Endgame Problems 1

Review by the Author

General Specification

Preface

The book contains 150 endgame problems and introduces the theory necessary for their solution. There are 20 new tactical problems on the 11x11 board and 130 evaluation problems studying modern endgame theory under territory scoring.

For problems of endgame evaluation, the book achieves a revolutionary concept: correctness of the answers. For this purpose, I have studied endgame theory for 2.5 years before creating the book and spent as much time on proofreading as on writing it.

Tactical Problems

The 20 whole board problems have the task "Black to play and achieve the maximum count". We practise playing all our sente moves, tactical reading, life and death, and tesujis.

At first glance, these problems appear to be for 10 kyus. However, most of them can be demanding for dans. The reader does not know in advance whether a tie with the count 0 is good enough or he can achieve a win with the count 1, whether he should play sente or kill, and what tesujis must be deployed.

The hidden difficulty serves two purposes: improving presumes solving problems above one's current level; after overcoming the hurdle at the beginning of the book, the evaluation problems appear relatively easier so that we can better learn evaluation. The answers to the whole board problems show every relevant variation and decision.

Theory

Since endgame evaluation requires application of theory, the necessary theory is summarised on 35 pages. Therefore, this book can be read independently, although readers of the first half of Endgame 2 - Values and a representative selection of the basic theory in Endgame 3 - Accurate Local Evaluation are prepared better.

Explanation of theory is distributed to several chapters and explained before its first use. Furthermore, references enable a choice of reading a whole theory chapter or swapping between its sections and related sections of subsequent problem chapters.

The basic theory of gote versus sente, counts (the local positional values) and move values is explained twice using different approaches. Furthermore, footnotes on the pages with answers to the problems, an appendix explaining conventions of diagrams, variables and calculations, and an index assist the reader. For example, if he forgets what a 'gote count' is, several tools explain him its calculation as an average. Similarly, he can recall easily the different calculations of Black's versus White's 'gains' (which express how much a player's move shifts counts in his favour).

The theory explains the basic concepts and values of modern endgame theory. In particular, we learn the ordinary types 'local gote' versus 'local sente' (one player has a sente sequence) of local endgame positions. Furthermore, there are the hybrid type 'ambiguous' and ordinary kos. A local endgame with long 'traversal' sequences (with at least 3 moves worth playing successively) can be a 'long gote' or 'long sente'. We distinguish the types of local endgames to calculate their appropriate values. Furthermore, value conditions verify that we calculate the right values. For long types, we also determine for how long local play should proceed before playing elsewhere. We also consider whether ko threats can be preserved.

Endgame Problems 1 emphasises the basic theory and skips advanced theory. Therefore, local gote is distinguished from local sente by the most popular kinds of conditions, which compare a move value of the initial position to a follow-up move value of a follow-up position ('follower'). This book does not study alternative value conditions, options and sophisticated methods of fast evaluation, which Endgame 3 - Accurate Local Evaluation explains but whose practice is postponed for Endgame Problems 2.

Evaluation Problems

The 130 evaluation problems with relatively large diagrams have realistic, basic shapes. They vary from the most basic to intermediate difficulty. The non-standard shapes and evaluation in the answers of all problems are new.

The problems study every basic kind of local endgame: without follow-up, simple gote with gote follow-ups of one or both players, simple gote with iterative gote follow-ups, simple gote with sente follow-ups, simple sente with gote or sente follow-ups, long gote, long sente, with basic endgame kos, ordinary kos, ambiguous local endgames and mixed shapes. Complex kos, which require advanced theory, are the only noteworthy omission.

Whenever necessary, the answers are very detailed. They analyse move by move and position by position. Calculation proceeds backwards: we calculate the counts and move values of the follow-up positions before we derive the values of the initial local endgame. At every step, we use a value condition to verify that we calculate the right gote or sente values. For long sequences, we also determine their lengths and calculate the gains of their moves. The detailed calculations including verifications enable the reader to understand their correctness. Some advanced problems have short naive answers and detailed accurate answers so that we see when they agree or the naive answers are wrong.

Values are 'tentative' until they are confirmed. Tentative values are denoted gently in the text and by a different font for letters of variables. The reader can ignore this aspect or read the text more deeply by raising his awareness.

The variables C and M denote counts and move values, respectively. If several values are calculated, suffixes refer to the numbers of diagrams or moves.

Except for introductory examples, the book omits trivial text. For every diagram with a settled position, the caption simply states its count. The reader is expected to verify it by adding Black's and subtracting White's points of the marked intersections. Every stone with the label 'A' is worth 1 point for its captor. The label 'H' denotes half a point or minus half a point. When a gain is calculated from the previously determined counts before and after a move, the reader should look up the related diagrams without explicit reference. Instead of repeating the obvious every time, such conventions are declared once in the appendix. The footnotes contribute to keeping the text clean.

As a consequence, it can concentrate on the important values and calculations. From the introduction of theory, we know that negative counts favour White. Here is a sample, in which the footnotes are unshown:

"The initial local endgame with the black follower's count B = 1 in Dia. 26.1 and white follower's count W = -3 in Dia. 26.2 has the gote count

C = (B + W) / 2 = (1 + (-3)) / 2 = -1

and gote move value

M = (B - W) / 2 = (1 - (-3)) / 2 = 2."

Every important calculation appears in its own row to ease its reading. After the declaration of the calculated value, the formula is stated, the actual numbers are inserted and transformed.

Conclusion

We improve finding sente plays, tesujis and our tactical reading. Endgame Problems 1 teaches the relevant theory. Provided we embrace the effort necessary for calculations and their notation, we learn correct evaluation of every basic type of local endgame and its follow-ups. We calculate and verify counts, move values and gains.

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

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