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Shape
PageType: Path   Difficulty: Beginner   Keywords: Shape

Japanese: 形

Introduction

Shape is a quality of a group of stones of the same color. This quality is highly influenced by the enemy stones present in the same area.


Good shape

Let's try to give a proper definition of "good shape".

Objectives:

Characteristics:

  • efficiency ( = degree of success / stones used)
  • flexibility

Sidebar - Good shape according to Francis Roads

In an article of the British Go Journal 62, available [ext] online, Francis Roads gives the following criteria for good shape:

  1. It maximises liberties
  2. It maximises eye-making potential
  3. It keeps options open
  4. It influences as much of the board as possible
  5. It denies the opponent good shape

--Stefan


So, stones have good shape when they are connected or will easily be connected, make an eye or will easily make an eye with a minimum number of stones, and maintain a certain amount of flexibility.

An indication of good shape, is the number of liberties they have. Mathematicians might want to calculate the LibertiesStonesRatio

Second, good shape will also appear as such to the human eye. We start from 5 basic geometric shapes.

[Diagram]
Diag.: The circle

The circle is better known in Go as a ponnuki. The stones are connected and form an eye at A. The ponnuki mostly occurs after a capture of a stone at a, so the net investment of stones is 3. The LibertiesStonesRatio is 9/3 = 3


[Diagram]
Diag.: The ellipse

The ellipse is better known in Go as a tortoise shell. It expands the virtues of the circle and the eye at A or B is already a real one. The tortoise shell mostly occurs after a capture of stones at a and b, so the net investment of stones is 4. The LibertiesStonesRatio is 12/4 = 3.


[Diagram]
Diag.: The parabola

The parabola makes an eye at a. Mostly it occurs with enemy stones at A and B, so the net investment is 3 stones. The LibertiesStonesRatio is 10/3 = 3.3


[Diagram]
Diag.: The square

The square is more of a light? shape, ready to sacrifice one of its corner stones. It focuses more on connection and less on eye shape, as it has a weak point at A. The net investment is 4. LibertiesStonesRatio : 12/4 = 3.


[Diagram]
Diag.: The parallellogram

Has the same features as the square. LibertiesStonesRatio : 14/4 = 3.5



The rule of thumb for deciding upon good or bad shape is:

All subsets of the basic five shapes are good shape

Please be careful in thoughtlessly applying this rule.


Let's have a look at configurations of two stones. The more they occur in the basic 5, the better.

[Diagram]
Diag.: The ikken-tobi

The configuration of two stones that occurs most in the basic 5, is the one-point jump, or ikken-tobi. It makes a virtual connection, and starts to form an eye at A. The point A is at the same time its weakness. But it is unwise for white to immediately strike there.

(LibertiesStonesRatio = 3.5 ; occurence frequency = 12)


[Diagram]
Diag.: White tries to split the ikken-tobi

Black makes up his mind about which stone is less important - here the marked stone, and connects the other one at 4. Now he has a cutting point at a. If White cuts, Black can continue at b (strong) or c (peaceful) I won't go into the details of the continuation, but it is white who faces the difficulties in this battle.



[Diagram]
Diag.: The keima

The keima comes second in frequency of occuring in the basic 5. It is a more agressive move than the ikken tobi. It has weak points at A and B, but again, without help from surrounding stones, it is unwise to exploit the weakness immediately.

(LibertiesStonesRatio = 4 ; occurence frequency = 12)


[Diagram]
Diag.: White tries to split the keima

Black can forcefully split with A, or capture 1 with B.



[Diagram]
Diag.: The kosumi

The kosumi has only the virtue of connecting 100%: the moves A and B are miai. It makes hardly any eye shape. It is also slower in jumping to the center.

(LibertiesStonesRatio = 3 ; occurence frequency = 9)



[Diagram]
Diag.: The iron pillar

The iron pillar is a 100% connection in a strict sense: the stones can only be removed from the board together. If no enemy stones have forced this shape (like a tsuke at A for instance) then this is not such a good shape because of its lacking flexibility.

(LibertiesStonesRatio = 3; occurence frequency = 4)



[Diagram]
Diag.: The hazama tobi

This configuration, the Hazama Tobi, is essentially played as an invitation for white to split at A. Black then decides which stone to sacrifice and builds a strong shape or a wall with the other one, exploiting the pressure on the cutting stone.

(LibertiesStonesRatio = 4 ; occurence frequency = 3)



Other moves, like the ogeima and the niken-tobi, also occur in some shapes, but I won't discuss them for the moment.

So, let's move to configurations of three stones now.

  • Ikken-tobi from an iron pillar

[Diagram]
Diag.: Ikken-tobi from an iron pillar

This shape makes a 100% connection, eye-shape at a, and it is flexible, because at all times black can decide to abandon either the lone stone, or the iron pillar.

(LibertiesStonesRatio = 3; occurence frequency = 6)


[Diagram]
Diag.: If white tries to split ...

Black is connected.



[Diagram]
Diag.: The dog's head

There is a proverb saying that the horse head (the marked stone at A instead), is better. One should see this in the context of jumping to the center. As a shape, the dog head fulfills the purposes of connection and eye shape.

(LibertiesStonesRatio = 3.7 ; occurence frequency = 6)



[Diagram]
Diag.: The tiger

Caution with the tiger's mouth shape ! If there is a white stone at A or C, the tiger makes a nice connection, blocking an enemy stone. If there is a white stone at B, then this shape makes atari, and the stones are efficiently used. However, if no white stone is present at A, B or C, then the tiger shape is not very efficient. Since it is too slow. It would like to make a ponnuki, but white can spoil this too easily with a move at D.

(liberties/stones ratio = 3.5 (if a white stone at A); occurence frequency = 6)



The keima jump from the kosumi

[Diagram]
Diag.: The keima jump from the kosumi

This shape has a high frequency in the tortoise shell. It connects, makes eye shape at A, and is fast moving into the center.

(LibertiesStonesRatio = 3.3 ; occurence frequency = 4)



The following are examples of good shape with 4 stones, that occur in the ellipse and the parabola.

[Diagram]
Diag.: The bamboo joint

(See also BambooJoint.)

(LibertiesStonesRatio = 2.5; occurence frequency = 1)

These figures seem to indicate that the bamboo joint is bad shape. Too pity we have no consistency here.


[Diagram]
Diag.: (no name provided)

(LibertiesStonesRatio = 3; occurence frequency = 2)


[Diagram]
Diag.: (no name provided)

Usually there are enemy stones at A and/or B.

(LibertiesStonesRatio = 3.3 ; occurence frequency = 6)


[Diagram]
Diag.: (no name provided)

Same remark

(LibertiesStonesRatio = 3; occurence frequency = 4)



Bad Shape

Okay, let's talk about the acme of bad shape, the empty triangle. (See TheEmptyTriangleIsBad)

[Diagram]
Diag.: The empty triangle

First, why is it called empty ? Because, one would expect this shape to result from an attack on the kosumi:


[Diagram]
Diag.: The filled triangle

White 1 tries to cut the kosumi, but black connects at 2 and makes a nice shape, immobilizing the white stone at 1. Now the black triangle is filled with a white stone, as opposed to the preceding diagram, where A is empty. Hence, the empty triangle .



Now why is this empty triangle bad shape ? Well,

  • it has a useless stone
  • it makes no real eye shape despite the use of three stones
  • its LibertiesStonesRatio is 7/3 = 2.3
  • it's utterly inflexible, because all of the three stones must be saved or sacrificed together.
  • and indeed, it does not feature in one of the 5 basic shapes

Compare this to

[Diagram]
Diag.: Ikken-tobi from an iron pillar

Where

  • there is no superfluous stone
  • eye-shape is starting to form
  • the LibertiesStonesRatio is 9/3 = 3
  • there is flexibility


Almost all extensions of the empty triangle are bad too. (This is food for the mathematician: restrictions of good shape are good shape - extensions of bad shape are bad shape). Her are several of them: (See also The Farmers Hat)

[Diagram]
Diag.:

[Diagram]
Diag.:

[Diagram]
Diag.: The farmer's hat

[Diagram]
Diag.:

[Diagram]
Diag.:


Two remarks about the preceding diagrams:

  • the point A is always empty, otherwise they can be good shape
  • if those stones serve to destroy eye space, different laws apply. Empty tiangles are often nice eye-destroyers.

I'd like to introduce you to the shape game, which wouldn't surprise me to be invented by Bruce Wilcox too.

[Diagram]
Diag.: The shape game

White to move and make a living group. Black to prevent that. Black has to mind only about destroying white's shape, since his stones are connected by the marked stones at the sides anyway. Likewise, White has to care only about good shape: connect and make eyes.



See also:


Remarks

Authors: Dieter Verhofstadt, Stefan Verstraeten



This is a copy of the living page "Shape" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.