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Shape
PageType: Path
Difficulty: Beginner
Keywords: Shape
IntroductionThe following theory on shape comes from what I remember of what I have been told by Margo Briessinck (1 kyu BGF) and he got it from a lecture by Bruce Wilcox. I hope this does not violate any copyright. You are all invited to add, comment and improve on this article. Topics which touch the 'shape' issue (which is sort of central to Go :-) are discussed in the pages on Thickness and Aji, as well as the pages related to Shapes And Connections. --MortenPahle
Good shapeFirst, let's try to give a proper definition of "good shape". Objectives:
Characteristics:
Sidebar - Good shape according to Francis Roads
In an article of the British Go Journal 62, available
--Stefan
So, stones have good shape, when they are connected or will easily be connected, make an eye or will easily make an eye, and that with a minimum number of stones, maintaining a certain amount of flexibility.
An indication of good shape, is the number of liberties they have. Matematicians (as I) 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.
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
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.
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
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.
Has the same features as the square. LibertiesStonesRatio : 14/4 = 3.5
The rule of thumb for deciding upon good or bad shape is:
Let's have a look at configurations of two stones. The more they occur in the basic 5, the better.
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)
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 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)
Black can forcefully split with A, or capture 1 with B.
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)
The iron pillar is a 100% connection in a strict sense: the stones can only 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)
This configuration is essentially played as in 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.
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)
Black is connected.
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)
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
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.
(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.
(LibertiesStonesRatio = 3; occurence frequency = 2)
Usually there are enemy stones at A and/or B. (LibertiesStonesRatio = 3.3 ; occurence frequency = 6)
Same remark
(LibertiesStonesRatio = 3;
occurence frequency = 4)
Bad ShapeOkay, let's talk about the acme of bad shape, the empty triangle. (See TheEmptyTriangleIsBad)
First, why is it called empty ? Because, one would expect this shape to result from an attack on the kosumi:
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,
Compare this with
Where
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)
Two remarks about the preceding diagrams:
I'd like to introduce you to the shape game, which wouldn't surprise me to be invented by Bruce Wilcox too.
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. Original author: Dieter Verhofstadt General remarks
This is a copy of the living page "Shape" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |