it shouldn’t be surprising that there will be a lot of discussion, not all of it friendly. For instance, from the chapter on Efficiency, here is a position demonstrating the sub-principle Risk versus Reward.

It should be remarked that all of Bill’s positions are intended to be checker play problems, but here he freely admits that the solution is partly based upon future cube action. Bill’s solution is 13/9, 11/9(2), a play that is safer than 11/7(2), but leads to a fairly efficient pass when White fails to hit. I recalled this as a problem from Inside Backgammon, but thought that the solution back then was to play the completely safe 13/11, 12/6. My copies of that magazine are packed away in boxes, so I simply put the problem to Snowie, checking to see if perhaps the original included a solid prime for White(in which case the safe play is correct), instead of one containing a blot. It turns out that on the lower levels Snowie sees Bill’s play as a blunder. However, on its highest rollout settings - 3-ply checker, 3-ply cube, 100%, huge – it finally reverses itself, and makes Bill’s play .081 better. (Or does it? Using the Rollout With Doubling Cube In Play feature, the Live Cube result still has the safe play .058 better! I will give Bill the benefit of the doubt, but I wish Olivier would tell us, once and for all, which set of numbers to trust, and why, and possibly do away with the ones that are flawed.) So where’s the beef? Well, if Bill had simply put the cube on White’s side of the board, not inconceivable in this position, his play would be unambiguously correct, and would still illustrate his point quite nicely.

This comes slightly later in the Efficiency chapter, from the section dealing with Handling Dead and Semi-Dead Checkers. One might guess that, coming from that section, the correct play is not 6/3. The best play is the perhaps surprising 7/5, 6/5. This play is still correct if the blot on the 8-point is moved to the 5-point (so that fives are no longer duped), though not right by as much. If White’s 3-point is made, 6/3 becomes correct. Now this section deals with unstacking loaded points, so what about 8/7, 6/4? It turns out that that play is a distant fourth. One could write a nice, short article about this position. In fact, one could write a nice, long book called MODERN BACKGAMMON – ANNOTATED, filling in the details that Bill omits. It is hard to fault Bill for not writing the 800 pages that this book might have become, and yet many positions, such as this one, cry out for a little more. (There are several reasons that making the 5-point is better than slotting the 4-point. One is that, in the event of a hit, we need that extra tooth to bite back. Another is that we are not necessarily trying to prime White. We hope in the near future to be bearing in, clearing the barpoint, so its value is of short duration. Also, numbers that cover the bar may also clear the midpoint.)

Chapter Four treats Non-Commitment. Here Black plays 18/13, 18/15 because 13/8, 13/10 is too “committal.” Clearing the 18-point is one of Black’s immediate goals, and doing so now gives only four more shots than clearing the midpoint. Bill points out that if Black clears the midpoint, he will be “committed” to cleaning up his outfield blots, hopefully making good new points in the process, and will be prevented from his primary goal of bringing his back checkers home. But I am not sure that it follows that, by not committing himself one way, he is not committing himself another. Twenty shots versus that board, with the barpoint no longer a safety valve, seems pretty committal in its own right. Stick this problem back in Chapter Two, and say that it illustrates Risk Versus Gain, and no one would blink. Place it here, and the reader wonders whether he is dealing with a unifying principle, or merely fun with semantics.

And speaking of fun with semantics…Chapter Five is devoted to Robustness. Bill defines that as “the ability to play numbers while maintaining the key features of the position.” Fine, except he then goes on to say: “Chess has an analogy to robustness in the idea of zugszwang, a German phrase which means move-compulsion.” I don’t know German, so I’ll trust Bill that zugszwang is a phrase, not a word. I do know that it means the opposite of what Bill is getting at with Robustness. Bill knows it too; he just didn’t say it very well.

Perhaps the most acrimonious debate will revolve around whether Bill’s ideas have merit, or are merely clever packaging for what might otherwise be another random set of positions. I may have implied as much when I discussed position 4-21 above, so let me say that I think Bill is onto something. I don’t fully understand it (and suspect Bill might admit the same), but I think he has spotted something, or some things, that are tangible, if evanescent. Perhaps you recall the story of the three blind men touching the parts of an elephant, its tail, its ear, its tusk, and describing them variously as a snake, a palm frond, or a spear? We laugh at their failure, but they didn’t “fail.” Each partially succeeded. This time, all of us are blind, and only Bill has been brave enough to reach out and touch the elephant.

So let me introduce you to one more position.

How many positions like this pass over our boards, unnoticed and unmentioned? Bill comments: “My guess is that virtually every strong player would play 24/20 in a shot?” Bill would have; I would have. Only two categories of players, I think, would not: beginners; and those shown this as a “problem,” and my guess is that both those groups would then keep the anchor. The beginners because “splitting is dangerous;” the others because “obviously, there’s a trick.” That leaves no category of players who would get this one right! The correct play is to make the minor split of 24/23. Bill tells us that Snowie would then play 13/9, while Jelly slightly prefers 11/7. Ranking those two plays is unimportant, what is important is that all other plays are blunders. Bill puts this into a “…core of positions where humans have not and likely cannot catch up to the nets.” And then does a remarkable job of attempting to catch us up. His two pages of analysis are classic Robertie displaying the painstaking attention to detail that made his name twenty years ago when he demonstrated (in LEE GENUD Versus JOE DWEK) how a match should be analyzed.

This book is filled with gems like the one above. Sure, you and your friends will pick this book apart. You will argue over Bill’s definitions, question some of his plays, and debate whether he has simply repackaged old ideas in new wrapping paper. I know this because I know you will buy this book. You must. You must because in the coming years the articles you read will discuss positions in the terms Bill has just defined. You must because in your chouettes your teammates will rebut your play because it is “overly committal,” or “not sufficiently robust!” Finally, you must buy it because, if you read this book, you WILL become a better backgammon player.

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