By Nam Chi-hyung

There are many Baduk proverbs about a bend, and ``a double-bend creates a liberty'' is one of them. It means that a bend is also useful in a capturing race.

Before we go on to see examples of the usage of a bend in a capturing race, let's clarify the difference between a ``double-bend'' and a ``two-step-bend.'' A two-step-bend means two successive bends occurring in the same line of play, like a ``two-step-ko.'' The second bend is dependent on the first bend.

Diagram 1

Black 2 and 4 compose a ``double-bend'' against White's attachment at 1 and the bend at 3. Black's bend with 4 cannot exist without the bend with 2.




Diagram 2

Black 1 is the first step of the ``two-step-ko'' in the corner. The ko with A follows the winning of the ko with 1.

In contrast, in a ``double-bend'' or a ``double-ko,'' the bends and the kos do not occur in the same line of play.

Diagram 3

As White captures Black A with 1, Black captures White B with 2. Thus, the two kos are happening in the same situation and are related to each other, but each ko can be fought regardless of the other ko's existence.


Diagram 4

Here is an example of a ``double-bend.'' As in the above-mentioned proverb, Black can create an additional liberty with a ``double-bend'' and win the capturing race where White has 4 liberties (x-marked points), compared to the 3 that Black has (▲-marked points) at the moment.


Diagram 5

Black 1 and 3 compose a ``double-bend'' here. As you can see, these two bends are not physically connected with each other, but allow Black to win the race.





Diagram 6

When White plays 1, it is important for Black to fill White's liberty with 2. If Black captures White 1, it turns into a ko by White B. White cannot play A right after Black 2 to lessen Black's liberties, but has to play B first.




Diagram 7

Let us look at an example from an actual game. This took place in the game between Changho Lee (B) and Satoru Kobayashi (W) in 1997. Now it is White's turn and the groups of Black and White on the lower side are struggling to kill each other.





Diagram 8

The complicated sequence here shows that White loses the fight. (The actual result is a ko, which is quite unfavorable for White. Please verify the result yourself.) The reason why White loses the fight is that White omits a bend.





Diagram 9

A simple bend at 1 changes the situation 180˚. The sequence from White 3 to 23 is the same as the sequence from 1 to 21 in Dia.8. However, here, Black has to play 24 before connecting at 1 to make White's eye at 18 false. This is the power of White's bend at 1. Owing to this one move, the black group is captured by White. To save the group, Black should ignore White 1 and seek a living in the corner. Then, White will also live on the side by giving an atari at 2.

chihyung@mju.ac.kr

The writer is a baduk professor at Myongji University and a professional player of the game.