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Vision Laughs at Counting

Danny Kleinman     1980     438pp

Available as a Two-volume, self-published, spiral bound edition, and individual ( revised) editions - Volume 1 - 'Vision Laughs at Counting'; and Volume 2 'Advice to the Dice Lorn'.

Note: the latest editions have been revised with modern board diagrams, which corrects a major deficiency in the originals


The two volume 'Vision' set is my favourite backgammon book (I bought it twice, just for the benefit of the revised board positions). Kleinman is arguably the most knowledgable deep theoretician of the game, and his dynamic prose never fails to keep the reader entertained. At $80 for the set, Kleinman's wisdom doesn't come cheap, but money players will soon find that their investment is recovered many times over, from careful perusal of the text.

Kleinman's forte is chouette play and much of the first volume focuses on chouette strategy and tactics; including the mechanics of play and the deeper psychology of the game and money management. The author takes a theme, for example 'killing and maiming numbers' - describes and explains the theory and illustrates the concept by reference to problem positions. The lesson is reinforced in humoress vignettes which take the form of letters to Miss Lonely Blots (Kleinman's alter-ego) from a motley crew of fictious backgammon stereotypes 'Frankie Fiveroller, Seymore Sykologist etc'.

As hinted by the title, Kleinman's magnum opus is dedicated to the elaboration of the two major elements of the game - vision and counting. Kleinman teaches the reader to focus on the dynamism of the game and to assess the key priorities as the game unfurls. "At the highest levels, backgammon geniuses see what the rest of us can only struggle to figure out."

Often the advice is relatively simple - how to perceive the dice rolls (individually and in combination), "Don't reach for a checker until you decide where to move it. And don't play any of your numbers until you decide how you intend playing the rest". Further pearls of vision wisdom - "You must see the whole board..you cannot sit scrunched up... with your eyes focussed on just one sector. Sit back comfortably where you can see it all...Never let your opponent lean his elbow over a blot...Dont leave your arm stretched out to grasp a checker or a a die, for that will obscure part of the board." Simple stuff, but vital information for the beginner (or intermediate) that seldom warrants mention in most backgammon texts.

Kleinman is a great teacher. He has the rare ability to frame complex technical issues in illuminating analogies which stick in the readers mind. For example, 'The Chemistry of Anchors' assess the function and value of various anchor points - from the 'golden' five-point to the 'iron' ace-point. 'The Anatomy of Primes' elaborates the important function of blockades by reference to dynamic prime fields, prime acreage and prime wilderness. Like many great teachers Kleinman critiques the classics - the standard reference works of other experts - and sets out a concise summary of Magriel's 'Backgammon' in just five illuminating pages.

Kleinman is perhaps noted most for his mathematical genius, and the author certainly has a gift for putting a number to every conceivable concept of the game. Readers fluent in mathematics will delight in Kleinmans essays on; 'Backgammon as a Problem in Mathematics'; 'The Prime Leaping Problem'; and 'The Cube Equations', while the mathematically illiterate will benefit from countless numerical mnemonics, handy tips and hints.

The second volume contains extensive content on cube theory with reference to money games, chouette and tournament matches, amply illustrated with match equity tables, gammon price tables, and of course, lots of mathematical formulae. Kleinman signs off on a light note with a section on backgammon philosophy and humorous series of quizes which includes a test of the readers temperment and attitude for hustling.

Heres an overview of the overall content

Volume 1
Welcome to the Chouette (30 pages)
Vision (67 pages)
Counting (26 pages)
Racing (49 pages)
Gammons (24 pages)

Volume 2
Cube (48 pages)
Tournament (44 pages)
Mathematicians Delight (23 pages)
Rules and Variations (13 pages)
Laughs (14 pages)
Quizzicale (56 pages)

In summary, if I could only keep one backgammon book then this would be the one. Whats that I can't count both volumes as one? Hmmm tough choice then.

Mark Driver, 12/09/01


Seminal work on match play, money play, doubling cube, races, and more. Kleinman is very prolific. His analyses are often more mathematical than the average reader can handle, but Real Mathematicians [tm] and even the layperson with math aptitude shouldn't be fazed. A Real Mathematician wouldn't call Kleinman's math "deep", but it sure is accurate, and you won't find anything similar anywhere else. He does the important work of formulating the right problems the right way, where many others couldn't.

Drawbacks: his books are self-published with lousy layout and graphics. He's supposedly not that great a player (I've never seen him play), so his analyses often lack the world-class insight into the thought processes of the strong practical player that you could get from a Goulding or a Robertie. In particular, his middle-game intuition seems less than world-class. But these drawbacks are more than made up for by the wealth of information in his books, which I still haven't completely soaked up after many years. Kleinman is a subtle thinker and a meticulous analyst of the countable, and he does a lot to develop backgammon "vision." His stuff is often uproariously funny, but sometimes one gets impatient trying to filter out what's relevant to the practical player from the humor.

All his books are "must have's" for the serious player. They're a bit expensive since I think he bears all the production costs himself, but for the serious player they're worth every cent.

Marty Storer, May 1992


Vision Laughs at Countingcontains much sound advice on the practical aspects of bg play (e.g., sections on bg hustlers, bg cheaters, chouette money management), seminal advice on handling the doubler, and even a few unprecedented mathematical characterizations of certain aspects of certain positions (e.g., how many pips to penalize a player for having one or more checkers on the bar). The book is generally insightful and often very amusingly written, but not suitable as an introductory text, sometimes obsolete, and sometimes simply wrong; and though it is the only text by Kleinman that I have read, I have good reason to believe that that judgment applies to Kleinman's other texts, as well.

John Bazigos, June 1993


For me, Vision Laughs At Counting is a "must-have" because it contains analyses that are really useful for aspiring backgammon programmers. It is hard to express backgammon fundamentals in exact formulae, and Kleinman has done this for some crucial positional concepts. To a backgammon programmer, the time saved by not having to analyze this stuff for oneself is worth many times the cost of the book.

On the down side, that material occupies less than 50 pages out of 450. The rest of the material is very amusing, but reading it probably cost me about as much time as the analyses saved me. (OK, I admit I enjoyed every minute. But I really should have been programming.)

In terms of the backgammon content, I think the book overemphasizes exact calculations of roll sequences. In fact, sometimes the differences between plays are expressed in terms of 1/46656! This is hardly the sort of difference that separates aspiring experts from experts. The book is at its best when it summarizes the conclusions of such calculations in terms of general principles, and at its worst when it lets the calculations stand on their own.

OK then: programmers should buy a copy immediately. Players who expect a book to greatly expand their horizons might be disappointed. But if you expect a book to amuse you, and hope to learn a thing or two, then you will be happy with Vision Laughs At Counting.

Brian Sheppard, July 1997


Other book reviews welcome! Email them to DocMartin@Gammoned.com

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