Kosumi: pros and cons
The kosumi (diagonal connection as seen in Diagram 1) is a very strong, unsplittable shape, in its basic form. For example, if White plays at A, Black plays at B, and vice versa, a situation known as miai. A and B are miai, and therefore the black stones are always connected.
Diagram 2 :
When Black invades at 1, the kosumi at 2 is an appropriate response, because it prevents black 1 from linking up with the marked stone. On the other hand, playing at A instead of white 2 would allow Black to connect underneath.
Diagram 3 :
Jumping to 2 instead of playing the kosumi, would wreak havoc on White's position. If he wants to, White can still capture black 1 after black 3, but after black 11, it becomes obvious waging war on black 1 by playing at 2 results in a Pyrrhic victory.
Diagram 4 :
However, in a situation like this, where Black cannot make a base on the lower side, it is important to move away safely, but quickly. The ikken tobi, or one-space jump, is employed in such instances. A kosumi at A would only provoke white B, turning the marked space into secure territory. Basically, then, the kosumi has an inert feel to it.
Diagram 5 :
Black 1 is the vital point of this shape. Why ? If White wants to move out in the center, he can do so by playing at 2. The moves to 9 then follow naturally. White's group lacks eye shape, and its only raison d'tre seems to be escape. This kind of play lacks backbone. The kosumi seems to be the cause of this, which is why it's referred to as the hebo kosumi, or "duffer's kosumi" in English go lingo. Notice black 9-it makes a good shape (a cross between the mouth shape and the bamboo connection), while defending against the cut at white A, followed by black B and white C.
Diagram 6 :
That leaves white 2 as a response to black 1. But black 3 is just right, as it is on the head of two (white) stones with black 1 occupying the vital point. However, after white 6, Black needs to defend right away against the cut with black 7 because of damezumari (lack of liberties) of the marked black stones.
Compare this with Diagram 5-thanks to white 2, Black had to invest a move at 3, which White used to attack at 8 and play at 10 and 12 to make an eye shape. So even though White's situation is not ideal, it is still preferable to that in Diagram 5.
Diagram 7 :
Now notice something else: the kosumi in Diagram 5 became a hebo kosumi because it didn't affect any of the black stones, but instead allowed Black to build up a nice wall. This is because black 1 (in that diagram) already occupied the vital point of the kosumi shape. Thus, on a local level, black 1, as well as A, B and C in this diagram seem to be vital points for attacking the kosumi.
Problem 1 :
White has just played the marked stone. Black needs to move away. How ?
Problem 2 :
This shape resembles what we looked at before. Black 3 and 5 are a powerful combination because they induce the moves 8 and 10. Black 11 is a necessary evil to protect against the cut between black 5 and 7. White 12 is joseki, as is black 13, which takes the vital point again. Where should White play next ?
Problem 3 :
If Black wants to attack White, what should his first move be ?
Solution 1 :
This is a tricky shape, but it appears frequently. Black 1 is probably best. White will likely draw back with 2, after which Black can make a shape with 3 through 7.
Reference 1 :
Black 1 will be negated by white 2. Black 3 is often a good move, but white 6 and 8 is a clever combination forcing Black to live on the edge, while White builds a nice wall.
Reference 2 :
This is another pitfall Black should be aware of. If Black omits black 3 in Reference 1 and tries the hane (a diagonal connecting stone) at 3, white 4 becomes the vital point and Black is forced to make a bad shape (empty triangle of black 1, 7 and the marked stone) to forestall a white connection underneath (below the marked stone). After white 8, Black is fighting an uphill battle.
Solution 2 :
White 1 induces black 2, allowing White to defend against the cut at A by playing 3, then escape with 5. In the end, white 7 makes a fair bit of profit and a strong group, but Black has a multitude of options now ranging from B through D and even tenuki (play elsewhere).
Solution 3A :
Black 1 is the vital point to attack White's eye shape. White can opt for running out into the center with 2. This is a strategy often employed when the black marked stone is at A. In this case, the moves through 13 will follow, and white 4 through 12 do not impact the Black position above it. In other words, even though White won't die, his stones are ineffective.
Solution 3B :
The option shown here is more realistic. White 2 is a tesuji (locally clever move) worth remembering. Usually the moves through 6 follow. White's position is low, and Black has no reason to be dissatisfied.