Solution 1 : Black should play at 1, which roughly would extend his territory to that delineated by the X's. If White can exchange A for black B and C for D, his corner territory stretches along the *s'. But Black gets more than 30 points against White's 13. That is why White usually will not invade at a very early stage, even taking into account Black's extra move.
Reference 1 : If Black plays at 1 instead, he faces three disadvantages:
1. White would play a kikashi at 2, a forcing move that Black should answer with 3. This would deprive Black of eye shape, which could be a decisive factor in the fine line between thickness and target of attack.
2. Black's sphere of influence is about one line less and the territorial difference would be around five points.
3. In the endgame, after Black has turned the right and lower side into actual territory, White can play again A for black B and C for D. But in addition he can play E for F and G for H in sente (moves Black must answer). This is worth another two points.
Reference 2 : Playing tenuki (elsewhere) is not on our short list of solutions either. After black 1 plays elsewhere, White 2 would rip apart the black would-be wall. Even though Black offers strong resistance, after white 14 and 16, Black is squeezed and White would play at either A or B. Instead of Black, White would hold sway in the center. In terms of territory, the difference between Solution 1 and this one might easily amount to 50 points !
Solution 2 : White 1 is correct. Black 2 is joseki (standard corner exchange). Usually white 3 (or 5) follows. Black can exchange 4 for 5 later.
Compared to a white move at D, white 1 offers various benefits. It makes an eye at D and it allows 5 in response to black 4.
Also compared to directly playing 3 or 5, white 1 has the benefit of allowing White to resist a black move at A by playing at B. Thanks to White's move at 1, Black will need to add a move at C, otherwise his stone at A gets taken.
Solution 3 : White 1 is correct. The moves to 4 follow.
Reference 3 : White 1 looks tempting, but Black would play atari at 2 and puts the pressure on with 4. Black gets a strong shape and White will need an extra move to live.
Reference 4 : After white 1, Black could press at 2, too. The difference is that White can now play at 3 and 5 leaving Black with a weakness at A and gain more territory in the corner.
Solution 4 : To understand this problem we need a lot of background information. But let's just start with the solution. In response to the marked white move, if Black simply connects at A, this will have no bearing on the right side. But the combination of black 1 and 3 do. If we assume White escapes with 4 to 8, Black 9 and 11 bring to light defects in White's shape. Black 13 then invades the corner. If White assumes an noncompromising stance with 14 and 16, the combination of 17, 19 (white 20 would take the place of 11 after its capture) and 21 to capture the whole corner.
For what actually happened, let's look at this NEC Cup game played between Cho Chikun, defending titleholder, and Masao Kato, 9-dan. Kato was Black.
Diagram 1 : Black immediately starts an attack with 7 and 9. To play boshi (capping move) at 15, Black takes a loss by exchanging black 11 for white 12 and 13 for 14. This constitutes an immediate loss because White gets territory, but Black hopes for compensation by attacking 6 and 10. White 18 is the marked move in Solution 4. However, white 20 deviates, invalidating that diagram. Hideo Otake, the official commentator, said this move alone was worth the trouble to come and have a look at the game. It demonstrates Cho's flexibility and keen understanding. Later, after Black has settled his center group, white 20 will offer more resistance to a black invasion at D.
Black 21 and 27 prevent a cut at A and B. White 22 and 24 are kikashi that ensure a safe exit before making shape with 26. This move is better than playing at C which has more attacking potential around 27. But 26 is aiming at attacking the three black stones around 22.
A white move around 32 was anticipated, but white 28 is a bolt from the blue. Its lack of elegance is easily compensated for by its forcefulness. Cho seems to dare Kato: "Catch me if you can." After black 37, White needs to defend against the cut at E. The question is where ?
Diagram 2 : White 38 is the move to do this. It is a light move, i.e. forms the beginnings of eye-shape while moving away, while attacking at the same time. See Reference 5. Black 39 and 41 were slow-refer to Reference 6. Black 45 is instructive in how it attacks the weakness of white 38.
Reference 5 : If white 1, black 2 and 4 strengthen him in sente after which black 6 becomes possible. After the sequence to black 12, White is in trouble.
Reference 6 : Black should play at 2. White's natural move is 3, but then the sequence to black 12 follows and the marked white stones die.
Problems
These problems are related to Diagram 2 above.Problem 1 : Instead of 41, playing one space higher at 1 seems to give Black more agility. However, a keima (knight's jump) is weak. How can White counter this ?
Problem 2 (refer to Diagram 2) : White 52 defends against a black cut at 56 but exposes him to a black kikashi at 53. Why not simply play at 56, or better at 53 to take sente ?
Problem 3 (refer to Diagram 2) : In response to 64, why doesn't Black simply play in between 61 and 63 instead of 65 and 67? Don't these moves strengthen White ?
Problem 4 : After black 3, the moves 4 to 12 form a middle-game joseki. How should Black defend against the cut at A ?
