Robert Jasiek's Go Theory Research

[Cassandra]

Sub-sub-variation D-E-F ?

[RobertJasiek]

If your question is meant to ask what is 'perfect play', this is a central(!) go term with the meaning "always at each turn, a then moving player chooses some move optimising the score for himself".

When you speak about something else, such as "have to choose move A (with a 'local gain' of 20 points) instead of move B (with a 'local gain' of 10 points) in the case that you were behind on the rest of the board by 5 points, if you ever wanted to win the game.", your (conscious or subconscious) aim is perfect play. Although perfect play is an interesting study topic in itself, it is independent of my ko definition.

Also therefore it is superfluous that you call your study of a few examples an "application" of my ko paper, and speculate about whether I benefit from or my opinion about your study.

Since my ko definition does not determine perfect play, the perfect play in (your) examples about studying perfect play cannot be understood by means of my ko definition. Since my ko definition determines kos, the definition could be applied also to your examples to determine any kos in them. The major thing that is in vain with your attempt to show an analogy is your still missing understanding of this difference of what my definition does not do versus does do. (For local/global, see my earlier messages.)

[RBerenguel]

If your question is meant to ask what is 'perfect play', this is a central(!) go term with the meaning "always at each turn, a then moving player chooses some move optimising the score for himself".

Shouldn't this be optimising the score given a perfect score estimation function (since optimising the score for oneself assumes there is some kind of score estimation method, and it has to be perfect if perfect play is expected,) or defining perfect play just as the move that maximises the likelihood of a winning result (since a winning result is just a matter of counting the real board under appropriate rules), which avoids having to get "score" into the definition?

[RobertJasiek]

There can be one or several 'perfect play' moves at a turn. One of them might be a pass.

Perfect play has nothing to do likelihood.

The, what you call, perfect score estimation function is the correctly anticipated score.

In principle, perfect play is given by min-max of the complete (follow-up) game tree with the scores given at its leaves (after succesive passes stopping every variation). The scores are given, because the rules are given and must set the used scoring method. (Infinite sequences and special scores / game end conditions can complicate matters.)

In informal terms, perfect play is given by the imagined (follow-up) variations, the choices among them and the scores of the positions created after successive passes. At his imagined turn, Black maximises the (final) score. At his imagined turn, White minimises the (final) score (by convention, negative scores favour White).

[Cassandra]

Sub-sub-variation D-E-F ?

Dear Robert,

Please remember that I once wrote about "Main line", "variations", and "sub-variations" with regard to the flow of mutual discussion.
My statement has been meant as a hint that you -- as usual, when you have the feeling to be in the defensive -- opened a minor aspect of another topic that I had never mentioned before.
But may it be as it is. "Perfect play" has nothing to do with what I intended to explain to you.


I am afraid that you are unable (may be unwilling) to realize the equivalence between

My application for "Life & Death" / "Semeai"
A1) "You have to choose move A (with a 'local gain' of 20 points) instead of move B (with a 'local gain' of 10 points) in the case that you were behind on the rest of the board by 5 points, if you ever wanted to win the game."
>>> Move A leads to "GLOBAL living".
A2) "There is no need that you choose move A (with a 'local gain' of 20 points) instead of move B (with a 'local gain' of 10 points) in the case that you were ahead (or behind) on the board by 15 points. You will win (or lose) anyway."
>>> Move A does not lead to "GLOBAL living"; is one was interested in, one could achieve "LOCAL living".

Your application for "Ko"
B1) "Please assume that Komi is k1 points, and S1-scoring applies."
>>> Board points P1, ... , Pn are GLOBAL-ko-intersections.
B2) "Please assume that Komi is k2 points, and S2-scoring applies."
>>> Board points P1, ... , Pn are no GLOBAL-ko-intersecions; if one was interested in, board points P1, ... Pm could achieve the property "LOCAL-ko-intersection".


In principle, the application of your "ko-definitions" depends on the current score of the game. But -- in my opinion -- this cannot be a valid basis for a "theory", as I tried to make evident with my "Semeai-application". With your kind of presentation, you try to be suggestive of massive insights into "strategy" that would derive from it. But you have done no more than a circular reasoning.

At the end of the day, your definitions imply
"Answer your opponent's move, only in the case that the outcome of the game depends. If you were ahead -- even after not answering -- then do not place a stone. If you were behind anyway, then pass all the time from now on."

This has nothing at all to do with "perfect play", but is bad playing style.

[RBerenguel]

There can be one or several 'perfect play' moves at a turn. One of them might be a pass.

Perfect play has nothing to do likelihood.

The, what you call, perfect score estimation function is the correctly anticipated score.

In principle, perfect play is given by min-max of the complete (follow-up) game tree with the scores given at its leaves (after succesive passes stopping every variation). The scores are given, because the rules are given and must set the used scoring method. (Infinite sequences and special scores / game end conditions can complicate matters.)

In informal terms, perfect play is given by the imagined (follow-up) variations, the choices among them and the scores of the positions created after successive passes. At his imagined turn, Black maximises the (final) score. At his imagined turn, White minimises the (final) score (by convention, negative scores favour White).

The likelihood is the number of branches in the follow up containing a "win" vs those containing a "lose." Maximising it should keep it larger than 1. Just generalises to non completely minimax scenarios the maximisation (for example, plain ol' tree searches.)

You said "optimising the score for himself," and this statement was lacking a definition of score (or score estimation) for optimisation purposes. What you should have said if wanting to keep it short is "guaranteeing a winning follow up sequence". For example. Optimise was the problem, because you are not optimising anything, in any case you are maximising it.

[RobertJasiek]

Cassandra, playing word games about "global" and "local" do not establish - what you pretend was established - equivalence. Maybe you have been motivated by my paper to think about global and local aspects in your examples, but motivation is not equivalence. Do not speak about equivalence when there is none. Equivalence has a strict meaning in mathematics. Speak about something else, maybe about 'motivation' or about 'similarity'.

The application of my ko definition does not depend on the current score of the game, but it depends on the current-position, the komi and the possibility to win.

Since my ko definition does not depend on the current score of the game, it is immaterial whether you conclude from the opposite "cannot be a valid basis".

At the moment, I am not yet suggestive about massive insights into strategy derived from applying the ko definition. The definition relies on complete strategies, but it does not distinguish perfect play strategies from non-perfect-play strategies etc. Study independent of my paper can study how strong or weak (how many points less are achieved by) particular strategies are in relation to perfect play.

I have NOT done circular reasoning. Think again. In my paper's definition, strategy is complete. In your studies, strategies are partial, because you concentrate on only a very few move decisions. Besides, your strategies are (I hope) chosen well for your study purpose. IOW, you use more specialising instances of (partial) strategies. Being more specialising is not circular reasoning.

(Strictly, strategy in my paper depends on move-sequences using the default restriction rules. You use strategy in a different rules embedding.)

My definitions do not imply "Answer your opponent's move, only in the case that the outcome of the game depends.". Such a kind of consideration is not used for all my definitions, but only for global-ko-intersection.

Your guess "If you were behind anyway, then pass all the time from now on." is wrong, e.g., because "being behing" is not a condition in my definitions. I guess I know what you are aiming at, but a) for basic-ko-intersection it is not a problem, b) for local-ko-intersection the players are required to comply with the definitions, c) same for global-ko-intersections.

RBerenguel, there is no likelihood larger than 1. (It is trivial to speak of the likehood 1 always. This amounts to perfect play being independent of likelihood.)

NO, NO, NO, perfect play is NOT ONLY about finding a winning sequence, but perfect play is about ALSO finding a score-maximising/-minimising move.

For Black, optimising is maximising. For White optimising is minimising. For the generic player, it is "optimising for himself".

[Cassandra]

The application of my ko definition does not depend on the current score of the game, but it depends on the current-position, the komi and the possibility to win.

Dear Robert,

Are you really sure that this are two different pairs of shoes ?
What is "possibility to win" (contents / value) ?

NO, NO, NO, perfect play is NOT ONLY about finding a winning sequence, but perfect play is about ALSO finding a score-maximising/-minimising move.

"Perfect" depends strictly on what is the aim that you want to achieve.

As far as I know, the aim of the game that I know as "Go" is to win. Or -- assuming that Go has been "solved", and the "ideal" result were a Jigo -- the aim is at least not to lose. (( This case will not be considered below, to help simplifying the text. ))

Winning a game of Go does NOT have anything to do with "maximising" / "minimising" the SCORE. This is appreciated by many people as one of the advantages of the game of Go.


This means that the leaves of the tree (considering the final result of the game) can have the properties "win", "lose" (, or "Jigo") only.

If the cumulative result at a branching point of the tree were "lose" for one player, "perfect play" in the real world for this player would demand to play a move that calls "I surrender".


This takes us back to your distinction between "local" and "global". Only in the case that we have "LOCAL" as our field of obversation, maximising / minimising the (then "LOCAL") score makes sense. This is because we do not know anything about the world outside "LOCAL", and want to be on the sure side, to prepare for any surprise that might wait for us in "GLOBAL".

Only in this case, assessing the ("LOCAL") score makes sense, because we know that, when the final result will be calculated, all local scores will be combined, and included.


As I have demonstrated in my "Life & Death"- / "Semeai"-application, it is possible to achieve the "GLOBAL" aim of the game, without being dependent on achieving every aim to "LOCALLY" maximise the score. This is why neither the distinction between "LOCAL Semeai" / "GLOBAL Semeai" does make any sense, nor your Ko-related distinction.

[Cassandra]

Dear Robert,

I will really quit your thread now.

It seems to me that you neither want the slightest support nor understand the meaning of the German "Analogie" (e.g. explained here: http://de.wikipedia.org/wiki/Analogie_%28Rhetorik%29).



Let us assume a situation, where 20 Go-players are asked to give their assessment of a position and to make a suggestion where to move next.

It is not unlikely that the saying "Viele Köche verderben den Brei" / "Too many cooks spoil the broth" could be applied on this scenario.

Your reaction will be

-- There is not even one cook amoung the players asked.
-- We talk about the game of Go, not about French Cuisine.
-- The saying does not apply.

[RobertJasiek]

'Perfect play' is defined, see above. If you have not understood it, read it again. There is nothing more to discuss what 'perfect' shall mean. 'Perfect play' is a fixed term; for that purpose, there is no extra meaning in considering the words separately.

'Perfect play' is defined regardless of what the game aim is. The term does not alter the game aim.

For the purpose of the term, the leaves have their scores as their values.

The whole board score can be maximised or minimised, regardless of whether you pretend that this was not so.

From your so called demonstration, it does NOT follow that a distinction between local- and global-ko-intersection did not make sense. For such a statement, you would need to prove that local-ko-intersection and global-ko-intersection would be the same when applied. Such a proof does not exist, because they are different, see the examples in my paper.

Discussing something else or discussing analogies is fine, as long as you do not also make false statements or conclusions about my paper's definitions.

[RobertJasiek]

Since 2013, I have also been busy with go theory research. Now, in 2021, I provide an update.



Robert Jasiek's Go Theory Research



http://home.snafu.de/jasiek/RobertJasie ... earch.html



Preface


My 1000 informal or semi-formal principles, of which many are important for go theory and more often correct than those by other writers, and minor definitions, research etc. are not mentioned here. After some preliminary studies, I began serious research in go theory in 1996.

The research is by Robert Jasiek unless other names are stated. Two or more names without attributes are listed in decreasing order of contribution. Names separated by a slash indicate equal contribution.

Outside the lists of most important inventions, bold font denotes the relatively more important research.

Many inventions reveal gaps in earlier common informal knowledge and in teaching by professional players. The "Neutral stone difference" is an example of a simple concept that professional players apply but amateurs often do not apply because it has not been taught by anybody except me, although each new neutral stone too many equals one pass during the middle game.

The two top inventions for players ("Playing simple gotes without follow-ups in decreasing order" and "Timing during the early endgame of playing in a local gote in an environment") are inventions from the view of mathematical research and confirm common informal knowledge. Some other inventions ("Non-existence of local double sente", "Counter-example for always seeking tedomari" and "Counter-examples for always playing a simple gote with one follow-up in an environment of simple gotes without follow-ups in decreasing order of move values") refute common informal knowledge. We cannot trust common informal knowledge but we can trust mathematical theorems.

Difficulty and effort of inventions do not correlate with their importance. It was difficult to prove "Timing during the early endgame of playing in a local gote in an environment" but took me only 20 minutes to prove "Playing simple gotes without follow-ups in decreasing order". Although the proof only needs school mathematics, several go players failed to prove it. I only list mine as "alternative proof" (instead of full "invention") because it expresses taking numbers in decreasing order, for which I could not find a proof but only much research by mathematicians on advanced alternating sums. Please let me know if you find some proof dated before 2021!

Although many simple but important inventions can be made, there are only a few serious researchers in go theory. A reason may be that simple but important theory does not pop up by itself. It requires years, or even many years, of study to see through the fog of less relevant knowledge.


Abbreviations


[A] = alternative proof
[C] = invented general major concept
[D] = definition or overview
[G] = general knowledge stated as principle, procedure, method, definition, rule or ruleset; applies to arbitrary values and arbitrary positions of a class
[.I] = invention
[T] = theorem and proof; therefore application is always correct
[W] = first or probably first to write down clearly verbal knowledge in English, German or possibly world literature
[*] = book
[m] = message
[p] = paper or webpage


The Most Important Inventions for Players


1. Playing simple gotes without follow-ups in decreasing order [GA] [*] [like taking numbers in decreasing order]

2. Timing during the early endgame of playing in a local gote in an environment [.IGT] [*]

3. Verify types of local endgames to determine their correct values. [.IGT] [*m] [Robert Jasiek / Bill Spight]

4. Equivalence of conditions (gote / sente count versus gote / follow-up move value versus sente / follow-up move value versus gote / sente move value) of local endgame with one simple follow-up [.IGT] [*m] [proofs Robert Jasiek, conjectures Bill Spight]

5. Neutral stone difference, neutral-or-dead stone difference [.ICGD] [*]

6. Earliest and latest moments of playing in a local endgame in sente or reverse sente depending on the enironment [.IGT] [*m] [Bill Spight, Robert Jasiek]

7. Several local endgames

- Creator starting in the larger local endgame with one follow-up [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Preventer starting in the larger local endgame with one follow-up [.IGT] [*m] [Robert Jasiek, Bill Spight]

8. Use the principle of extreme difference values to simplify reading for several iterative local endgames. [.IG] [*]

9. Approach plays affecting the score [.IGT] [*]

10. Direct connection, indirect connection [.IWGD] [*]

11. Influence stone difference [.ICGD] [*]

12. Re-definition of two-eye-formation [.IGD] [pm]

13. Definition of stability [.ICGD] [*]

14. Classification of regions [.IWG] [*]

15. Definition of current territory [.ICGD] [*] [there was the predecessor Cho Chikun]

16. Value of a fighting region [.ICGD] [*]

17. Relation between area count and territory count [.IG] [*]

18. Timing during the late endgame at low temperature of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

19. For a local sente during the early endgame at high temperature, play in the environment [.IGT] [*]

20. Ordinary evaluation of long sequences by the method of making a hypothesis [.IG] [*]

21. Evaluation and choice in a ko exchange [.IWG] [*]

22. Method of comparing two sequences combined with the method of comparing counts during the late endgame in a local endgame with one follow-up in an environment [.IGT] [*m] [Robert Jasiek, Bill Spight]

23. Method of comparing two sequences combined with the method of comparing counts during the late endgame in a local gote with two simple follow-ups in an environment [.IGT] [*]

24. Generalised connection (n-connected) [.ICGD] [*]

25. General definition of thickness [.ICGD] [*] (informal and formal versions; simplified types; degrees and evaluation)

26. General definition of influence [.ICGD] [*] (informal and formal versions; degrees and evaluation)

27. Non-existence of local double sente [.IGT] [*m] [Francisco Criado, Robert Jasiek, Bill Spight]

28. Evaluation of global double sente [.IG] [*]

29. Method of value evaluation of all josekis, except those with global (ko or semeai) fights [.ICG] [*]

30. New Semeai Formula [.IG] [*]

31. Local endgame with gote and sente options in an environment

- Timing during the early endgame at high temperature of playing in a local endgame with gote and sente options in an environment [.IGT] [*]

- Timing during the early endgame at low temperature of the preventer playing in a local endgame with gote and sente options in an environment [.IGT] [*]

32. Ko and dame endgames under area scoring [.IWGT] [pm]


The Most Important Inventions for Advance of Go Theory


1. General definition of ko, regardless of position and ruleset [.IGD] [p]

2. Timing during the early endgame of playing in a local gote in an environment [.IGT] [*]

3. Local endgame with one follow-up in an environment

- Timing during the late endgame at low temperature of the creator playing in a local endgame with one follow-up in an environment [.IGT] [*m] [Bill Spight, Robert Jasiek]

- Timing during the late endgame at low temperature of the preventer playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of the creator playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of the preventer playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Method of comparing two sequences combined with the method of comparing counts during the late endgame in a local endgame with one follow-up in an environment [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Equivalence of a) the method of comparing two sequences combined with the method of comparing counts, b) the method of comparing two sequences combined with the method of comparing net profits, and c) the method of applying a principle of playing in a local endgame with one follow-up in an environment during the late endgame [.IGT] [*]

- For a local sente during the early endgame at high temperature, play in the environment [.IGT] [*]

4. Local gote with two simple follow-ups in an environment

- Method of comparing two sequences combined with the method of comparing counts during the late endgame in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at low temperature of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at medium temperature with larger follow-up of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at medium temperature with smaller follow-up of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Equivalence of a) the method of comparing two sequences combined with the method of comparing counts, b) the method of comparing two sequences combined with the method of comparing net profits, and c) the method of applying a principle of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

5. Several local endgames

- Creator starting in the larger local endgame with one follow-up [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Preventer starting in the larger local endgame with one follow-up [.IGT] [*m] [Robert Jasiek, Bill Spight]

6. Local endgame with gote and sente options in an environment

- Timing during the early endgame at low temperature of the preventer playing in a local endgame with gote and sente options in an environment [.IGT] [*]

- Timing during the early endgame at high temperature of playing in a local endgame with gote and sente options in an environment [.IGT] [*]

7. General definition of thickness [.ICGD] [*] (informal and formal versions; degrees and evaluation)

8. General definition of influence [.ICGD] [*] (informal and formal versions; degrees and evaluation)

9. Capturable-1, local-2, capturable-2 [.IGD] [pm]

10. Alive in Japanese 2003 Rules equals alive in World Amateur Go Championship Rules model [.IT] [m] [proof Chris Dams, conjecture Jasiek]

11. Method of value evaluation of all josekis, except those with global (ko or semeai) fights [.ICG] [*]

12. New Semeai Formula [.IG] [*]

13. Re-definition of strategy, hypothetical-strategy, force, prevent [.IWGD] [pm] [there were the predecessors Bernd Gramlich and Robert Pauli and also researchers of mathematics or abstract games]

14. Equivalence of conditions (gote / sente count versus gote / follow-up move value versus sente / follow-up move value versus gote / sente move value) of local endgame with one simple follow-up [.IGT] [*m] [proofs Robert Jasiek, conjectures Bill Spight]

15. Non-existence of local double sente [.IGT] [*m] [Francisco Criado, Robert Jasiek, Bill Spight]

16. Scoring

- For any standard area komi, odd board parity and even seki parity, the winner is the same under area and territory scoring. [.IGT] [*m]

- For any standard area komi, odd board parity, even seki parity and the territory score 0.5, the winner under territory and area scoring is the player of the last play. [.IGT] [*m]

17. Earliest and latest moments of playing in a local endgame in sente or reverse sente depending on the enironment [.IGT] [*m] [Bill Spight, Robert Jasiek]

18. Generalised connection (n-connected) [.ICGD] [*]

19. General classification and definition of basic-ko types, regardless of position and ruleset [.IGD] [p]

20. Generalised territory (n-territory) [.ICGD] [*]

21. Influence stone difference [.ICGD] [*]


The Most Difficult Inventions


1. Japanese 2003 Rules [.IG] [p] [11 months of full-time work after 10 years of preliminary study]

2. General definition of ko, regardless of position and ruleset [.IGD] [p] [~3 months of full-time work after 13.5 years of preliminary study]

3. Timing during the early endgame of playing in a local gote with two follow-ups and unequal move value in an environment [.IGT] [*] [3 weeks of full-time work after 3.5 years of preliminary study]

4. Timing during the early endgame of playing in a local gote with one follow-up and unequal move value in an environment [.IGT] [*] [3 weeks of full-time work after 3.5 years of preliminary study]


Endgame


Theorems

Combinatorial Game Theory

- Monotonicity and continuity of enriches scores [GA] [*] [Francisco Criado, Robert Jasiek]

- Equal scores in case of large enough temperatures [GA] [*] [Francisco Criado, Robert Jasiek]

- Orthodox forecast theorem [GA] [*]

Fundamentals

- Playing simple gotes without follow-ups in decreasing order [GA] [*] [like taking numbers in decreasing order]

- Equality of move value and gains in a local gote [GA] [*]

- Count of a local gote, ordinary ko or ko threat [GA] [*]

- Impact of net profit on counts [GA] [*]

- Net profit of starting in an ideal environment [GA] [*m]

- Maximum net profit of starting in a simple environment [GA] [*]

- Error tolerance of two values (gains) taken alternately [.IGT] [*]

- Bounds of inserting a value in an ideal environment [.IGT] [*pm] [Robert Jasiek, Francisco Criado]

- Bound of adding a move value to an alternating sum [.IGT] [*pm] [Robert Jasiek, Daniel Hu]

- Adding two values to an alternating sum [.IGT] [*pm] [Daniel Hu, Robert Jasiek]

Evaluation of Local Endgame with One or Two Follow-ups

- Equivalence of conditions (gote / sente count versus gote / follow-up move value versus sente / follow-up move value versus gote / sente move value) of local endgame with one simple follow-up [.IGT] [*m] [proofs Robert Jasiek, conjectures Bill Spight]

- Equivalence of counts and white-counts of local endgame with one simple follow-up [.IGT] [*]

- Equivalence of move values for Black's and White's value perspectives of local endgame with one simple follow-up [.IGT] [*]

- Non-existence of local double sente [.IGT] [*m] [Francisco Criado, Robert Jasiek, Bill Spight]

- Equivalence of tentative move values and counts of local endgame with one or two unsettled sente followers [.IGT] [*]

Evaluation of Local Endgame with Gote and Sente Options

- Equivalence of conditions (gote / sente count versus gote / sente move value) of local endgame with a player's simple gote and sente options [.IGT] [*m] [proofs Robert Jasiek, conjectures Bill Spight]

- Equivalence of counts and white-counts of local endgame with a player's simple gote and sente options [.IGT] [*]

- Equivalence of move values for Black's and White's value perspectives of local endgame with a player's simple gote and sente options [.IGT] [*]

Evaluation of Local Endgame with Long Sequences

- Method of comparing the opponent's branches, 3-move traversal, evaluation due to reversal [.IGT] [*m] [Bill Spight, Robert Jasiek]

- Method of comparing the opponent's branches, 4-move sente sequence, determination of counts and move values [.IGT] [*]

- Method of comparing the opponent's branches, 3-move reverse sente sequence, determination of counts and move values [.IGT] [*]

- Methods of comparing counts or move values, and their relations [.IGT] [*]

- Study of the method of making a hypothesis, T-orthodox implies T is at most the gains [.IGT] [*] [Francisco Criado, Robert Jasiek]

- Study of the method of making a hypothesis, T-orthodox implies the move value is at most the gains [.IGT] [*] [Robert Jasiek, Francisco Criado]

- Study of the method of making a hypothesis, smaller move value after traversal [.IGT] [*]

Early Endgame of Local Gote in an Environment

- Timing during the early endgame of playing in a local gote with one follow-up and unequal move value in an environment [.IGT] [*]

- Timing during the early endgame of playing in a local gote with one follow-up and equal move value in an environment [.IGT] [*]

- Timing during the early endgame of playing in a local gote with two follow-ups and equal move value in an environment [.IGT] [*]

- Timing during the early endgame of playing in a local gote with two follow-ups and unequal move value in an environment [.IGT] [*]

- Timing during the early endgame of playing in a local gote in an environment [.IGT] [*]

Late Endgame of Local Endgame with One Follow-up in an Environment

- Timing during the late endgame at low temperature of the creator playing in a local endgame with one follow-up in an environment [.IGT] [*m] [Bill Spight, Robert Jasiek]

- Timing during the late endgame at low temperature of the preventer playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of the creator playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of the preventer playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Difference of the net profits of Black versus White starting alternating play on an alternating sum [GA] [*]

- Method of comparing two sequences combined with the method of comparing counts during the late endgame in a local endgame with one follow-up in an environment [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Method of comparing two sequences combined with the method of comparing net profits during the late endgame in a local endgame with one follow-up in an environment [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Equivalence of a) the method of comparing two sequences combined with the method of comparing counts, b) the method of comparing two sequences combined with the method of comparing net profits, and c) the method of applying a principle of playing in a local endgame with one follow-up in an environment during the late endgame [.IGT] [*]

Early Endgame of Local Endgame with One Follow-up in an Environment

- Timing during the early endgame at low temperature of the creator playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Timing during the early endgame at low temperature of the preventer playing in a local endgame with one follow-up in an environment [.IGT] [*]

- Timing during the early endgame at high temperature of playing in a local endgame with one follow-up in an environment [.IGT] [*]

- For a local sente during the early endgame at high temperature, play in the environment [.IGT] [*]

Late Endgame of Local Gote with Two Follow-ups in an Environment

- Method of comparing two sequences combined with the method of comparing counts during the late endgame in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Method of comparing two sequences combined with the method of comparing net profits during the late endgame in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at low temperature of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at medium temperature with larger follow-up of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at medium temperature with smaller follow-up of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Equivalence of a) the method of comparing two sequences combined with the method of comparing counts, b) the method of comparing two sequences combined with the method of comparing net profits, and c) the method of applying a principle of playing in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Ignored tails during the late endgame in a local gote with two simple follow-ups in an environment [.IGT] [*]

- Increasing scores of the starting player for a local gote with two simple follow-ups in an environment [.IGT] [*pm] [Daniel Hu, Robert Jasiek]

- Decreasing scores of the second-moving player for a local gote with two simple follow-ups in an environment [.IGT] [*m] [Robert Jasiek, Daniel Hu]

Late Endgame of Local Endgame with Gote and Sente Options in an Environment

- Method of comparing three sequences combined with the method of comparing counts during the late endgame of the creator playing in a local endgame with gote and sente options in an environment [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Method of comparing three sequences combined with the method of comparing counts during the late endgame of the preventer playing in a local endgame with gote and sente options in an environment [.IGT] [*]

- Timing during the late endgame at low temperature of the creator playing in a local endgame with gote and sente options in an environment [.IGT] [*m] [Bill Spight, Robert Jasiek]

- Timing during the late endgame at low temperature of the preventer playing in a local endgame with gote and sente options in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of the creator playing in a local endgame with gote and sente options in an environment [.IGT] [*]

- Timing during the late endgame at high temperature of the preventer playing in a local endgame with gote and sente options in an environment [.IGT] [*]

Early Endgame of Local Endgame with Gote and Sente Options in an Environment

- [Bill Spight solves the timing during the early endgame at low temperature of the creator playing in a local endgame with gote and sente options in an environment] [.IGT] [*m]

- Timing during the early endgame at low temperature of the preventer playing in a local endgame with gote and sente options in an environment [.IGT] [*]

- Timing during the early endgame at high temperature of playing in a local endgame with gote and sente options in an environment [.IGT] [*]

Several Local Endgames

- Creator starting in the larger local endgame with one follow-up [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Preventer starting in the larger local endgame with one follow-up [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Additional details for playing in the larger local endgame with one follow-up [.IGT] [*m] [Bill Spight, Robert Jasiek]

Scoring

- Relation between komi, area scores and winners [.IGT] [*m]

- Relation between area and territory scores [.IGT] [*m]

- For any standard area komi, odd board parity and even seki parity, the winner is the same under area and territory scoring. [.IGT] [*m]

- For any standard area komi, odd board parity, even seki parity and the territory score 0.5, the winner under territory and area scoring is the player of the last play. [.IGT] [*m]

- Approach plays affecting the score [.IGT] [*]

Other Theory

Evaluation

- Verify types of local endgames to determine their correct values. [.IGT] [*m] [Robert Jasiek / Bill Spight]

- Types of sequences [.IG] [*]

- Simplifications of local evaluation [.I] [*]

- Evaluation of global double sente [.IG] [*]

- Ordinary evaluation of long sequences by the method of making a hypothesis [.IG] [*]

- Fast evaluation of long sequences by the method of comparing the opponent's branches [.IG] [*] [Bill Spight, Robert Jasiek et al]

- Fast evaluation of long sequences by the method of comparing counts [.IG] [*]

- Fast evaluation of long sequences by the method of comparing move values [.IG] [*]

- Net profit 0 of a sente sequence [W] [*]

- Describing traditional endgame theory as if derived from modern endgame theory [.IWG] [*]

- Relation between area count and passes [WG] [*]

- Relation between area count and territory count [.IG] [*]

Strategy

- Do not always play in decreasing order of move values but use better theory. [.IGT] [*m] [Robert Jasiek, Bill Spight]

- Interrupt local sequences in time. [.IGT] [*m] [Robert Jasiek / Bill Spight]

- Strategy depends on the parity of the number of multiples. [W] [*m]

- Strategy depends on the local endgame / ensemble, the environment, its temperature and sometimes its second-largest value. [.IGT] [*m] [Robert Jasiek / Bill Spight]

- Use the gote move value for the timing during the early endgame of playing in a local gote. [.IGT] [*]

- [Bill Spight finds use of the sente move value for the timing during the late endgame of playing in a local gote.] [.IGT] [*m]

- The creator chooses the gote option during the early endgame at high temperature if playing locally in a local endgame with gote and sente options in an environment. [.IGT] [*]

- Exact theory for local endgames with simple follow-ups serves as an approximation for local endgames with iterative follow-ups. [.IGT] [*]

- Several local endgames each with one follow-up can be partially simplified by the theory for larger such local endgames. [.IGT] [*m]

- Application to strategy and positional judgement during the middle game [.IGT] [*m] [Bill Spight, Robert Jasiek]

- Earliest and latest moments of playing in a local endgame in sente or reverse sente depending on the enironment [.IGT] [*m] [Bill Spight, Robert Jasiek]

- Use the principle of extreme difference values to simplify reading for several iterative local endgames. [.IG] [*]

- Translation of relevant combinatorial game theory (including low-level theory and corridors) to go theory. [.IGT] [*m] [Robert Jasiek, Bill Spight et al]

- Conditions for preserving ko threats [.IG] [*]

- Evaluation and choice in a ko exchange [.IWG] [*]

Definitions

Terms

- White-count [.ID] [*]

- Ideal environment [.ID] [*m]

- Tail [.ID] [*]

- Alternating sum [.ID] [*m]

- Alternating sum of tails [.ID] [*]

- Alternating sum for medium temperature with larger follow-up [.ID] [*]

- Alternating sum for medium temperature with smaller follow-up [.ID] [*]

- Alternating sum for high temperature [.ID] [*]

- [Daniel Hu defines scores of playing locally after 2I or 2I+1 moves] [.ID] [p]

- Traversal, traversal sequence [.IWD] [*]

- Creator [.ID] [*]

- Preventer [.ID] [*]

- Gote-sente-difference [.ID] [*]

- Larger local endgame with one follow-up [.ID] [*m]

- Standard area komi [.ID] [*m]

- Local stone difference [.ID] [*]

- Clarified use of the term net profit [W] [*m]

Value Conditions of Terms

- Privilege [WD] [*]

- Gain [W] [*m]

- Simplifying redefinition of sente count [D] [*]

- Simplifying redefinition of move value 0 of settled position [D] [*]

Values of Local Endgames

- Tentative gote or sente counts and move values of local endgame with one simple follow-up [.ID] [*]

- Tentative gote or sente counts and move values of local endgame with two simple follow-ups [.ID] [*]

- Tentative gote or sente counts and move values of local endgame with a player's simple gote and sente options [.ID] [*]

- Overview of gote or sente counts and move values of local gote, local sente or ambiguous local endgame with one simple follow-up [.ID] [*]

- Overview of gote or sente counts and move values of local gote, local sente or ambiguous local endgame with a player's simple gote and sente options [.ID] [*]

Types of Local Endgames

- [Bill Spight defines the types (local gote, local sente, ambiguous of a local endgame with one simple follow-up.] [.ID] [m]

- Types (local gote, Black's / White's local sente, local sente, Black's / White's / doubly ambiguous, ambiguous) of local endgame with two simple follow-ups [.ID] [*]

- Overview on types of local endgames [.ID] [*]

- Types (local gote, local sente, ambiguous) of local endgame with a player's simple gote and sente options [.ID] [*]

- Overview of conditions of local gote, local sente or ambiguous local endgame with one simple follow-up from Black's or White's value perspective [.ID] [*]

- Types (local gote, local sente, ambiguous) of local endgame with a player's simple gote and sente options [.ID] [*]

- Overview of conditions of local gote, local sente or ambiguous local endgame with a player's simple gote and sente options [.ID] [*]

Test Sequences

- Test sequences for a local endgame with one follow-up in an environment [.ID] [*m] [Bill Spight, Robert Jasiek]

- Test sequences for the creator starting in a local endgame with gote and sente options in an environment [.ID] [*m] [Bill Spight, Robert Jasiek]

- Test sequences for the preventer starting in a local endgame with gote and sente options in an environment [.ID] [*]

Examples

- Counter-example for always seeking tedomari [.I] [*]

- Counter-examples for always playing a simple gote with one follow-up in an environment of simple gotes without follow-ups in decreasing order of move values [.I] [*]

- Rare example of local endgame with a player's simple gote and sente options, late endgame, low temperature, the opponent's correct start in the environment [.I] [*]

- Counter-example for comparing move values instead of gains to decide
traversal [.I] [*]

- [Francisco Criado shows two rare counter-examples for which the method of making a hypothesis is wrong so thermography is required] [.I] [*]


Tactical Reading and Move Decision


- Method of regular reading [WG] [*]

- Method of test reading [.IG] [*]

- Method of local Move Selection [WG] [*]

- Move choice: 2 methods [WG] [*]

- Reduction of a big moyo: 2 methods [WG] [*]


Strategy


General

- Re-definition of strategy, hypothetical-strategy, force, prevent [.IWGD] [pm] [there were the predecessors Bernd Gramlich and Robert Pauli and also researchers of mathematics or abstract games]

- Answer-strategy, answer-force [.IGD] [p]

- Virtual-force [.IGD] [p] [there is a related term by other researchers]

- Strategic planning: 4 methods [WG] [*]

- Offering a strategic choice [WG] [*]

- Use and transformation of influence or thickness [WG] [*]

- General fighting strategy [WG] [*]

Strategic Concepts

- Generalised connection (n-connected) [.ICGD] [*]

- Generalised life (n-alive) [GD] [*]. [A related prior concept is 'possible omission number'.]

- Generalised territory (n-territory) [.ICGD] [*], 1 derived definition (half territory) [.ICG] [*]

- General definition of influence [.ICGD] [*] (informal and formal versions; degrees and evaluation)

- General definition of thickness [.ICGD] [*] (informal and formal versions; degrees and evaluation)

- Influence stone difference [.ICGD] [*]

- Definition of stability [.ICGD] [*]

- Territory efficiency [.IGD] [*] [prior work by Yang Yilun and possibly others]

- Investment [.ICGD] [*]

- Playing elsewhere: 1 method [.IG] [*]

- Mobility [.IWCG] [*]

- Types of fights [WG] [*]

- Fighting region [.ICGD] [*]

- Value of a fighting region [.ICGD] [*]

- Neutral stone difference, neutral-or-dead stone difference [.ICGD] [*]

- Potential [WG] [*]

- Development [WG] [*]


Capturing Races


- New Semeai Formula [.IG] [*]

- Usual move order [WG] [*]

- 6 classes of basic capturing races [.IG] [*]

- Complete study of 93 cases of basic capturing races [.IWG] [*]

- Re-definition of 5 types of basic capturing races [.IWGD] [*] [there was the predecessor Richard Hunter]

- Fighting liberties [.IGD] [*]

- Definition of semeai-eye, stable / unstable eye, strong / weak eye [.IGD] [*]

- Characterisation of strong semeai-eyes [.IWG] [*]

- Correction of 6 kinds of mistakes in literature [.I] [*]


Joseki


- Functional classification of josekis [.IG] [*]

- Value classification of josekis [.IG] [*]

- Method of value evaluation of all josekis, except those with global (ko or semeai) fights [.ICG] [*]

- Application to ca. 400 josekis [.IG] [*]

- Classification of every move type and meaning occurring in joseki [.IGD] [*]

- Classification of strategic lines [.IG] [*]

- Classification of group meanings [.IG] [*]

- Joseki structure by their strategic choices [WG] [*]


Positional Judgement


- Definition of current territory [.ICGD] [*] [there was the predecessor Cho Chikun]

- Classification of groups [WG] [*]

- Classification of regions [.IWG] [*]

- Positional judgement: various methods, procedures, aspects [.IG] [*] or [WG] [*]

- Unsettled Group Average [.IWGT] [*] [there were predecessors among CGT endgame researchers]

- Definition of quiet group, quiet position [.IWGD] [*] [there were predecessors among computer-go researchers]


Ko and Other Restrictions


- General definition of ko, regardless of position and ruleset [.IGD] [p]

- General classification and definition of basic-ko types, regardless of position and ruleset [.IGD] [p]

- Ko and dame endgames under area scoring [.IWGT] [pm]

- Ko and dame endgames under Ikeda Territory I Rules [.IGT] [m]

- Cycle Law [.IT] [m]

- Default Restriction Rules [.IG] [p]

- Local-ko-intersection [.IGD] [p]

- Global-ko-intersection [.IGD] [p]

- Dead Ko [.IWGD] [pm]

- Closed Death [.IGD] [pm]

- Semi-stable Ko and its variants [.IWGD] [pm]

- Definition of external / internal ko [.IGD] [p]

- Preliminary definitions of pass-fights [.IGD] [m]

- No frequent pass-fights under Ikeda Territory I Rules [.IT] [m]

- Preliminary definitions of pass-fights [.IGD] [m]


Life + Death and Scoring


- Local-1 [WGD] [pm]

- Capturable-1, local-2, capturable-2 [.IGD] [pm]

- Definition of [the scoring term] region [.IGD] [pm]

- Definition of [the scoring term] territory [.IGD] [pm]

- Definition of [the scoring term] group [.IGD] [m]

- Definition of independently-alive [.IGD] [pm]

- Definition of in-seki, seki [.IGD] [pm]

- Definition of dame [.IGD] [pm]

- Definition of eye-point, eye, eye-space [.IGD] [pm] [there were predecessors]

- Re-definition of two-eye-formation [.IGD] [pm]

- Alive in Japanese 2003 Rules equals alive in World Amateur Go Championship Rules model [.IGT] [*m] [proof Chris Dams, conjecture Robert Jasiek]


Rules

Particular Rules

- Fixed-ko-rule [.IG] [m]

- Natural Situational Superko [.IWG] [pm]

Rulesets

- Simple Rules [WG] [p]

- Multi-player Go Rules [WG] [p]

- Japanese 2003 Rules [.IG] [p]

- Simplified Japanese Rules [.IG] [p]

- Simplified World Mind Sports Games Rules [.IG] [p]

Commentaries

- Commentaries on Ing Ko Rules [.IG] [p]

- Commentaries on Japanese 1989 Rules [.IG] [p]

- Commentaries on World Amateur Go Championship Rules [.IG] [p]

- Commentaries on Verbal Japanese Rules [.IG] [p]

Theory

- Prisoner counting for stone scoring [.IT] [m]

- Solution for the World Mind Sports Games 2008 Rules' Supplementary Ko Rule [.IG] [p]


Shapes


- Pendulum Ko [.IG] [m]

- A new type of double ko [.IG] [m]

- Infamous Ko [WG] [m]

- 1 joseki [.IG] [*]


Other Terms


- Direct connection, indirect connection [.IWG] [*]

- Mobility / usefulness count / difference [.ICG] [*]

- Lake, lake size [WG] [*]

- Eye value [WG] [*]

- Approach block [WG] [*]

- External / internal liberty shortage [WG] [*]

- Action [.IG] [*]

- Gote-like, sente-like [.IG] [*]

- Reduction-or-invasion [.IG] [*]

- Prisoner-difference [WG] [pm]

- Locale [WG] [*m]

- Stone difference [.IG] [*]

- Definition of proto-group [.IGD] [*]