sábado, 22 de diciembre de 2007

Lesson 4: Connection and Cutting

4.1 Rationale

The fundamental aspect of each and every Go battle is about connecting and cutting. In general, it is a good idea to connect your groups together, and to cut your opponent’s group into two or more groups.

Getting your groups connected often reduces the burden of managing two or more separate groups to managing only one large group. This is especially true when it comes to making eyes when your groups are surrounded and in trouble. As united means strength, cutting your opponent’s groups often mean that your opponent is weakened and you stand to gain advantage.

Therefore, the awareness of connecting and cutting groups is vital in the game of Go.

4.2 Direct Connecting And Cutting

Diagram 4-1

Diagram 4-2

A simple demonstration can be seen in Diagram 4-1 and Diagram 4-2. We compare the two diagrams. When white connects at 1 in Diagram 4-1, we see that white becomes strong and may even threaten the two black stones; whereas if black cuts instead at Diagram 4-2, the two separate white stones are greatly weakened and white has to manage them separately.

Diagram 4-3

Diagram 4-4

We shall now take a look at Diagram 4-3 and Diagram 4-4. It is an obvious example of how connecting and cutting makes a huge difference in the game. In Diagram 4-3, black connects at 1, leaving the two disconnected lone white stones with their survival threatened. The same thing goes for Diagram 4-4 should white connects at 1 instead.

Diagram 4-5

Diagram 4-6

Suppose it is black’s turn and he connects at 1 in Diagram 4-5. This connection ensures that this combined large group has two eyes, and therefore he lives. If, unfortunately, white gets to cut black into two groups at 1 in Diagram 4-6, then we see two separate groups with one eye each – and both groups are dead.

We observe that in most of the cases, it is usual to cut at where the opponent can connect.

Diagram 4-7

Diagram 4-8

Diagram 4-9

The connection of the three black stones in Diagram 4-7 is not complete. Hence, white is able to cut black into two by playing at 1. Black answers by blocking white’s advance at 2, but white can sever the connection at 3, leaving black with two disconnected groups.

See Diagram 4-8, and it is rather obvious that white can connect his stones at 1 if is his turn to play. But now it is black’s turn, so black will squeeze at 1, causing white to have two points for cutting at A and B. Unfortunately, white cannot connect at A and B during a turn: if white plays at A, then black plays at B; if white plays at B, then black plays at A. In any case, the two white stones at the bottom is disconnected.

In Diagram 4-9, black can cut white at 1. When white saves his two stones at 2 and ataris black 1, black can play at 3 to save black 1 and ensures that white is cut into two. Of course, black can elect to play at 2 to cut white in the first place.

4.3 Connecting By Capturing

Sometimes, the opponent’s stones cutting a player’s stones have some weaknesses. In many cases, these are presented in the form of stones that can be captured. So, if the opponent’s stones that prevent the connection of a player’s groups can be captured, then the player’s groups are connected.

Diagram 4-10

Diagram 4-11

Diagram 4-12

The black triangle stone in Diagram 4-10 seems to cut white into two groups, so white is in trouble. Unfortunately for black, the triangle black stone is under atari. So white 1 removes that stone from the board, and thus gets his two groups connected.

Yet another example is seen in Diagram 4-11. When white captures the two black triangle stones with 1, the interior and exterior white groups are now merged as one and now white is in an advantageous position.

We notice that in Diagram 4-12, the two white triangle stones separate the two black groups. However, white has its own defect: black cutting at 1 will kill the two white triangle stones. With the two stones dead, the two black groups are now connected.

4.4 Cases When Cutting Is Ineffective

We cannot say that cutting the opponent’s group is 100% effective. Some groups just cannot be disconnected despite the apparent weakness in their links. There are other cases where cutting just will not make any difference in the opponent. In other situations cutting may even put the opponent in an even better position.

Diagram 4-13

Diagram 4-14

Diagram 4-15

For white to cut the black groups at A in Diagram 4-13 is totally unnecessary. The reason is that the two black groups have two eyes each, so both groups are alive. Compare this with Diagram 4-5 and Diagram 4-6 and the difference is obvious.

We notice that in Diagram 4-14, it is not possible for black to cut the white group at A. If black does so, he would be putting his two stones (including the stone at A) in atari, and yet it is white’s turn. White can then play at B to capture these two stones. In a game, we should be on alert – always watch out for ataris.

We take a look at Diagram 4-15 and we can see a cutting point at A. But it is useless for black to cut at A, as it simply introduce a dead black stone at A. To make things worse, if black really plays at A, white can just ignore and play elsewhere.

The above three diagrams, Diagram 4-13, Diagram 4-14 and Diagram 4-15, demonstrates cases when cutting is ineffective. Hence, we should avoid playing such kinds of moves. As for the opponent player, connecting the groups in these three diagrams are not needed – wasting moves as well.

4.5 Keeping Stones Connected

As explained in the beginning of this lesson, it is usually a good idea to keep your stones connected. This statement is especially true for beginners. However, it is very often that we see beginners play a lot of nonsensical moves that result in their stones all scattered and separated. This will result in a large advantage for the opponent, who will have pleasure capturing the many scattered groups or manipulate these groups to his own benefit. This section is written specially for such beginners, in the hope that they will commit less such mistakes.

Diagram 4-16

Diagram 4-17

Consider the situation in Diagram 4-16, and it is white’s turn now. As the reader, it may be interesting to note how you would play. Playing at A is a suggested move which keeps the white stones connected.

Diagram 4-17 shows typical moves of some beginners. They think that from white 1 onwards, they are trying to attack the black stone or to capture it. All the black moves are very natural and totally correct, keeping his stones in one piece and evading white’s attack. At the end of the sequence after black 16, we can see very clearly that black is in one chain while white is all scattered and separated, with places for black to cut everywhere. This is not the way white should play.

[More Stuff] – Handicap Games

When the two players with different standards are playing Go, it is usual for the stronger player to give handicap to the weaker player so that the game would be fairer. For players with very small difference in strength, it is usual to allow the weaker player to take black without komi. Otherwise, the weaker player will be given a handicap of two to nine stones. The weaker player takes black and places two to nine stones at the marked points (known as star points or handicap points), after which white will play his first move.

By default, these are the handicap points where to place the handicap stones (from black’s viewpoint):

§ Two stones: upper right and lower left corners.

§ Three stones: upper right, lower left and lower right corners.

§ Four stones: all four corners.

§ Five stones: all four corners and the center point.

§ Six stones: all four corners, left and right sides.

§ Seven stones: all four corners, left and right sides and center point.

§ Eight stones: all handicap points except the center point.

§ Nine stones: all handicap points.

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