Rational Endgame

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Rational Endgame is a book by Antti Törmänen about modern endgame theory.

Rational Endgame
By: Antti Törmänen
Publisher: Hebsacker Verlag


[ext] Review, discussion and some errata on L19

Review by Robert Jasiek

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: +


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.


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.


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.


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.


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.

Rational Endgame last edited by DuEm6 on June 22, 2021 - 06:30
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