Robert: if go knowledge cannot be used to criticize your papers, then why do you call it Go Theory Research?
I will be more specific. You refuse to acknowledge errors in some of the KO shapes in your paper, arguing that they match your initial definition even though they cannot be formed following logical play. If we cannot bring anything from outside your definitions into the discussion, and if your definitions do not match logical play, why should this be called go research?

Btw, that "theory goes through stages" thing is completely wrong. Factually wrong. A theory is created to explain an empirical observation, it is connected to reality. If it does not match reality, the theory is wrong. Theories do not exist in some sort of ether.

Robert, I'm a little baffled what exactly you think you're doing. In one post you think you're providing a model of reality, yet in another post you think you're doing math and hoping that your work will be extended or applied.

If you're trying to do math then by your own admission there may still be counter-examples lurking around. Real math involves proofs, excluding the possibility of any counter-example rather than just hoping you're right. Right now it looks like you've got what amount to a series of unproven (and maybe unprovable?) conjectures and those aren't strong enough to be extended by other work.

On the other hand if you're modeling reality and going the applied then I have to ask where you think this is going to lead. Thomas Wolf has improved a computer's ability to do tsume-go, along the way making progress on deciding how to prune a widely branching decision tree. The Monte Carlo go people have created a stronger go player, and the CGT researchers have put endgame positions on a firm mathematical footing (with actual proofs). How does a still possibly flawed ko definition help advance...well anything?

Right now this looks very much like someone pretending to be doing archaeology by digging up his backyard and posting about it on his website (or possibly something like this: http://www.suslik.org/Humour/General/general4.html).

Perhaps a succint summary will help clear these confusions from your mind and ours. A common question is to ask for a three sentence "elevator" summary of your work. What is your work and why is it relevant? Three sentences only, and you can't pretend that you have anything stronger than conjectures.

Robert - if I may be so bold here and offer a public advice... it might be a good time for you to bow out of the thread with some graceful 'lets agree to disagree' or 'lets take it in private' or something. People are ganging up on you (as is often the case, unfortunately), tempers are running high, and I don't see any big chance of reaching any agreement with anybody, regardless of who is right or wrong - since nobody seems to listen to nobody, and not its juts a brawl, I think. If you think they are wrong, so be it, just leave it at that.

Just saying...

_________________
- Bantari
______________________________________________
WARNING: This post might contain Opinions!!

Oh, don't worry about ganging. I'm done commenting any more here (except for this comment, of course.)

_________________
Geek of all trades, master of none: the motto for my blog mostlymaths.net

Dear Robert,

In my opinion, your claim to provide to better insight into "ko strategy" is based on a kind of circular reasoning.

One tiny example from "Life & Death" to make this apparent:


# # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # #


„Common understanding“: Four empty points in row are alive.

Click Here To Show Diagram Code

[go]$$B Alive, a and b are Miai.
$$ +---------------
$$ | . a b . O X .
$$ | O O O O O X .
$$ | X X X X X X .
$$ | . . . . . . .[/go]

# # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # #

An application of my understanding of your “Ko-methodology”.


# # # # # # # # # # # # # # # # # # # # # #

Click Here To Show Diagram Code

[go]$$B „Locally alive“
$$ +---------------
$$ | . . . . O X .
$$ | O O O O O X .
$$ | X X X X X X .
$$ | . . X . . X .
$$ | X X X X X X .
$$ + . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B „Locally Unsettled“
$$ +---------------
$$ | . 1 . . O X .
$$ | O O O O O X .
$$ | X X X X X X .
$$ | . . X . . X .
$$ | X X X X X X .
$$ + . . . . . . .[/go]

because of A)

Click Here To Show Diagram Code

[go]$$B „Dead“
$$ +---------------
$$ | . X 1 . O X .
$$ | O O O O O X .
$$ | X X X X X X .
$$ | . . X . . X .
$$ | X X X X X X .
$$ + . . . . . . .[/go]

and B)

Click Here To Show Diagram Code

[go]$$W „Alive“
$$ +---------------
$$ | . X 1 . O X .
$$ | O O O O O X .
$$ | X X X X X X .
$$ | . . X . . X .
$$ | X X X X X X .
$$ + . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$B „Alive“
$$ +---------------
$$ | . X 2 . O X .
$$ | O O O O O X .
$$ | X X X X X X .
$$ | . . X . . X .
$$ | X X X X X X .
$$ + . . . . . . .[/go]

White pre-empted a local loss.

# # # # # # # # # # # # # # # # # # # # # #

Click Here To Show Diagram Code

[go]$$B „Globally alive“
$$ +-------------------------------+
$$ | . . . . O X . O . O X . O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | O O O O O X X X X O O O O . O |
$$ | X X X X X X X X X O O . O . O |
$$ | . X X . X X O O O O . O O . O |
$$ | X X X X X X O O O O O O O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „Globally unsettled“
$$ +-------------------------------+
$$ | . 1 . . O X . O . O X . O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | O O O O O X X X X O O O O . O |
$$ | X X X X X X X X X O O . O . O |
$$ | . X X . X X O O O O . O O . O |
$$ | X X X X X X O O O O O O O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „Alive“
$$ +-------------------------------+
$$ | . X 2 . O X . O . O X . O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | O O O O O X X X X O O O O . O |
$$ | X X X X X X X X X O O . O . O |
$$ | . X X . X X O O O O . O O . O |
$$ | X X X X X X O O O O O O O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „White wins the game“
$$ +-------------------------------+
$$ | . X O . O X 5 O 3 O X 4 O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | O O O O O X X X X O O O O . O |
$$ | X X X X X X X X X O O . O . O |
$$ | . X X . X X O O O O . O O . O |
$$ | X X X X X X O O O O O O O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „White + 4“
$$ +---------------------------------+
$$ | . X O . O X X . X . X O O . . O |
$$ | O O O O O X . . . X X X O . . O |
$$ | O O O O O X X X X O O O O . . O |
$$ | X X X X X X X X X O O . O . . O |
$$ | . X X . X X O O O O . O O . . O |
$$ | X X X X X X O O O O O O O O O O |
$$ +---------------------------------+[/go]

White pre-empted a global loss.

# # # # # # # # # # # # # # # # # # # # # #

Click Here To Show Diagram Code

[go]$$B „Globally dead“
$$ +-------------------------------+
$$ | . . . . O X . O . O X . O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | X X X X X X O O O X X X O O O |
$$ | X X X X X X O O O X X X O . O |
$$ | . X X . X X O O O X X X O . O |
$$ | X X X X X X O O O X X X O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „Globally unsettled“
$$ +-------------------------------+
$$ | . 1 . . O X . O . O X . O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | X X X X X X O O O X X X O O O |
$$ | X X X X X X O O O X X X O . O |
$$ | . X X . X X O O O X X X O . O |
$$ | X X X X X X O O O X X X O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „Globally unsettled“
$$ +-------------------------------+
$$ | . X . . O X . O . O X 2 O . O |
$$ | O O O O O X O O O X X X O . O |
$$ | X X X X X X O O O X X X O O O |
$$ | X X X X X X O O O X X X O . O |
$$ | . X X . X X O O O X X X O . O |
$$ | X X X X X X O O O X X X O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „Dead“
$$ +-------------------------------+
$$ | . X 3 . O X . O . O . O O . O |
$$ | O O O O O X O O O . . . O . O |
$$ | X X X X X X O O O . . . O O O |
$$ | X X X X X X O O O . . . O . O |
$$ | . X X . X X O O O . . . O . O |
$$ | X X X X X X O O O . . . O O O |
$$ +-------------------------------+[/go]

Click Here To Show Diagram Code

[go]$$B „White wins the game“
$$ +-------------------------------+
$$ | . X X . O X . O . O . O O . O |
$$ | O O O O O X O O O . . . O . O |
$$ | X X X X X X O O O . . . O O O |
$$ | X X X X X X O O O . . . O . O |
$$ | . X X . X X O O O . . . O . O |
$$ | X X X X X X O O O . . . O O O |
$$ +-------------------------------+[/go]

White pre-empted a global loss.


# # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # #

The choice of moves depends on general principles (if you like "strategy") of the game.

"Locally ..." / "Globally ..." does not provide any benefit to this. Nor does the status change within move sequences.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

uPWarrior, my papers can be commented on (in particular: criticised) in at least two different major manners by referring to: a) the concepts in the papers themselves or b) comparing (a) with knowledge outside (a).

A (ko shape) example is not an error because of not being constructed by nice alternation. The paper allows any position to be studied, whether constructed nicely or not. (Do you complain that 99% of all go problem positions are not constructed nicely? No? Why then do you complain about my examples? So that you want to allow only 1% of all positions so that my paper is worth 99% less because of being allowed to be applied to only 1% of all legal positions?) In summary, it is meaningless to criticise my paper for showing also artificial examples. Instead, it would be meaningful to create another research topic to distinguish "nice" from "awful" example / problem / game positions.

"Logical play" can include a player's passes, while the opponent plays, then the opponent's passes, while the player plays; i.e., each position can be constructed by logical play, and I have proven this many years ago to show that each position can recur in a cycle, if the players "cooperate". What you mean is not "logical play", but is "nice alternating play" for some meaning of "nice". Maybe you mean "strategically perfect play". But do you? After all, this would end in arguing that most actually played games might not be studied, because their positions are not created by perfect play. Being able to study also the bad positions is a great advantage! It allows us to comment on player mistakes at all. And you want to exclude that from go research?!

pwaldron, the maths I am doing when modelling the real world does not need to be without counter-example to be maths. It would be nice if a counter-example did not exist, and even nicer if this could be proven. So far, I have presented positive evidence for my model, while the negative evidence is still very much incomplete. It is the same as with maths models in physics: the currently good models are those for which all positive examples (tests / observations) work, while the negative examples are very incomplete.

We know very many shapes that are non-cyclic (from played games or book diagrams), and the cyclic shapes in my paper.

What is missing is a complete classification of all shapes of all positions and then the theorem relating my ko definition to that classification. With my paper, there is at least this research aim. Before my paper, there was mainly dust.

Why do you think that other work cannot extend mine? It is straightforward: classify all shapes.

You ask how a ko definition is going to contribute to solve go. View it in its context: everything can be defined (see my many other defined go terms), principles / propositions can be applied to the defined things (I have done so with proofs for quite a few propositions; check rec.games.go archives), this approach can be extended to reading and decision making. It is not necessary to see definition-based go theory independently; one can also research in relations between the fields CGT, MC, etc. and definition-based theory.

"What is your work and why is it relevant?" I have answered this before, and it is more than conjectures.

Cassandra, what have your local / global examples to do with my ko paper?

It shows the result of your paper's methodology, applied on another issue. Should be appealing to you.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

You apply only a distinction of local versus global and you do so independently of the paper's definitions. In particular, you use a) "global" and "local" in an informal sense, while the paper defines "global-ko-intersection" and "local-ko-intersection" with a formal meaning, and b) "ko strategy" in an informal sense, while the paper defines "strategy" with a formal meaning. Therefore your statement "circular reasoning" is not justified at all.

Dear Robert,

I had neither expected that you would like my application, nor that you would take pleasure in it, nor that you would make the slightest attempt to benefit from it.

Perhaps you can befriend yourself with the thought that as "mistaken", "misunderstood", "misinterpreted", "ugly", "unwordly", "absurd", and "incomplete", as you will value my application example, is the "common world's" evaluation of your Ko-theory paper.

As well as my application will not have caused any increased insight into "Life & Death theory" with you, your Ko-theory paper will not cause any increased insight into "Ko theory" with the "common world". This is because it is "common knowledge" that you would 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. This is true, even if move A comes from "Life & Death", while move B comes from "Endgame".

It makes no sense at all to give this move (or the board-point in your theory paper) the property "global" that it will not achive in the case that you are ahead (or even behind) on the rest of the board by 15 points. As well as you cut move sequences into slices, in a desperate attempt to evaluate every single board-position independently, you cut the above mentioned "common knowledge" (or "common principle" / "common strategy") into slices to base various independent "xyz theory (insight)" on this.


# # # # # # # # # # # # # # # # # # # #

However, all attempts with using analogies to help you understanding the "common world's" problems with your theory paper(s) were in vain.

So I do not expect at all that you will benefit from looking at yourself in the mirror.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Cassandra, already in my paper I explain that it determines ko, but does not determine perfect play. You over-interpret my paper if you think that it determined perfect play.

Sub-sub-variation D-E-F ?

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

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.)

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?

_________________
Geek of all trades, master of none: the motto for my blog mostlymaths.net

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).

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.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

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.

_________________
Geek of all trades, master of none: the motto for my blog mostlymaths.net

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".

Dear Robert,

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



"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.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

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.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

'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.