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A Static Treatise on Shape
Keywords: Shape
Taken from shape. There seems to be a strong opinion, both here and on rec.games.go, that shape is something dynamic. See also the haengma page and discussion. Also the shape page was longer than a subject page should probably be. Therefore, I have moved this static treatise to a separate page. The ideas come from BruceWilcox and were taught to me by the unrivaled webmaster of the BGF, Margo Briessinck. I have worked out the concepts a little more. --Dieter 1. Good shapeGood 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
The circle is better known in Go as a ponnuki. 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. Without a previous capture, the circle is overconcentrated.
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 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 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.
Has the same features as the square. Liberties/stones ratio : 14/4 = 3.5
The rule of thumb for deciding upon good or bad shape is:
Please be careful not to apply this rule thoughtlessly. Note also that this is a controversial statement, particularly regarding the dog's head or sake bottle shape.
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 strike there immediately. (Liberties/stones ratio = 3.5 ; occurrence 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 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)
Black can forcefully split with a, or capture 1 with b.
The kosumi has only the virtue of connecting 100%: the moves a' and a'' 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 nobi 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)
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.
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)
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's head fulfills the purposes of connection and eye shape. (Liberties/stones ratio = 3.7 ; occurrence 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. 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); occurrence 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 for moving into the center. (Liberties/stones ratio = 3.3 ; occurrence frequency = 4) The following are examples of good shape with four stones, that occur in the ellipse and the parabola.
(See also BambooJoint.) (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.
See TableShape (Liberties/stones ratio = 3; occurrence frequency = 2)
Usually there are enemy stones at a and/or b. (Liberties/stones ratio = 3.3 ; occurrence frequency = 6)
Same remark (Liberties/stones ratio = 3; occurrence frequency = 4) 2. Bad ShapeOK, 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 to
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). Here are several of them: (See also Farmer's Hat)
Two remarks about the preceding diagrams:
You can exercise your feeling for shape in the shape game; it wouldn't surprise me if it were invented by Bruce Wilcox, too. This is a copy of the living page "A Static Treatise on Shape" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |