Endgame 3 - Accurate Local Evaluation

Review by the Author

General Specification


The subtitle Accurate Local Evaluation is the book's program: it evaluates local endgame positions accurately. During all phases of the game, correct local evaluation is a requirement for very good global decisions. Whenever tactical reading is too complex, we also need strategy, approximative positional judgement or more precise endgame evaluation. The latter can often replace global reading by a combination of local reading and value comparisons.

The values of a local endgame depend on its type and lengths of sequences. Do we have a local gote or sente? For how long should local alternating play proceed? When must we interrupt and play elsewhere? By answering these essential questions, we can calculate the values correctly. Therefore, we avoid losing many points due to evaluation mistakes.

The book is the result of 15 months of full-time work. Half of it has been research, which has been necessary to fill huge gaps in earlier theory and create a consistent, sufficiently complete and well applicable, general theory of endgame evaluation. Previously, we were only given the chance to compete with 9 dans on the topic of getting the last point. This book enables every serious learner to reach this level on the much broader topic of local endgame evaluation. This is so because the methods and principles often represent truths derived from mathematical theorems. The value calculations in the examples are supported by meticulous proofreading.


An introduction gives an overview on the contents and demonstrates that we lose points in every local endgame by evaluating it wrongly when confusing gote with sente or misjudging for how long we should continue local play. The book presumes fluent application of the basics of modern endgame theory: the count (positional value) and move value (value of a move) of a local gote or sente endgame and its followers (follow-up positions); the gain of every individual move (the value of how much a player's move shifts counts in his favour); negative numbers favouring White. Although readers of Volume 2 are familiar with these basics, Endgame 3 - Accurate Local Evaluation can be read independently because the chapter Basics summarises them. The book concludes with an appendix, which lists keywords and the conventions for diagrams and variables. The major contents is presented in the following three parts:

Evaluation of Local Endgames with Short Sequences

Unless we have a simple gote without follow-up, a local endgame with short sequences has follow-ups of one of both players. After the first move, we need to know whether the opponent must reply immediately. Depending on the answer, the local endgame is a 'local gote', 'local sente' or their hybrid, which is called an 'ambiguous' local endgame. The book distinguishes and determines these types objectively. For this purpose, we verify whether some value condition is fulfilled. Such a condition compares two particular move values or counts. For example, a move value of the initial local endgame is compared with the follow-up move value in the position created by the first move. We can choose our preferred kind of value condition because the book offers four alternative kinds (and a fifth kind designed for long sequences, which can also be applied to short sequences).

A local gote has a 'gote count' and 'gote move value' while a local sente has a 'sente count' and 'sente move value'. Calculations of gote values differs from calculations of sente values. Initially, we do not know the type of a studied local endgame yet. Therefore, we consider 'tentative' values. We can confirm them by confirming a value condition. For example, if we compare a tentative gote move value of the initial local endgame to a smaller follow-up move value, this condition of decreasing move values confirms the gote move value and type 'local gote' of the local endgame.

The book explains the similarities and differences of value conditions for local endgames with Black's follow-up, White's follow-up, both players' follow-ups or less valuable iterative follow-ups. A short section on multiples provides additional insight. Usually, values are calculated from Black's perspective (positive values favour Black). However, the reader can also study the optional sections on White's perspective, for which counts, calculations and conditions differ.

We need different conditions and verify additional assumptions for those local endgames with a player's gote or sente options. For them, the reader can choose among two kinds of equivalent value conditions.

The theory is explained in detail by introductions, value conditions stated as formulas, principles and text, summarising tables and value trees. To ease learning of the theory, the examples are very basic. For every example, the book demonstrates calculations for all possible, alternative value conditions. Some examples are close calls, for which only accurate calculations can determine the right values.

Evaluation of Local Endgames with Long Sequences

Not surprisingly, evaluation becomes more difficult if a local endgame allows Black or White to start a long sequence. While the values of a local endgame with short sequences are derived from the followers after one or two moves, we might need to derive the values of a local endgame with long sequences from followers created after three or more moves. We calculate their gains to determine the lengths of any traversal sequences. For this ordinary evaluation of long sequences, we apply the method of 'making a hypothesis':  we assume some long sequences, derive tentative values accordingly and check whether they are consistent because the conditions comparing the gains are fulfilled. If necessary, we test an alternative hypothesis. On confirming a hypothesis, we know that its values are correct.

The scope of examples varies from simple to advanced - from three to nine moves worth playing successively. The meticulous calculations proceed move by move and position by position. Every type of local endgame is discussed. There are also counter-examples including a crucial one refuting wrong earlier theory.

We can sometimes apply one of the three sophisticated methods of fast evaluation: 'comparing the opponent's branches', 'comparing counts' and 'comparing move values'. If certain assumptions are fulfilled, we can greatly accelerate calculation of initial values. Examples demonstrate how very much analysis can sometimes be accelerated. Diagram trees assist our perception. Font aspects enrich the presented information.


The book is not for you if you die on seeing explicit calculations. Variables play an important role in the value conditions. Analysis of an example involves several different values, which the book identifies by their names (the variables). These names (or single letters) are chosen carefully to make their meaning apparent at a glance whenever possible. While experienced readers of calculations can understand their meanings easily, others may find the learning curve steep. At a few places, detailed prose provides additional explanation for beginners. If, however, every calculation was hidden in prose, the text would have to be split into five books. It is simply impossible to teach a great amount of advanced contents also for beginners in a single book. Endgame 3 - Accurate Local Evaluation is for intermediate to strong players prepared to invest the necessary effort. How else can we expect to reach understanding beyond 9 pro level?

Although research developing, and completing invention of, the theory has been much more demanding than anything I have studied before, the now available theory is well applicable. We must learn some value conditions and spend the necessary effort on doing the calculations while not accidentally confusing values. Tactical reading can be more difficult as soon as we become as familiar with endgame calculations as we are with tactical reading. Both are essential. A major part of our effort lies in recalling several intermediate values, which we need until determining the desired initial values. Hence, the reader's major effort is two-fold:  he must become familiar with the notation of values and calculations in the book; he must practise calculations until they become his second nature, quite like tactical reading.

Why do we invest in such effort? We can greatly simplify our tactical reading and enable decisions when it would be too complex. We must not neglect any central topic of go theory, such as endgame evaluation. Our weakest skills impede our strength. If we are weak at endgame evaluation, we must study it.

What the Book Is Not

The book is neither an introduction for beginners nor an 'Endgame Evaluation for Dummies'. School mathematics is sufficient and there is no advanced mathematics, such as calculus, combinatorial game theory, difference games (further research is needed), construction of trees (the few trees in the book are visualisation aids), thermography, cooling and infinitesimals. The book skips the finest global evaluation, with which one might get the last play according to the theory in Volume 2 or the book Mathematical Go Endgames. Complex kos, whose local evaluation also depends on the global context, are not explained. Although a few problems test understanding of the most difficult topics, systematic training of the theory is planned for the separate book series Endgame Problems. Global endgame evaluation (better than the principle of usually playing in order of decreasing local move values) and mathematical proofs of theorems are scheduled for later volumes.


Endgame 3 - Accurate Local Evaluation teaches essential theory previously neglected by everybody (except Bill Spight). If we take evaluation as seriously as tactical reading and invest the necessary effort of calculation, we learn to avoid countless evaluation mistakes, whose loss is circa 1/2 to 5 points per local endgame.

* =  These are the endconsumer prices in EUR according to UStG 19 (small business exempted from VAT).

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