![[Welcome to Sensei's Library!]](images/stone-hello.png "Sensei's Library")
Review: The Endgame (Ogawa / Davies)
Although this is an old book first published in English in 1976, it is still sold because it is well-known and part of the Elementary Go Series. There are still only a few English endgame books so the book remains an option to be considered. My impression when I read the book as circa a 5 kyu is almost the same as when I reread it in 2018, 28 years later, as a 5 dan and endgame researcher, except that then it was the only English endgame book and now I can better justify my impression.
The book has five chapters. Chapter 1 uses one game to introduce the endgame informally. The game comments are mostly uninteresting descriptions ("White 38 threatened an invasion of the upper right corner again, so I defended at 39.") but interludes prepare the reader softly for the next chapter, show variations of enclosure josekis, which a reader of expected rank may find useful, or give a sample illustration of counting territory during the game. For that purpose, the diagram annotation is a bit strange: for the sake of counting in pairs, two adjacent intersections carry the same integer.
Chapter 2 is the core of the book. It explains evaluation of moves of local endgames. First, some theory is explained shortly. Second, nine problem diagrams each with three local endgames, a few answer diagrams and one combination diagram per problem train application of the theory. Apparently, the combination diagrams presume an unshown whole board context during the early to intermediate endgame, where the three local endgames must be played first in their correct move order.
Chapter 3 shows a good variety of the most basic endgame tesujis and a few problems for each type. If you have not seen the monkey jump or other tesujis of a comparable, basic level before, the chapter should be useful.
The macroendgame (transition from the late middle game to the early endgame) is the topic of chapter 4. There are nine whole board problems each with five moves to choose from. The answers are short. That is all. Chapter 5 is similar but shows two games during the intermediate endgame, each with ten problems and multiple choice among three candidate moves.
Except for the interludes in chapter 1, the chapters 1, 4 and 5 are mostly filling material trying to compensate the too short theory in chapter 2. In particular the macroendgame would have deserved general theory and at least careful approximative calculations of the move values of the top two candidates. Instead, we mostly get disappointing informal text, such as "Although tbe continuation is a bit difficult, there is no question that Black 1 is the right move".
Chapter teaches move values of gote, sente, reverse sente and double sente for traditional endgame theory, where you multiply by two for playing in sente or reverse sente to compare with playing in gote. The book compares "Black goes first" and "White goes first" but avoids a term for the calculated difference value. It compares the two resulting local positions but avoids terms for them (nowadays we call them black and white follower) and the counted value (we would call them the count). It counts locally but does not explain the concept of locality (which I would call the locale). It studies follow-ups but avoids this term like the plague. To calculate the impact of a follow-up on a move value, it sometimes considers the white follower's white follower or the black follower's black follower but, as we know, avoids these terms. Instead, it uses various, confusing, informal descriptions for the same term, concept or value. The reader must enlighten himself. Likewise, the book describes newly acquired values by different phrases with a preference for "to gain". As a consequence, the author herself lacks a clear understanding and sometimes makes the mistake of adding gote and sente gains without first calibrating such different values.
Furthermore, the book tries to simplify. It approximates by rounding to avoid fractions and prune the impact of iterative follow-ups on move values. Although this works for the simple examples in the book, this also means that the reader does not learn determination of move values of local endgames with intermediate to large iterative follow-up positions. The book speaks of average, mathematical average or mean (all meaning the same) but does not explain how to calculate an average. For the simplest calculation, the calculation shown multiplies a value by 1/2, puts this in brackets and adds this to some previously calculated value. Otherwise, the book avoids brackets for arithmetic. It invents, however, a creative alternative use for brackets to indicate a rounded value as being slightly smaller, such as "5(-)", or larger, such as "5(+)", than an integer. It also avoids negative numbers but speaks of White's points. This may work for the simple examples of the book, but the reader does not learn proper calculation in general. Funnily, the book cannot quite admit to avoid negative numbers when writing "the total difference is 1+1=2 points". If White's points were accounted properly as negative points, we would indeed have the difference "1 - (-1) = 2". After dissolution of bracket and minus signs, this becomes the sum stated in the book.
Does the reader profit from all those attempts of simplification? Hardly. Besides the few principles hidden in ordinary text, he has to make sense of several different methods of how a gote follow-up is calculated. Sometimes it is the average of two numbers, the average of one number (and - not declared by the book - the number zero), derived from the white follower's white follower and an average, or derived from the black follower's black follower and an average. Without the underlying theoretical explanations why each method works and produces correct move values, it can be hard to understand everything while overcoming confusion.
At least, the move values in the book are correct if we tolerate approximations. Sometimes the author was lazy and an approximation is correct only plus-minus 2 points. The explanation of theory for sente, reverse sente and double sente is even shorter. The relative value of sente or reverse sente are explained by an argument fitting modern endgame theory: points per difference in the numbers of played stones. Unfortunately, this is the only aspect of modern theory in the book.
More confusion arises when gote and gote (or sente and sente) have different meanings. Either word might refer to the type of local endgame or to the kind of sequence but the book never says "gote sequence" or "sente sequence" when it means such. The reader must always disambiguate the context, especially when both contexts occur in the same sentence. Worst of all, we learn that a reverse sente "is gote". What this means is that a move played in reverse sente starts a gote sequence. Such problems occur when a book does not properly introduce the basics and avoids by far too many terms, which would clarify everything.
Not surprisingly, the book introduces double sente as "either side can play in sente", means local double sente and is unaware of its inexistence. As a consequence, the answers to the problems calculate move values in double sente even when the most obviously the follow-up threats are too small by far. In the most obvious example, the author noticed this by herself ("Black 1 is not necessarily sente, either.") but did not draw the right conclusion. The harm from this conceptual mistake is limited though because the book offers useful practical advice for when to play double sente.
From the theory and problems in chapter 2, the reader learns calculation of move values of gote or sente without follow-up. Hardly from the theory alone - but from the combination of theory and problems. Learning reverse sente is made more difficult. Maybe the bright reader also learns calculation of a move value if the local endgame has simple, direct follow-ups. However, calculation of a move value is peculiar in the book: only intersections of either player's territories with changes are counted by mentally comparing two diagrams. This works for the simple examples in the book but the method might fail for more difficult examples.
Endgame evaluation in the book misses the following theory: in general exact move values instead of approximations, move values of local endgames with iterative follow-ups and larger impact than rounding approximations, a careful explanation of the basics, basic terms, basic concepts other than move value, count of an initial local endgame, counts of followers, evaluation of ordinary kos or ko threats, gains (when Black's and White's moves gain different amounts not both described by the move value), net profit, theory relating the different values, careful study of different kinds of follow-ups, modern endgame theory, microendgame, area scoring, a clear distintinction of sente and gote, ambiguous local endgames, evaluation of long local sequences, value theory for move order during the early and late endgames, advanced theories.
The book is written for beginners of endgame theory. Apart from the additional chapters, it only touches the only one aspect of move value. The unclear, confusing presentation with countless omission especially of basic descriptions make good understanding of the contents unnecessarily hard especially for the intended readership. Theory and didactics of the book are outdated.
About the reviewer: Robert Jasiek is a researcher in the endgame and other go theory, author of endgame books and other go books, and go teacher.[1]