# A Static Treatise on Shape

Keywords: Shape

This (static) treatise on shape has been taken away from the general article on shape, because it fails to adequately take the dynamic nature of shape into account. As the original author I no longer support the view laid out here. The ideas come from Bruce Wilcox. I had worked out the concepts a little more. The readers can take from this page what they think is valuable. --Dieter

Comment [1]

### 1. Introduction

Good shape will appear as such to the human eye. We start from five basic geometric shapes.

An indication of good shape, is the number of liberties they have. Mathematicians might want to calculate the Liberties/stones ratio

### 2. Five geometric shapes

The circle

The circle can refer to two different shapes, depending on whether a stone has been captured in the process. The stones are connected and form an eye at a.

The real ponnuki occurs after a capture of a stone at a, so the net investment of stones is 3. The Liberties/stones ratio is 9/3 = 3. This is considered good shape.

The diamond occurs when no stone has been captured at a. The liberties/stones ratio is 9/4 = 2.25. This shape is overconcentrated.

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 Liberties/stones ratio is 12/4 = 3.

The parabola

The parabola, or mouth shape, makes an eye at a. Mostly it occurs with enemy stones at a and b, so the net investment is 3 stones. The Liberties/stones ratio is 10/3 = 3.3

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. Liberties/stones ratio : 12/4 = 3.

The parallelogram

The parallelogram has the same features as the square. Liberties/stones ratio : 14/4 = 3.5

### 3. Rule of thumb for good shape

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 not to apply this rule thoughtlessly. [2]

### Good shape of two stones

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

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 strike there immediately. See cutting the one-point jump.

(Liberties/stones ratio = 3.5 ; occurrence frequency = 12)

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.

The keima

The keima comes second in frequency of occurring in the basic 5. It is a more aggressive 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.

(Liberties/stones ratio = 4 ; occurrence frequency = 12)

White tries to split the keima

Black can forcefully split with a, or capture 1 with b.

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.

(Liberties/stones ratio = 3 ; occurrence frequency = 9)

The stretch

The stretch 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.

(Liberties/stones ratio = 3; occurrence frequency = 4)

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.

(Liberties/stones ratio = 4 ; occurrence 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 a stretch
Ikken-tobi from a stretch

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 connected pair of stones.

(Liberties/stones ratio = 3; occurrence frequency = 6)

If White tries to split ...

Black is connected.

Imagist Nevertheless, this can be considered an inefficient shape. See Ikken-tobi from a stretch.

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's head fulfills the purposes of connection and eye shape.

(Liberties/stones ratio = 3.7 ; occurrence frequency = 6)

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. It is too slow. It would like to make a diamond, but White can spoil this too easily with a move at d.

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

The keima jump from the kosumi

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 for moving into the center.

(Liberties/stones ratio = 3.3 ; occurrence frequency = 4)

This shape is also refered to as Panther. (Go Winds Fall 2003, vol 7, Num 3)

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

The bamboo joint

(Liberties/stones ratio = 2.5; occurrence frequency = 1)

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

The table shape.

Table shape

See TableShape (Liberties/stones ratio = 3; occurrence frequency = 2)

(no name provided)

Usually there are enemy stones at a and/or b.

(Liberties/stones ratio = 3.3 ; occurrence frequency = 6)

(no name provided)

Same remark

(Liberties/stones ratio = 3; occurrence frequency = 4)

The empty triangle

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

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 Liberties/stones ratio 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 five basic shapes.

Compare this to

Ikken-tobi from a nobi

Where

• there is no superfluous stone
• eye-shape is starting to form
• the Liberties/stones ratio 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). Here are several of them: (See also Farmer's Hat)

The farmer's hat

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 triangles are often nice eye-destroyers.

You can exercise your feeling for shape in the shape game; it wouldn't surprise me if it were invented by Bruce Wilcox, too.

[1]

Bill: I have to demur. I think that many of the supposed examples of good shape on this page are not good in themselves, because they are over concentrated. I. e., like the empty triangle, but not so bad. They may form good shape when enemy stones are about, however.

Charles Bill, I guess from many of your past comments that you apply a tacit convention, that points marked as empty are (by default) taken as empty. Now in some cases that seems reasonable. But in other case, less so. For example, the usual thing in explaining a go position, face to face, is to set it up on an area of the board, and assume one can have a localised discussion of it. Also, some search programs will take an empty intersection to be empty (by default), and you must mark any 'wild card' intersections (allowed to be empty, Black's or White's). But again this is not a universal convention - I have used search programs that take the opposite attitude, that an empty intersection is a 'wild card'. Therefore, I think it could be helpful to spell this all out somewhere.