Life In 19x19

Two new books of my endgame theory series are available as a printed edition or PDF file: Endgame 4 - Global Move Order and Endgame 5 - Mathematics.


Endgame 4 - Global Move Order - Description

This comprehensive book with 268 pages for players from 8 kyu to 9 pro explains the correct order of moves on the global scale during the early and late endgame. It does not just fill a gap in the literature but contains so many inventions that it doubles the theory of global endgame decisions. Most of the theory even represents absolute truth verified in Volume 5.

The book covers every basic type of local endgame with gote or sente follow-ups, gote and sente options, several or iterative follow-ups. The global environment is taken into account during the early and late endgame. The reader can learn his favourite method by comparing counts or net profits, or applying a principle. By comparing the right values, we decide whether to play locally or the most valuable move in the environment.


Endgame 5 - Mathematics - Description

This textbook with 240 pages for experts presents definitions, 149 theorems and their proofs to establish endgame evaluation as always correct truths. While Volumes 2 to 4 explain modern endgame theory for players, Volume 5 verifies the theory mathematically. The book also introduces the practically relevant parts of combinatorial game theory, thermography and scoring. The book studies local and global evaluation, all basic types of endgames, short and long sequences, either starting players, all temperatures, the early and late endgame, different methods of evaluation and their equivalence.


Links

Endgame 4 - Global Move Order

Webpage: http://home.snafu.de/jasiek/Endgame.html
Cover: http://home.snafu.de/jasiek/Endgame_4_Cover.png
Sample: http://home.snafu.de/jasiek/Endgame_4_Sample.pdf
Table of Contents: http://home.snafu.de/jasiek/Endgame_4_TOC.pdf
Review by the Author: http://home.snafu.de/jasiek/Endgame_4_Review.html
https://www.lifein19x19.com/viewtopic.php?f=57&t=18386

Endgame 5 - Mathematics

Webpage: http://home.snafu.de/jasiek/Endgame.html
Cover: http://home.snafu.de/jasiek/Endgame_5_Cover.png
Sample: http://home.snafu.de/jasiek/Endgame_5_Sample.pdf
Table of Contents: http://home.snafu.de/jasiek/Endgame_5_TOC.pdf
Review by the Author: http://home.snafu.de/jasiek/Endgame_5_Review.html
https://www.lifein19x19.com/viewtopic.php?f=57&t=18387

Wouahhh,great work. Still thinking aabout the volume 4. I am waiting the endgame problems 2 ^^

My current plan is to write a few other books in between but I have raw material for Endgame Problems 2 about standard shapes, such as corner kos or joseki follow-ups. A later volume of Endgame Problems should practise the theory of Endgame 4.

Great ^^ I will wait ^^

Citation reference: viewtopic.php?p=273675#p273675

John Fairbairn wrote:Apparently there is a "well-known fact" that I did not know, to the effect that "in a half-point game the side that fills in the last dame loses." I assume that dame here is being used somewhat loosely (as is common) for the last necessary move.

It was mentioned in 1997 on rec.games.go that a Japanese journalist observed a relation between last move, 1/2 point game and winner. Then, I devised a first proof for the special case of 5.5 komi and some further simplifying assumptions. Later, I generalised a bit. However, the so far most general version appears in my book Endgame 5 - Mathematics.


"Definition 40 [standard area komi]

Standard area komi has the form K := 2z - 0.5 for some whole number z.

[...]

Presuppositions

Assume no handicap stones and single passes. Apply the territory score together with the conditions 'unequivocal', 'without two-sided dame and teire', 'without capturable stones in sekis', 'without asymmetric sekis'. Have no suicide, standard area komi, an odd parity of the number of intersections on the board, a final position with an even seki parity and the territory score 0.5.

Theorem 144 [last play indicates winner]

The winner under territory and area scoring is the player of the last play."

Note that 6.5 komi is non-standard area komi. See pp. 215 - 226 of Endgame 5 - Mathematics for explanations for the presuppositions and the mathematical proof of the theorem. The proof of theorem 144 is a one-liner but the proofs of some of its referenced, applied theorems each cover several pages. For informal descriptions, see the book Endgame 2 - Values, chapter 6.1.

In the thread Go maths literature,

https://www.lifein19x19.com/viewtopic.php?f=15&t=19571

dhu163 asks for my endgame theory and its concepts in Endgame 5 - Mathematics applicable also during the opening and middle game. Let me give such references as follows.

General concepts: count and white-count, gote count, sente count, tentative gote count, (a player's) tentative sente count, score *, move value, gote move value, (a player's) sente move value, tentative gote move value, (a player's) tentative sente move value, gain, net profit, (concepts of) alternating sum, temperature and value of starting in an environment, high temperature, low temperature, gote-sente-difference, local region (or local endgame), environment, ideal environment, follow-up and follower, early endgame (in contrast to late endgame), larger local endgame, parity, standard area komi *, tail, traversal, value perspective

* = hardly useful during the opening and middle game.

Types of local regions (or local endgames) and related concepts: without follow-up, one follow-up, follow-ups of both players, with gote and sente options, local gote, (a player's) local sente, (a player's or doubly) ambiguous [local region / endgame], creator, preventer

Methods: applying a principle, comparing counts, comparing move values, comparing net profits, comparing the opponent's branches *, comparing two sequences, comparing three sequences, making a hypothesis *, reading and counting

Theorems / propositions (and their numbers):

- equality of move value and gains in a simple gote (10, 19)

- playing simple gotes in order of decreasing-or-constant move values (11) [Everybody assumed this the most frequently applied principle but I have proved that this is correct in general indeed. This 'first take the larger cake' is a well-known principle in number theory or the mathematical theory of alternating sums and so basic that I could not find a proof elsewhere so had to prove it presumably again by myself. No problem as it was a 20 minutes exercise, which every maths student should be able to do quickly, or should not study mathematics:)]

- equivalence of comparing a) tentative sente and gote counts, b) tentative gote move value and follow-up move value, c) tentative sente move value and follow-up move value, and d) tentative sente move value and tentative gote move value (12~16, 23~24)

- equivalences of counts and white-counts, and of move values using Black's or White's value perspectives (17~18, 25~26)

- non-existence of a local double sente (20)

- relation of the count of a local gote, ordinary ko or ko threat to the move value (27)

- the net profit of any alternating or non-alternating sequence transforms the initial count to the resulting count (29) [This is absolutely basic, of the utmost importance and characterises net profit as well-defined.]

- net profit T/2 of starting in an ideal environment (50) [Bill Spight had known this, of course.]

- maximum net profit T of starting in a simple environment (51)

- timing of a local gote (55~59) [Everybody had assumed the 'obvious' but I proved it and found bounds for premature or delayed timing.]

- timings for playing in a local endgame / region with one follow-ups during the early or late endgame, at low or high temperature, with the creator or preventer starting (62~63, 68~69, 73, 84~85, 89)

- difference of net profits of Black versus White starting alternating play (72)

- equivalence of different methods (83, 109)

- still tenuki from a local sente during the early endgame at high temperature (90)

- timings for playing in a local gote with follow-ups of both players at high, low or medium temperatures (93, 95, 99, 103, 107, 110) [In particular, at low temperature play locally!]

- timings for playing in a local endgame / region with gote and sente options during the early endgame at low or high temperature (130~131, 134)

- order of playing in several local endgames / regions (137~139)

Of the aforementioned topics, the following is part of (strong) go players' general informal, approximate knowledge:

General concepts: score, [modern] move value, gote move value, (a player's) sente move value, local region, environment, follow-up and follower, value perspective.

Types of local regions (or local endgames) and related concepts: without follow-up, one follow-up, follow-ups of both players.

Method: reading and counting.

Contents of theorems:

- playing simple gotes in order of decreasing-or-constant move values

- equivalence of counts and white-counts

- timing of a local gote


The most glaring missing, not generally known knowledge is:

- concept: [the] count

- types of local regions (rather than moves): with gote and sente options, local gote, (a player's) local sente, ambiguous

- theorem: net profit T/2 of starting in a "fair" environment (only students of modern endgame theory are aware of this)