Review: Rational Endgame


General Specification

* Title: Rational Endgame
* Author: Antti Törmänen
* Publisher: Hebsacker Verlag
* Edition: 2019
* Language: English
* Price: EUR 17 (softcover), EUR 27 (hardcover)
* Contents: endgame
* ISBN: 978-3-937499-10-9 (hardcover)
* Printing: good (hardcover)
* Layout: almost good
* Editing: almost good
* Pages: 122
* Size: 154mm x 215mm (hardcover)
* Diagrams per Page on Average: 3
* Method of Teaching: examples, principles
* Read when EGF: 13k - 5k
* Subjective Rank Improvement: o
* Subjective Topic Coverage: - to o
* Subjective Aims' Achievement: +


Terminology

While introducing modern endgame theory under territory scoring mainly for beginners, the book uses some terms but avoids explicit terms for other concepts. However, it goes too far in its attempt to be less technical and more beginner-friendly. For better understanding this review, it is necessary to first describe the used and avoided terms.

The book emphasises the type of local endgame positions abiding by the rule of both players' moves being worth the same, being stable in the sense of possibly having less valuable subsequent moves or being not sente. Such or similar descriptions refer to what everybody else calls gote (local gote endgames or gote moves) or gote with gote follow-ups. The book does not use the word gote at all. The chapter When Responding Does Not Incur A Loss introduces two more types: "an endgame situation where responding does not take a loss" (what recently every other writer about the endgame calls an 'ambiguous' local endgame) and 'sente' defined as "'forces a response from the opponent' and 'that can be responded to without taking a loss'".

Thankfully, the book evaluates both local endgame positions and moves. For the value of positions, it uses phrases such as 'expected territory', 'expected score', 'expected outcome', 'local score' and 'net score' avoiding what every other endgame expert calls the 'count'. This is unfortunate for two reasons: 1) the central concept of modern endgame theory remains deemphasised and fuzzy; 2) elsewhere the term 'score' only refers to the final points difference at the game end. Instead of speaking of 'followers' or 'follow-up positions', when referring to their resulting counts, the book speaks of 'the possible futures' after Black or White starts.

The author's motivation seems to be to avoid technical-sounding terms (such as '(the) count' and 'follower') and use informal phrases or fancy terms (such as 'expected territory' and '(a) future'). While this may work within the book, it is a bad preparation for explanations of modern endgame theory outside this book.

The author defines the 'value of a move' as what Bill Spight and the reviewer call the 'gain', which is the difference of the counts before and after the move. Later, the author also uses an alternative calculation for the value of a move; that calculation every other endgame expert uses to define 'move value': the book might explain this as the difference of the two possible futures per played move. He can do so because both values are the same for the frequently discussed gote with gote follow-ups. Hence, a Törmänen-move-value is a gain and is not what everybody else calls a move value. Only within the book, the harm caused is marginal because it hardly studies intermediate to advanced local endgame positions for which move value and gains differ. For sente, the book briefly mentions that black and white moves have different values just to immediately deemphasise this by a recommendation to disregard a sente move's value. Treating gain and move value as if they were the same is another attempt by the author to simplify introduction to modern endgame theory but he creates unfortunate confusion for endgame discussion as soon as the theory leaves the scope of the book and enters the world. As much as I applaude the author for emphasising gains, I have to criticise him for recklessly creating the confusion with move values instead of saying 'a move gains' or 'the gain of the move is'.

The book avoids the terms 'excess (move)' and 'tally' but explains these concepts informally and implicitly throughout the text. As a consequence, confusion sometimes arises when 'moves' means 'number of a player's excess moves' or a division by 2 occurs without explanation and reference to excess moves of both players' sequences to the futures. Not only for terms - other difficulty sometimes occurs when the book has explained a primary concept but rushes ahead to a secondary concept without first explaining such a next step to the reader. The book might speak of a 'move' when referring to a gote sequence.

Instead of the usual terms 'settled' and 'unsettled', the book uses the terms 'finished' and 'unfinished'. Although they are also understood easily, they are less precise when a finished position still allows an encore.


Calculations

There is no endgame evaluation without calculations. Although negative numbers are shortly mentioned, fractions (even if 1/12 of a point) are calculated accurately and one formula is stated as an anecdote, the book deemphasises explicit mathematical calculations and does not use variables. Instead, calculations are buried in prose.

For example (p. 49), here is an extract from an iterative calculation: "If White plays at 'a', he secures one prisoner, and the remaining local score is the reverse of DIA. 2: that is, an average of one point for White and 1/3 point for Black, i.e., 1/3 point for White. Adding in the three captures Black has, we get 2 2/3 points for Black."

The book never explains how to calculate an average of Black's and White's futures but simply states the two numbers from which an average is calculated, possibly whose they are and the number representing their average. In my opinion, it would greatly help some readers if a formula or method for calculating an average was explained at least informally.

Fractions are annotated in tiny font with sloped line. This may be somewhat hard to read for the shortsighted. That said, there is no easy solution for books with very many fractions. A book can do alike, write fractions as ordinary text as above or double the number of pages for some mathematical annotation of fractions in large font. Each choice has its advantages and disadvantages.

When the book speaks of, or means, calculation of a difference, it sometimes calculates a sum instead. Some readers might be lost while others would understand that the book tries to hide double negation.


Overview

The first four chapters use very basic examples to explain the value of a move and the count of a local endgame position that is a gote, a gote with gote follow-ups, ambiguous or a sente. A very short explanation of one condition for having sente is given but the reader might have difficulties perceiving its relevance or applying it to colour-reversed positions because related explanation is missing. There are hints to consider global context when evaluating a double sente but the traditional local evaluation remains unconvincing.

The forth chapter evaluates move values and counts of basic endgame kos, one ordinary ko, a two-stage ko, one approach ko and one ten-thousand-year ko. Not surprisingly, evaluation of the approach ko does not cover different move values depending on the global environment but the introduction is helpful nevertheless.

Although the book introduces the importance of endgame aspects throughout the game and the global context, explanations focus on small local endgame positions preferably during the late endgame.

The book has only a few problems, and their answers, meant as representative samples: 6 standard local problems of move value calculation (but not of the initial positions' counts), 8 standard tesuji problems (after only one cute example) and 5 difficult 13x13 problems. The 5 whole board problems "Black to play and achieve a tie" are for (high) dan players and the only part of the book, whose correctness I have not verified yet because verification would require much more variation than the entertaining main variations of the answers provide.

The chapter Professional-Style High-Speed Counting tries to apply the idea of Cho Chikun's / the reviewer's territorial positional judgement for the opening and middle game to local endgame positions. Although some fast approximation might be useful because we do not always need exact values, the chapter is disappointing because of its conceptual inconsistency and disregard for a sente requirement: according to the author, one player might reduce in sente while the opponent might reduce in gote. The bombastic title makes up the unripeness of the chapter.

Another chapter offers a useful introduction to the topic of getting the last move. However, the reader needs to look elsewhere for an order of endgame moves or difficult shapes.

Similar to the Miai Values List at Sensei's Library, there is a list of a few dozen, mostly standard shapes with their move values stated but without any calculation or explanation. The advanced reader can use the shapes as bonus problems. Everybody else has some reference to get a rough idea of small versus larger moves.

The final chapter provides mostly rules history, a lengthy example of Chinese Counting and a few hints for the differences of area scoring versus territory scoring. Again, one must look elsewhere for a much more detailed treatment of the latter.


Technicalities

The highest page number is 122. Subtracting 6 initial pages and 3 empty pages, and accounting circa 10 pages for rules history, a superfluous discussion of numbers of stones surrounding an empty space in the center and an overly large Xmas tree example, the book has only 103 pages explaining endgame theory. Together with a generous layout and little use of small font, the price of EUR 17 (softcover) is relatively high. Although it is not a rip-off, and prices of some non-Go textbooks can be higher, the reader also pays for the art of omission.

The hardcover and binding are very good, the paper and printing are good. I have slight reservations about the layout (too small inner margin and too wide outer margin for too little use by occasional additions make reading awkward) and the editing (we can overlook the few typos but the more relevant aspect is when the editing affects the contents: the description of a difference should not be contrary to the actual calculation; after two komis stated in the preceding sentence, the following scoring principles are ambiguous).


Correctness versus Mistakes

While endgame books teaching traditional endgame theory have been cans of mistakes, Antti Törmänen joins the writers of endgame books teaching modern endgame theory who share its spirit of precision and correctness. The calculations and value are correct, except for a) the few aspects mentioned below, b) the insufficient aspects of theory mentioned further above, c) the careless equation of gain and move value and d) ambiguity of move value calculation in two examples of Appendix A in which the outer territory region beyond the diagram shown might be relevant.

A minor mistake occurs twice in the principle of playing moves in order of their decreasing values. A 'usually' is missing because there are a) anomalies for local endgames with follow-ups and b) the aspect of getting the last move.

The following major mistake has little impact on the reader while reading this book but hurts his potential improvement of endgame evaluation and seems to indicate a knowledge gap of the author. The mistake is to automatically treat every long alternating sequence as if it is a single move, equate the sequence's net profit to its first or last play's gain and equate its gain to the move value derived from the sequence. Since most examples in the book are fairly simple, mistakes are scarce and small. The related mistakes are: 1) although accidentally the move value is correct, p. 50, DIA. 8 should show a 4-play sequence instead of a 3-play sequence because the fourth play also gains enough; 2) p. 108, 3-point moves, fifth example, move 3 only gains 2 15/16 so cannot belong to a sequence determining the tentative move value 3. The error of 1/16 is small but, in the reviewer's experience, intermediate local endgames can give rise to evaluaton errors of each up to 5 points when perceiving and evaluating long sequences naively.


Omission

The book omits every advanced topic of endgame evaluation and only touches the discussed topics. This seems to be the major intention: to only provide a first introduction and give a glimpse on endgame evaluation.

Within the intended scope of the book, however, there are glaring omissions of important topics of basic endgame evaluation: 1) frequent endgame mistakes of kyus, such as playing small endgame prematurely early during the game or conquering small and neutral instead of large and valuable regions; 2) evaluation of gote with sente follow-up and sente with gote follow-up (only an omission of sente with sente follow-up can be excused because it is somewhat advanced).

The omissions are in stark contrast to the inclusion of much less relevant topics of special ko shapes, a sophisticated method of approximation, getting the last move, tesuji (which only infrequently occur and whose relative impact is small compared to the important missing topics), whole board problems for dans and scoring details.

The omission of the mentioned essential basic topics has prevented a 'o' rating of Subjective Topic Coverage. Together with the absence of a sufficient number of very basic problems training every concept of endgame evaluation, the Subjective Rank Improvement (after reading the book once) cannot exceed the optimistic 'o'.

Instead of including the additional teaser topics tempting first second impressions when first opening the book, it would have profited much from the more important but missing topics.


Who Should Read the Book?

The book is for
* beginners knowing nothing about endgame evaluation,
* players interested in a first understanding of modern endgame theory and initially overwhelmed by the depth of alternative texts,
* strong kyus or dans interested in a specific topic and spending the book's price regardless of only needing a few pages,
* players sick of countless mistakes in old endgame books and welcoming every book with almost correct contents,
* haters of mathematical annotation.

The book is not
* a broad survey on the fundamentals,
* a detailed, extensive, deep study of modern endgame theory for intermediate to advanced learners,
* a rich problem collection,
* for haters of prose encrypting calculations.


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.

I always keep that in mind when i read a Robert Jasiek's book review

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<meta-discussion>

I contribute contents instead of proving an ability of clicking on Likes buttons.

FYI, I have spent 6 hours on writing the review after circa 18 hours on reading the book carefully enough to assess correctness of its contents, as soon as I got the book.

</meta-discussion>

Are you aware of the not so innocent origins of the 'like' button?

Have a read https://www.independent.co.uk/life-style/gadgets-and-tech/facebook-like-inventor-deletes-app-iphone-justin-rosenstein-addiction-fears-a7986566.html

When reading a review by someone it's always worth bearing many things in mind (of course).. but there is more than one reason why someone might not use a 'like' button.

Cher Robert,

Thank you for this review.

I sent an email to Antti congratulating him on the book's publication. We had a brief exchange about it. I decided not to buy it, not because I anticipated any problems with it, but I was not in its intended audience.

I am glad that the book follows O Meien's lead in using gains instead of the old fashioned way of evaluating move values, which have been the cause of much confusion. I also got the impression from Antti that the book was aimed at players who are not particularly mathematically inclined. That sounded good, since there are a lot of people in that boat. But now I hear that he calculates 1/12ths. Tilt! Even I, who happily calculate much higher denominators, say that practical players have little use for denominators greater than 4.

It also sounds like he puts a lot of stuff into a fairly short book aimed at beginners. But, unlike traditional texts and like O Meien and Jasiek, he provides accurate calculations (with perhaps some exceptions). That's all to the good.

I was wondering how he would manage with avoiding the terms, sente and gote, and it sounds like he stumbled there. OC, modern bots get by quite well without those concepts, so it should be doable. In studying the Elf commentaries, I have noticed that quite often Elf will recommend a sequence that plays sente elsewhere before coming back to the play in the actual game. That makes perfect sense, but why? Taking the sente should not alter the traditional evaluation, and, unless some previous mistake has been made, allowing the opponent to take the reverse sente should not make much difference to the probability of winning or losing, but Elf calculates surprisingly high winrate differences between the two sequences. I don't know about other bots. Anyway, we humans are currently unable to calculate winrates, so it seems like we are stuck with sente and gote.



That is not a bad way of introducing the idea of local sente, instead of relying upon a vague sense of a forcing move. But, OC, it is problematic, because by taking a loss he means taking a smaller gain. He told me that temperature is a term that he avoided. IMX, that was a term that went viral on rec.games.go in the 1990s, with a meaning different from that of the term in combinatorial game theory. I guess it did not spread very far among Western players since then. But it makes many things easy to explain. Such as this: "A sente sequence is one that raises the local temperature and has an even number of alternating plays."



For a book that tries to avoid an overly mathematical treatment, using mathematical terms like expected is problematical. I agree with Robert that score should be avoided for unsettled positions. Traditional texts simply say territory for both score and count, and I think that is fine for informal usage aimed at the non-mathematician. I use count because so many Western go players are mathematicians or highly numerate. BTW, average is a more accurate term than expected. Follow-ups is plain English, while possible futures is over general. By avoiding common go terms and introducing idiosyncratic terms, I am afraid that the book will make difficulties for its readers when they try to communicate with other go players. I realize that my use of terms such as temperature, count, ambiguous, komonster, hyperactive, and infinitesimal is open to the same criticism, but I am writing for a technical audience.



What regular texts call miai value and O Meien calls absolute value.



You mean the swing value (deiri value)? Oh, help!



FWIW, I would not burden the beginner's brain with advanced ko material. Particularly when the author does not understand it. (Sorry for the apparent snark, but advanced kos are difficult to understand.) Unfortunately, the man who pioneered the proper evaluation of them, Professor Elwyn Berlekamp, died recently. Shortly before he died he asked me to write something up about neutral threat environments (NTEs), which may be used for such calculations, and for which he regarded me as the top expert. He came up with the idea of NTEs early in this century. He and I talked about writing a book, but something always came up to delay it. When I am gone, who will write such a book? (I did write a paper for ICOB 2006, so the basic material is out there in the go community.)



FWIW, I would avoid overburdening the beginner's brain.



Glad to hear that. Beginner material that I read mentioned getting the last move, but made a hash of it, OC. If Antti has managed a useful introduction to that topic, more power to him. (But surely the difference between local sente and gote is pertinent, because a different player gets the last local play. How does he do without that?)



Bravo!

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I might have liked this post, but I didn't.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Not "swing" but "per played (excess) move".

Bill, you better write your book in time:)

I do not want to reveal too much of the contents but just say that his discussion of last move is on a very introductory level but instructive at that. Nothing special you would miss, Bill, except maybe to reaffirm your familiar didactic thinking about this topic.

OK, thanks.



Yeah, I think seances won't do the trick.



Very good.

Thanks.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Thank you for pointing out the error on page 106, 3-point move example five! I will fix this for future printings of the book. I'm lucky that the mistake was only 1/16 point.

For page 50, Dia. 8 I have to insist that the book is correct. Dia. 7 and Dia. 8 contrast the possible futures of the position, so one of the diagrams must have one more white stone played while the other must have one more black stone played. Of course, a four-move sequence would also lead to the correct score, but then Dia. 7 would be unnecessary.

In many simpler sequences, which can have constant gains, we would allow continued alternating play for all their moves and derive initial values from the position created after the sequences. Therefore, I prefer consistent analysis. Since the related theory is very new, details are open to discussion, of course:)

OK, you guys have got me curious. What are these two diagrams? The position must be something to have two experts disagree about it.

A note about long sequences. Go player have long recognized, by the seat of their pants, that long sequences are sometimes necessary for accurate evaluation. The most common, perhaps, is the hane-tsugi. OC, long sequences offer a number of chances for errors. Another mathematical go author and I have both admitted that we have gotten one or two of them wrong. The basic problem is that you can't always tell whether another play is right because you don't have enough information without trying the play out. Sometimes the easiest thing to do is to assume that a long sequence is necessary, in which case the original position is equivalent to a simpler one, and use a difference game, subtracting one position from the other, to check whether that is the case. OC, that's a bit rich for a beginner book.

In this case, Ten's remark that both the three move sequence and the four move sequence yield the correct score suggests that the original position is ambiguous. OC, if you do not mention sente and gote, the term, ambiguous, makes no sense.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Plays omitted, liberties made explicit for clarification.

Click Here To Show Diagram Code

[go]$$B p. 50
$$ ---------------
$$ | . . . . . O .
$$ | X O O O . O .
$$ | . X X O . O .
$$ | . . . X O O .
$$ | X X X X . . .
$$ | . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B p. 108
$$ ---------------------
$$ | . O . . . . . . X .
$$ | O . O . . O X . X .
$$ | O O X O O O X . X .
$$ | X X X X X X X X . .
$$ | . . . . . . . . . .[/go]

Thanks.

In the diagram from p. 108 the average gain for each player is 2 15/16, unless White can win the throw-in ko. We all agree.

Edit: I think I'm wrong about that.

Edit2: I am even wrong about my correction. Thanks to Robert for pointing that out.



In the diagram from p. 50 the average gain for each player is ⅓. We all agree on that, as well, I am sure. And the position is ambiguous.

Click Here To Show Diagram Code

[go]$$Wc
$$ ---------------
$$ | . 1 . . . O .
$$ | X O O O . O .
$$ | . X X O . O .
$$ | . . . X O O .
$$ | X X X X . . .
$$ | . . . . . . .[/go]

gains ⅓ pt. for a local score of -2. The original position has an average territorial value of -1⅔.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------
$$ | . 1 . . . O .
$$ | X O O O . O .
$$ | . X X O . O .
$$ | . . . X O O .
$$ | X X X X . . .
$$ | . . . . . . .[/go]

gains ⅓ pt. for an average local territorial value of -1⅓. But the local temperature remains the same, ⅓.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------
$$ | . 1 2 . . O .
$$ | X O O O . O .
$$ | . X X O . O .
$$ | . . . X O O .
$$ | X X X X . . .
$$ | . . . . . . .[/go]

gains ⅓ pt. for an average local territorial value of -1⅔ . But the local temperature remains the same, ⅓.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------
$$ | . 1 2 . . O .
$$ | X O O O . O .
$$ | 3 X X O . O .
$$ | . . . X O O .
$$ | X X X X . . .
$$ | . . . . . . .[/go]

gains ⅓ pt. for an average local territorial value of -1⅓. But the local temperature remains the same, ⅓.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------
$$ | 4 1 2 . . O .
$$ | X O O O . O .
$$ | 3 X X O . O .
$$ | . . . X O O .
$$ | X X X X . . .
$$ | . . . . . . .[/go]

gains ⅓ pt. for an average local territorial value of -1⅔. But the local temperature remains the same, ⅓.

We don't know the final result unless we know who fills the ko. For beginners I would show the filled positions, in addition to all the other diagrams. For experienced players I think it is enough just to indicate the ko. Showing four moves has the advantage of indicating the average territorial value of the initial position.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Avoid shorthands but do calculate the count of the position after move 2 to derive the gain of move 3.

Many thanks.

So the reverse sente gains 3 1/16 pts. as the average territorial value is -1 15/16.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Interesting read! And somewhat ironic I did not know this "like" button had been invented by Facebook.

But from the article, the origin of the "like" seems to really be innocent in fact, with unanticipated effect that became apparent later.

Although (but let's not hijack the thread's original topic) the "addiction" issue seems to be more on the receiver side than on the giver side, hopefully. Anyway,thanks for the link!

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I bought the PDF a couple of weeks ago. As a borderline dan player (*) it comes across to me as the first half of a very good book. I enjoyed it but wanted more! I suspect it would be very useful to people around 5 kyu, or even for stronger players who haven't previously studied endgame theory. Actually most of it would make sense to a 10k, but at that level there are more urgent things to study! For me there were no substantially new ideas, but it added some clarity to things that I've only partially understood in the past.

(*) I'm around 2 dan over the board in Australia, but 2 kyu on KGS.

Things I most liked:

• The elegant and clear prose style. Törmänen deals with some fairly technical concepts but manages to explain them in a way that's simple and straightforward without obviously dumbing it down. This is a big challenge for any technical writer! Overall the book was much easier to read than I expected for this subject matter.
• The pragmatic attitude. As well as explaining how to do exact calculations, it acknowledges that you won't always have the time (or energy or motivation?) to do the calculations in detail, and gives some advice for practical play.
• The layout. It's well spaced out and more attractive to look at than most English language go books. The wide margins allow for "footnotes" that are right next to the relevant text (no need to go to the bottom of the page, definitely none of the dreaded end-of-chapter notes), as well as mini-diagrams. The diagrams in the margin are really useful prompts, often reminding you of what you were reading a couple of minutes ago. (Unfortunately they weren't used in chapter 9, which is where they would have come in most useful!)

Things that weren't so great:

• In part it reads like a "sampler pack" of topics, with some subjects touched upon but not quite explained in enough detail to be useful.
• It doesn't even hint at the existence of "traditional" endgame theory. If this is your only introduction to the endgame, then you'll struggle to follow older books or game commentaries that use deiri counting.
• It's possibly not the best value for money, being short (126 pages including front and back cover) and slightly on the expensive side for an ebook. Personally I don't mind spending the money, because I know that go book authors tend to be horribly underpaid.

Chapter 1 introduces the basic ideas of how to count territory in the endgame and how to calculate the value of a move. The examples are very basic and crystal clear, including how to make sense of "half a point" if you've never seen it before, and accounting for simple follow-up moves.

Chapter 2 takes a close look at the meaning of "sente" in the endgame. It does something that's missing from a lot of endgame introductions: it makes it clear that sente is relative to the whole board position, and right from the start addresses the timing of sente moves. (My first introduction to endgame theory was the Ogawa/Davies book which, if I recall correctly, left me guessing on these points.)

Chapter 3 more or less reviews the ideas of the first two chapters with some slightly more complicated positions.

Chapter 4 gets into ko positions, so here you learn about "a third of a point". This was my favourite chapter, as it gets into two-step kos and approach-move kos, topics that can sound very confusing if not explained well, and gives clear examples of how to count them.

Chapter 5 consists of six problems to practice counting. I found that problem 2 was harder than problem 1. But overall the explanations are very clear. I would have liked to see a few extra pages here, perhaps 10 or 15 problems overall including some easier ones to warm up on, and maybe one or two more intricate ones at the end.

Chapter 6 was a bit puzzling. Törmänen describes a method for quick and approximate counting, based on the idea of "visible territory", something I haven't heard of before. I don't mind that there isn't a clear definition of the concept: after all it's just for rough estimates, and if two people interpret it differently and get slightly different counts, it's still delivering what's promised, as long as you can do the calculations quickly. But there are only two examples, one of them very simple, which isn't enough for me to feel confident using the method in my own games. Another couple of worked examples and some more problems to practice on would have helped a lot here.

Chapter 7 is about Tedomari. The examples are very clear in that you can see what tedomari is, and why it matters, as well as how to get the last point in the special case where all but one endgame move can be sorted into matched pairs. Unfortunately it doesn't give much hint as to how to handle other types of positions. It does teach you that playing the biggest move isn't always a winning strategy. But then you're left wondering what to do other than read to the very end of the game. Isn't the point of endgame theory that you can use your local evaluations to figure out the sequence of plays, so that you don't need to do deep global reading? This chapter seems to undermine those foundations without giving an alternative -- I'm sure that's not the real message, but this is another place where the book opens the lid on a new topic without giving much detail.

Chapter 8 is on endgame tesuji. There's an introduction walking you through how to think about a tesuji problem, and how endgame tesuji differ in character from other tsumego, then eight problems to practice on. The solutions are clear and detailed. But again I felt that it wasn't substantial enough to really be useful. Törmänen does suggest that if you want more, you might read the Guanzi Pu. Not bad advice, but perhaps a bit over the top? Maybe try 200 Endgame Problems first.

Chapter 9 is a "final exam" consisting of five 13x13 full-board exercises. Törmänen describes them as "extremely challenging" and seems to imply that you shouldn't expect to get the right answers, but you can still benefit from analysing them and then comparing your thoughts with the solution. On a first run through, I spent about 15 minutes trying to solve each problem, and probably achieved "partial credit" on each one. I did find this chapter interesting and rewarding. However, it felt more or less independent of the rest of the book. It doesn't really build on the theory of chapters 1-5; rather, each problem introduces a new idea or a new way of thinking. The explanations are clear and detailed.

There are two appendices which I wasn't sure what to make of. Appendix A has 74 positions ordered by move values from 1/3-point moves up to 7-point moves. It's not clear whether this is meant as a reference list, or whether you're intended to try and reproduce the calculations (or even memorise some or all of the values?) Appendix B is an essay on the history of go and the differences between Chinese and Japanese rules. It does include one example of how you should play an endgame position differently depending on the ruleset, but otherwise doesn't seem to relate to the rest of the book.

(Erratum: as mentioned earlier in this thread, one of the three-point moves in appendix A actually has a value of 2 15/16 points. This hasn't yet been fixed in the PDF. I didn't notice any other mistakes in this book.)

Overall I'd say this is very good on how to count reasonably simple positions but could use a bit more on how to choose the order of moves once you've done the counting, and it gives you a lot of tantalising hints on how much more there is to learn about endgame theory. All done in a very enjoyable and readable style, if a little shorter than I would have liked.

Up next: Robert Jasiek's endgame books. I've just bought the PDF of Endgame 2 -- Values, but I think it's going to take more than a couple of weeks to work through that one. I'll get back to you next year :-)

What is your opinion on avoiding the word "gote" in the book? Does this approach to terminology make understanding for you easier or more difficult?

I didn't notice that it was missing! Then again, I've read other works on the endgame, both older books and many pages on SL, so it's possible that I was mentally inserting the word "gote" without realising it.