The Curse of "Solving" Go Problems

[Cassandra]

... a combination of aims, sequences, decision-making and outcomes.

These are the core elements of a variation tree, and a variation tree is created (at least implicitely) when working on the solution to a problem. The variation tree created represents your current level of understanding. Taking this level as given, you can have found a solution to the problem (but may be for the time being only).

However, your variation tree still can be incomplete, so lacking the complete solution, for the following reasons:

-- You have not explored all essential variations.
-- You have not reached the maximum score possible (in the case the aim can be measured in points).
-- You have not considered the best resistance (especially in the case the aim can be measured in points).

But detecting any of these reasons usually demands a higher level of understanding. As an exception to the rule, a one-hit wonder might do the job, too.

+ + + + + + + + + +

Let's take Igo Hatsuyôron 120 as an example (aim: Black to play and win the game).

After 1.000 hours of work, in 1982, Fujisawa Hideyuji 9p considered the problem to be solved. Otherwise, he would not have published a solution.

In 1988, Cheng Xiaoliu 6p did not really challange this solution, but found a slight improvement for Black.

In 2005, Joachim Meinhardt discovered the correct moment for a yet known White move, turning it into the strongest White resistance, so challanging the previous solutions. But he was unable to find the necessary improvements for Black.

In 2007, Yamada Shinji 6p found another improvement for White, making the situation even worse for Black.

Also in 2007, I found the (probably) game-winning moves for Black (second Throw-in in the Hanezeki, Guzumi in the top right), but was very unsure about these, just because the final score reached was only "Black wins by one point". And you surely know about the (low) level of amateur play, especially in the endgame.

In 2009, Harry Fearnley found another improvement for Black, which removed our doubts about the outcome.
But it lasted until 2012 before we got get this line of play confirmed by a professional player.

In 2010, Cheng Xiaoliu published an improvement on his 1988 sequence, but this ended in Jigo only. And so cannot be considered to be "the" solution to the problem.

Thereafter, Joachim found an altermate move for Black, not considered by us until then, which leads to a very complex Ko-fight. We think that this move is no valid option for Black, because White wins here, but we cannot be entirely sure about this, because there is no prefessional statement yet, concerning the validity of this sub-variation.

In addition, there is the question remaining whether our result of "Black wins by three points" really is the "correct" outcome. Probably "Black wins by one point" would be the "ideal" result for the lifetime masterpiece of Inoue Dosetsu Inseki ? Where is the very well hidden White move, gaining two points ?

[RobertJasiek]

The variation tree created represents your current level of understanding.

1) Sequences can, but need not be, represented as a tree.

2) Understanding can include more than a tree, or the tree of considered sequences can be enhanced by additional information assigned to its nodes or edges. In particular, the tree of considered sequences does not include by itself the decision-making, but this must be added, e.g., as interpretation assigned to the nodes.

[Cassandra]

In particular, the tree of considered sequences does not include by itself the decision-making, but this must be added, e.g., as interpretation assigned to the nodes.

Why adding "choose the path that enforces the best fulfillment of the aim for you" to every node ?

[Kirby]

I am saying: There is very much different. This - what is very much different - is NOT (just) to simply practice more problems. Instead it (also) is '(the) theory of tactical reading'.

Okay. So to be clear, you are suggesting that doing problems is not enough, but I need to obtain this theory?

If so, do you have a recommendation for obtaining this theory?

[RobertJasiek]

Cassandra, nobody forces one to create inefficient data structures. However, each branching position's node requires some decisions. If, mentally, you want to use an efficient data structure, "store" a reference to / flag for the types of decisions made at the nodes, while you store their explanations elsewhere. "best fulfillment" is not the only kind of information needing assignment to the nodes. E.g., other information can refer to kinds of applied simplifications or knowledge gained from earlier studied nodes / sequences. Trees (or their equivalents) can be dynamic when, e.g., pruning already studied subtrees / branch variations.

Kirby, see http://www.lifein19x19.com/forum/viewto ... 92#p190292

[Cassandra]

Robert, I suppose that we have a different understanding about the properties of nodes, and branches. In my understanding, the aspects that you described are properties of the branches.

E.g. "This move will result in a change in the order of moves of ..." is no element needed to decide which branch to choose.

The same is true for e.g. "This move exploits a cutting point created earlier.", or "This move occupies a Nakade's vital point."

[RobertJasiek]

Although in principle a tree's components can represent anything, the standard is that nodes represent positions (or situations) and the edges represent moves. In informatics, the common assignment of properties is to a node or an edge - usually not to a set of edges. Your use of "branch" is ambiguous; it sounds like a set of two (or more) edges leaving from the same node. However, maybe you mean "one particular edge", in which case I would speak of a particular move / sequence / subtree starting from a next move. If you really must, speak of a "branch variation" as a variation leaving the particular branching position.

Indeed "This move will result in a change in the order of moves of ..." is no element[?] needed to decide which branch [variation] to choose. Tactical reading can do without "This move will result in a change in the order of moves of ..."...:) Tactical reading does not make predictions of what will happen but analyses moves and sequences to determine what DOES happen and then, after related reading, state that a particular move DOES (in this case apparently you mean) revert an already known position. We can then assign to this move the result of the reverted position. (But we can probably forget the detail of a different move order.)

Whether "This move exploits a cutting point created earlier." is needed to decide which branch variation to choose can depend on the aim(s) of the problem's starting position. Maybe the aim is "to exploit a particular cutting point" and reading shall determine whether the particular cutting point can, or cannot, be exploited? (Supposing we know what "exploit" means.)

"This move occupies a Nakade's vital point." more likely is an ill-formulated feature of a terminal position. Suppose the problem's aim (as a very special form of life and death problem) is to decide if the player can establish his stone on some nakade's vital point. At a branching position, we can assign to some next move whether it leads to success or failure WRT his task.

[Kirby]

Kirby, see http://www.lifein19x19.com/forum/viewto ... 92#p190292

I see. Thank you.

So I suppose the action items here for me are:
* Do more go problems.
* Read your theory book.

[RobertJasiek]

The sheer number of problems exercised might not do it; I suggest you also exercise those that you do more carefully and with achieving a better understanding (while applying theory).

[Kirby]

The sheer number of problems exercised might not do it; I suggest you also exercise those that you do more carefully and with achieving a better understanding (while applying theory).

Well, I must admit, I don't know much theory. The only thing I can think of at the moment is what Inseong refers to as "1-2-3 reading". Basically, when doing a life and death problem, try a simple first move from the outside to reduce eyespace. If the opponent has a refutation at position X, then try reading the problem by starting at move X.

It isn't something that works 100% of the time, but I do think it's helpful in guiding my search for a solution.

[Cassandra]

Although in principle a tree's components can represent anything, the standard is that nodes represent positions (or situations) and the edges represent moves. In informatics, the common assignment of properties is to a node or an edge - usually not to a set of edges. Your use of "branch" is ambiguous; it sounds like a set of two (or more) edges leaving from the same node. However, maybe you mean "one particular edge", in which case I would speak of a particular move / sequence / subtree starting from a next move. If you really must, speak of a "branch variation" as a variation leaving the particular branching position.

Indeed "This move will result in a change in the order of moves of ..." is no element[?] needed to decide which branch [variation] to choose. Tactical reading can do without "This move will result in a change in the order of moves of ..."... Tactical reading does not make predictions of what will happen but analyses moves and sequences to determine what DOES happen and then, after related reading, state that a particular move DOES (in this case apparently you mean) revert an already known position. We can then assign to this move the result of the reverted position. (But we can probably forget the detail of a different move order.)

Whether "This move exploits a cutting point created earlier." is needed to decide which branch variation to choose can depend on the aim(s) of the problem's starting position. Maybe the aim is "to exploit a particular cutting point" and reading shall determine whether the particular cutting point can, or cannot, be exploited? (Supposing we know what "exploit" means.)

"This move occupies a Nakade's vital point." more likely is an ill-formulated feature of a terminal position. Suppose the problem's aim (as a very special form of life and death problem) is to decide if the player can establish his stone on some nakade's vital point. At a branching position, we can assign to some next move whether it leads to success or failure WRT his task.

Dear Robert, sorry, but I will stop here.

I have the vague feeling that your theory makes mice elephants, and is hyping the self-evident.

And that it is NOT about "reading" (as understood by the usual Go player), but about "diciding", and "accumulation of knowledge" while / through reading.

[RobertJasiek]

Any good reading theory must build on the "obvious" basics. Nothing hurts reading more than neglecting them. A clear view on the basics is required for the "obvious" to work efficiently.

You seen to want keeping separate in terminology 'decision-making' ('deciding') and 'accumulation of knowledge' from 'reading', where presumably you mean imagining and constructing moves and sequences when saying 'reading'. We need to clarify what you mean by 'knowledge'. Is this the knowledge of which moves, sequences and their outcomes are being discovered while performing reading? I use 'knowledge' with a different meaning: one's learnt knowledge of theory etc. Instead of your 'accumulation of knowledge', I prefer to speak of (accumulation, if you like, of) 'information'. The problem with using the word knowledge when exploring variations is the ambiguity of the word. So please understand that below I speak of information instead of knowledge. So you want to keep separate in terminology the a) exploration of variations from the b) decision-making and information gathering.

Why?

Although, for the sake of it, one can choose whichever terminology one wants, I prefer to include everything under the term 'reading' because everything is involved and depends on each other. In other study fields, such as opening, endgame or whatever, we also do not separate methods of the opening or calculations for the endgame from either. In the study field of 'reading', even if one wanted (as you seem) to separate decision-making and information gathering in one's terminology, one must immediately overcome such a separation and combine a) exploration of variations with b) decision-making and c) information gathering. So the purpose of any artificial separation by terminology remains unclear.

A meta-discussion of what the "usual go player" understands under the tag 'reading' does not change this.

Reading for the sake of determining a problem's correct solution(s) involves (a), (b) and (c) even if one's terminology tries to pretend (b) and (c) would be separate. Except for the most trivial problems, reading does not determine a correct solution without incorporating (b) and (c).

And if everything had been as self-evident as you claim, you would not support an artificial separation. Part of the basics of reading theory is: (a), (b) and (c) are all needed in an integrative manner.

[RobertJasiek]

what Inseong refers to as "1-2-3 reading"

Is this a) reading the most interesing move first, then the 2nd, then the 3rd most interesting moves etc., (a good reading principle) b) reading move 3 before move 1 as a tesuji technique (not anything like a general reading theory but very specialised and often wrong) or c) something else?

[Cassandra]

... combine a) exploration of variations with b) decision-making and c) information gathering. So the purpose of any artificial separation by terminology remains unclear.

...

Reading for the sake of determining a problem's correct solution(s) involves (a), (b) and (c) even if one's terminology tries to pretend (b) and (c) would be separate. Except for the most trivial problems, reading does not determine a correct solution without incorporating (b) and (c).

Every problem becomes the more "trivial" the more we reach the final stages of the sequences. However, the more complicated a problem is, the more onion skins "hide" the relevant hints at the very beginning.

Once we have "really solved" a problem, we know it's entire variation tree. As I already wrote, decisions at all the nodes are quite trivial then: "Choose the branch that enforces the best fulfillment of the problem's aim."

But quite apparently, this is not what you do have in mind with your "reading theory". It seems to me that, with your "reading theory", you want to accomplish the following:

"In a state of incomplete information, come the solution as close as possible with the least possible effort."


As a matter of course, in order to accomplish this feat, you will have to gather information -- at every single node of a "really solved" problem -- about the characteristics of the position reached, as well as about the initial moves of the following branches.

You will have to analyse these information, in order to extract some kind of "knowledge", which might have helped you before (or in similar problems / situations thereafter) to decide on the move(s) that you want to evaluate in the first instance (the "most interesting move(s)", as you called it).

This implies that you want to create tools, with which one is able to prune a variation tree "successfully", although this is only partially seen.

[RobertJasiek]

It does not help us much that a) variations become the easier the more they approach terminal positions (because we still need to read on and compare with other variations) and b) an already completely read variations tree allows easy interpretation (because, except for the trivial problems, we can never construct such a complete tree. Therefore, yes,

"With incomplete information, approach the solution as closely as possible with the least possible effort."

reasonably characterises (my / good) reading theory. However, for local problems, it is almost always possible to formulate an aim so that reading determines whether the aim is either fulfilled or rejected. (Such as in "Are these two strings connected?" or "Is this group alive?".) The 'least possible effort' is an ideal but in practice it often is impossible because we do not know a priori which moves permit the least reading. Therefore, 'approaching' the ideal is what we can hope for.

Despite incomplete information, my reading theory maintains the feature of 'correctness'. Two principles for that are: "Ignore obvious failures." and "In case of doubt, consider each interesting next move.". I.e., if a move's failure is not obvious, verifying the move can be necessary. Immaterial variations may be pruned but interesting and unclear (whether immaterial or interesting) variations must be considered.

Your suggestion to gather information at every single node is bad and very inefficient. It suffices to gather information at the terminal positions, branching positions and the start position! Of course, my theory proposes the latter (with further simplifications).

Yes, information must be analysed to draw conclusions for the problem's aim.

Yes, "This implies that you want to create tools, with which one is able to prune a variation tree 'successfully', although this is only partially seen". The tools are methods and principles to be applied.

EDITs