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Dieter's ideas on Go Theory
    Keywords: Theory

June 2004 - The project mentioned below is discontinued. I'll leave the page as it is, because some people seem to have taken interest in it. --Dieter

Table of contents

Introduction

This page is a personal project by Dieter. It is an attempt to accurately describe Go theory. Go Theory starts with rules. From the rules we can derive principles. For a deeper understanding of those principles, we develop several concepts. The principles and the related concepts finally give rise to guidelines, or as they are called in Go theory, proverbs. The game has three aspects: technique, tactics and strategy, so proverbs will typically look at one of those three aspects.

Your comments below this document are appreciated.

Rules (R)

  1. The rule of capture
  2. The rule of scoring
  3. The rule of alternating play
  4. The rule of ko or forbidden repetion.

Principles (P)

  1. The principle of efficiency
  2. The principle of flexibility
  3. The principle of liberties
  4. The principle of life and death
  5. The principle of connection
  6. The principle of development

The principle of efficiency

From R2-scoring and R3-alt-play we can derive a meta-principle, namely that you should place your stones with a maximal effect.

Stones should be placed with maximum efficiency

The principle of flexibility

Go is a game of complete information, but it is far from being solved. Some board positions, however, are already solvable by the mind (killing large groups, endgame). In these situations, the player who sees a sequence giving him undisputed victory, will play out this sequence. This can be called "settling the shape". If settling the shape does NOT give a definite advantage, then it gives more information to both players. In particular, when the shape is settled with one move, the opponent is the first to adopt a way of playing that takes the settled shape into account.

Therefore, as long as it is unclear who is favoured by the board position, both players will keep their options open as much as possible. This applies also to parts of the board.

(i) Preserve flexibility as long as the position is unclear
(ii) Settle the shape when the position favours you

The principle of flexibility comes from general principles of gamesmanship and the rule of alternating play.

The principle of liberties

From R1 we deduce that liberties are important.

(i) Increase the liberties of your own stones
(ii) Decrease the liberties of your opponent's stones
(iii) Avoid decreasing your own liberties
(iv) Avoid increasing the opponent's liberties

counting liberties forms the basis of the theory of capturing races.

The principle of life and death

From the rule of capture and the rule of alternating play we also derive the second principle,

Some groups of stones can't be captured and are called alive

In particular this accounts for the concept of two eyes which forms the basis of the theory of life and death.

The principle of connection

From the principles of efficiency and liberties, we deduce that it is interesting to connect groups, for less stones are then needed to make them alive and the sum of the liberties of both groups will be all the greater.

(i) Connect your own stones
(ii) Cut your opponent's stones
(iii) Don't let your groups be sealed in
(iv) Seal in the opponent's groups

The principle of development

Increasing liberties, establishing a connection, surround empty points and creating space to make eyes are all some kind of development. We can also adhere a sense of direction? to the concept of development. We can thus state the principle:

(i) Develop your stones. Choose the best direction.
(ii) Reduce the possibilities for development of the opponent's stones. Force his development to go in an uninteresting direction.

Concepts (C) and proverbs

From the above six principles we can now derive the rest of Go theory, conventionally expressed through proverbs. This includes technique, tactics - which boils down to life and death and capturing races - and strategy. Throughout this development, several concepts? (C) will be defined.

Technique (T)

  1. Ladder technique. From liberties and connection.
  2. Net technique. From liberties and connection.
  3. Nets are better than ladders. From efficiency.
  4. Extend from atari, if increasing liberties is possible. From liberties and connection.
  5. Hane against the contact play. From liberties and development.
  6. Block the push through. From liberties and connection.
  7. Block the diagonal. From liberties and development.
  8. Extend from a diagonal contact play. From liberties and development.
  9. Connect against the peep. From connection.
  10. Hane at the head. From liberties and development.
  11. Stretch from a bump. From liberties and development.
  12. Extend from a crosscut in the absence of neighbouring stones. From liberties, connection and development.

Tactics

  • The theory of life and death forms an independent chapter which has been abundantly described. The positions called seki can be explained through the principle of liberties, much like the principle of two eyes.
  • The theory of liberties and capturing races has been documented by Richard Hunter.

Strategy (S)

A first strategic proverb, which is also applicable to technique and tactics, is derived from alternating play :

S1 The enemy's key point is yours

From the principle of flexibility we get a first concept, miai, and the according proverb:

S2 Look for moves that leave equivalent options.

The key concept in strategy is the balance of territory and thickness, which is guided by the principles of efficiency and development. Another way to look at this balance is the meaning of stones and urgent versus big moves.

Thickness: a group of stones which is firmly connected and which has sufficient eyespace.

Territory: an area which is surrounded: no cut possible by a thick group, and in which the opponent has almost no chance to create a living group.

The usual size of the board, together with these two concepts, gives rise to the following proverbs:

S3 The third line is the line of territory
S4 The fourth line is the line of influence

Hence,

S5 Gladly accept fourth line territory
S6 Third line to stabilize, fourth line to build

The meaning of stones or urgency

Stones that cut apart groups which are not yet thick are called cutting stones. From two eyes and efficiency we derive

S7 If cutting stones are not thick, strengthening them is urgent. Corrollary:
S8 Capture the cutting stones. Corrollary:
S9 Cut the side you don't want. Stones that cover a large area are important too, due to the concept of territory.

S10 Strengthening weak stones that cover a large area, is urgent. If those stones are not yet thick, strengthening them is urgent.

Stones that are close to your own or the opponent's thickness, have little room for development. Those are not important.

S11 Defending stones close to your own or opponent thicknes isnot urgent.

The meaning of areas or size (bigness) (B)

S12 Open areas, with a lot of room for development, are big.
S13 Areas close to own thickness, are uninteresting, because playing there is not efficient.
S14 Areas close to opponent thickness, are uninteresting.

We can summarize the meaning of stones and areas in the following strategic principles:

S11 and S13 can be summarized into the superproverb Play away from thickness.

As we can see from the above, territory exists only by virtue of thickness. Hence

S15 Play urgent moves before big moves
S16 When there is little urgency, play a move in open space.

More strategic proverbs

S17 Don't build influence in the direction of stable positions. From development, efficiency and thickness.
S18 Build box shaped territories (efficiency, territory)
S19 First corners then sides then center (efficiency)
S20 Approach from the wider side (development)
S21 Block on the wider side (development)

More concepts

Aji is the future potential of a position (stones) which is (are) temporarily lost. Bad aji gives more options (flexibility) to the player who locally has lost (stones).

%axd: shouldn't this be "*Good* aji gives more options..."? The two phrases seem to contradict each other.
%Dieter: In my viewpoint, the qualification of aji applies to the person controlling the local position. He can do so with good or bad aji. I am probably wrong in my interpretation.

Stones are light when they have a lot of flexibility. Heavy is the opposite. Mostly, if light stones will be captured, it will be small.

Shape is a characteristic of a number of stones. Determining principles are efficiency and flexibility. Objectives are eyespace and connection, leading to thickness and territory.

The study of the different shapes can be done independently. A static treatise on shape is a first attempt. It relies amongst others on the liberties stones ratio for efficiency. Subsets of good shape are good shape. Extensions of bad shape are bad shape.

%a.o. = amongst others?

Forcing moves are moves that force the opponent to settle the shape and reduce flexibility so that the forcing player can next play according to his opponent's choice.

More technical proverbs

T13 Capture the ladder as soon as possible. (reduce flexibility for the opponent)
T14 Don't try to cut the one-point jump unless it gives a clear advantage (liberties, flexibility)
T15 Don't cut knight's moves unless it gives a clear advantage (liberties, flexibility)
T16 Don't peep where you can cut (connection, flexibility)

Finally, I need a stronger explanation than the ones I have available for the idea that playing close to (strong) stones strengthens both sides. This is the basis for the theory of leaning attacks and sabaki techniques. It also explains why to attack from a distance. Proverbs yet to be included:

Reducing techniques

  1. Knight's move against capping play from the third line (3rd line and 4th line significance)
  2. One space extension against capping play from the fourth line (3rd line and 4th line significance)
  3. Reduce a framework by playing on the sector line (from attacking techiques and connection principle)

Attack and defense techniques

  1. Attack from a distance (that's a tough one, because it mixes technique with strategy)
  2. Make a base first, then jump to the center (eyespace over connection ??)
  3. Knight's move to attack (development)
  4. One space jump to defend (no clue, lightness and shape maybe)
  5. Two space jump to sacrifice (lightness)
  6. Boshi to attack (development)

Cutting and connecting principles

  1. Avoid connecting along dame warning (efficiency)

Your comments are highly appreciated.

Dieter


Deshi comments

[1] Charles I'm not aware of any principle exactly covering this point. But see make both ends strong.


RobertJasiek: TDerz, as below, "principle" need not have the same meaning as "tautology under 2-value logic" but can also be used in pretty informal ways. Nevertheless, strategic go theory can be derived from go rules by means of tautologies. This has become especially possible since the Japanese 2003 Rules. In fact, I have already made first attempts in that direction. E.g., it is pretty straightforward to define "life-and-death-group". In the Logical Rules of Go Robert Pauli has defined "2-eye-group". Under the Japanese 2003 Rules this is a concept already on a strategic level. One of the next things to do will be an attempt to prove when self-atari of a 2-eye-group makes sense. All such is low level strategy. It will take much more effort to reach high level strategy. OTOH, for other go rules, late yose or specialized ko play have been derived formally. That is also low level because it is close to the end of alternation, where the strategic complexity is "low". The same can be said so far about research under the Japanese 2003 Rules. Dieter is more optimistic but should just note that his principles are not tautologies.


TDerz Dieter, generally I would say, that I cannot derive several of the statements from the rules (R) and principles (P). We both will agree believing that they are true, but this derives more from 10.000 of played games and is usually heuristics. The term derives from means for me more has to do with, thus not indicating any wrong causality. The best example is for me The principle of two eyes: This group without two eyes is (also) alive.
With our background we know that we speak about seki, moonshine life etc. being this group.

For principles however, it can hardly be acceptable that both the affirmative and its opposite are true [2], there must be more, differentiating stuff to it. That is why they cannot be principles.

BTW, I am not a matematician, hence quite ignorant about the subject. I just feel that if these principles were really derivable from the rules, Go was programmable as TicTacToe?, Mühle or Reversi. This is not the case.

I know that the principles are inter-dependent, hence they are not axioms.

I agree with the principle of efficiency - because it is very vague! Dieter, I especially like the part about flexibility with regard to keeping options open. This part is very well written.

The problems start already with the The principle of liberties. I cannot increase all my stones liberties, I must decide and sacrifice some stones etc. for i-iv. (Interdependence of principles)

Other points: The principle of two eyes can be derived from R1+ R3 (eyes not explained & including two false eyes?). It is easy to agree on that.

The principle of connection only necessarily relates to P1 and P3, P2 is not needed.

Points i to iv I also emphasize often to Go learners, then coming to shape for achieving i-iv.

The principle of development

I think the references are actually different: Increasing liberties (P3), establishing a connection (P4), surround empty points (R2) and creating space to make eyes (P4) are all some kind of development.

Again, well written.


Concepts (C) and proverbs

  1. Hane against the contact play. From P2 and P3. (not P4)

Strategy (S)

S0 The enemy's key point is yours (from R3) Why?

From the principle of flexibility (P6) (P2?) ... The key concept in strategy is the balance of territory and thickness, which is guided by the principles of efficiency (P1) and development (P5). P6?

C2 Thickness: a group of stones which is firmly connected (P4) P5? and which has sufficient eyespace (P3). P4?

C3 Territory: an area which is surrounded (P4 P5?: no cut possible) by a thick group, and in which the opponent has almost no chance to create a lving group (P3). P4?

The meaning of stones or urgency (U)

U3 Stones that are close to the opponent's thickness, have little room for development (P5). P6? U4 Stones that are close to your own thickness also have little room for development (P5). P6?

The meaning of areas or size (bigness) (B)

B1 Open areas, with a lot of room for development, are big.(P5) P6?
B3 Areas close to opponent thickness, are uninteresting (B2 and P6?, not AP1) What is the A in AP1?

S12 Build box shaped territories (P1, C2)
I do not understand this term 'box'.

C5 Stones are light when they have a lot of flexibility (P6) P2 ?.

C6 Shape is a characteristic of a number of stones. Determining principles are efficiency (P1) and P2 (P6). Objectives are P4 (P3) and P5 ... C7 Forcing moves are moves that force the opponent to settle the shape and reduce flexibility (__P2 __) so that the forcing player can next play according to his opponent's choice.

More technical proverbs

T13 Capture the ladder as soon as possible. (P6) rather C4
T14 Don't try to cut the one-point jump unless it gives a clear advantage (P2, P6) and P3+P5
T16 Don't peep where you can cut (P4, P6) and P5

[2] TDerz I think this comes from Aristotelian logic with its the excluded third. Either Go needs some kind of special fuzzy logic (I think) weighing all kind of interrelated dogma(ta?) & evaluations against each other, or you could apply logic only retroactivley (playing it out and compare afterwards).

I believe, that even if we could play ALL possible Go games, match them and look for the widest winning path, we had big trouble to explain why a particular move is good or (relatively) bad. Often it was supposed that perfect play would be around 13 dan. Discussing moves of your own strength (= your own moves) is always difficult and the abstractness, therewith the discussion of the game becomes more difficult with higher level.


Dieter: Thanks for your comments Tderz. Just one reply for the moment:

The statements Every group with two eyes is alive and There is a group without two eyes that is alive are not each others' opposite. Groups with two eyes are a subset of alive groups, hence can be complemented with other kinds of groups (like seki). The converse statement would be there is a group with two eyes that is not alive. Now if that would be true, I can't call two eyes a principle but must indeed fall back to a heuristic. Your statement is the opposite of Only groups with two eyes are alive, which is not what my principle says. It's simple logic, really, there is nothing fuzzy going on here. (Maybe in Go, but not in this particular principle).

The fact that every group with two eyes is alive (cannot be taken from the board) does follow logically from the rules:

- the rule of suicide or the logical rules forbid existence of a played stone without liberties after the possible captured stones are removed - a player can only play one stone at the time (alternating play) - give a strict definition to an eye then make recurrent extensions of the definition

Since one cannot play inside one eye AND another at the same time, a group with two eyes is alive.

I a not saying I gave an inclusive definition of eye, neither is the derivation of the principle formulated so that no holes can be found. I am saying such is possible and that from the rules of play/capture/suicide and alternating play, the principle can be logically derived.

TDerz Dieter, thank you for pointing out the real opposite of the statement, using a NOT instead of the wrong, misleading without.

WRT your puzzling reference numbers, where they meant to be as I wrote it, or did you mean something, which I interpreted wrongly?

The principles expressed by the terms flexibility and development for example (seem to) overlap. Moreover, the explanation for

 the higher numbered development comprises lower numbered principles.

Is this intentionally? My honest question (no sandbagging, I'm a mathematic/logic layman) is: shouldn't principles be independently defined?

Otherwise it would make sense to formulate the ultimate principles "Win this Go game when starting with black" or "Make a draw when given the appropriate komi", being built up by the Rules R and all lower ranked principles P. How much teaching value would it carry? Most probably as much as the all-comprising Do not make mistakes.

Perhaps my argumentation here, to exaggerate the principles and then negate them, looks like eristic dialectic (quarrel), but I am of the opinion that principles should be rather something more antagonistic (while therewith interdependent) e.g. thickness vs. light etc. This would make clear that in Go one has to chose all the time: for example is it usually not possible to play a light, thick, fast developing, all-connecting single move. The better prioritizing derives from imagined future game positions and their evaluations.

Following this argumentation, I conclude (at least for myself) that Go is played by a top-down approach (look ahead, evaluate and chose moves which most likely lead to the most positive, attractive game position) and not by a bottom-up approach (be efficient, make liberties & eyes, connect and develop flexible). I admit that very fast Haya-Go might be played this way, although it is difficult to say what we think (and this will vary very much!).

In so many presentations of good Go players it is emphasized that Go is a game striving for harmony - a good balance of several(!) mutually excluding concepts. This is not an appeal to authority, rather I think these players express with these words harmony and balance all that what you start to analyze in detail on this page.

In fact, in view of above, the Principles seem Concepts to me (except P4 Two eyes).

I admit that I also believe that it should be theoretically possible to set up a logical system which completely explains Go and leads to the winning game (or a draw of two 13-dans). This logic system - if presented to us here and now - could be so complicated that we would not understand this and(?)/OR it would be another theory which does not help to improve our game [3]. Diter tries hard to fit something in between those two extremes.

Therewith my argumentation is a little bit inconsistent here (Go is not solvable by logic vs. there is a helping logical theory based on rules and axioms, not heuristics), this might be due to the complexity of the subject and/or my laymanship in both Go and logic.

[3] (off topic) Now I am very ignorant and call [ext] Combinatorial Game Theory such a theory of the second type (for me). Are there players who could benefit from it? Is it more than a formal way of describing what is going on in Yose?


Dear Tderz, thank you for devoting so much time to the project. It is true that the numbering and the references are confusing and sometimes plain wrong (corrected as of feb 2004 - most of the cross-referencing now undone). Please continue to comment on it. I highly appreciate the effort.

Dieter



This is a copy of the living page "Dieter's ideas on Go Theory" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.