Diagram 1: (This is also the solution to last week's problem: Where should Black play after White's last move at A.)
Black 1 and 3 are important moves. Let's see what these moves do. First, they make a base for Black's marked stones. Second, they take away the possibility for White to make a base for his stones (A and the stone marked with a cross). Third, they threaten to attack those stones with the next move. Fourth, Black has now strengthened himself so that he can also attack the white stones marked with triangles. And finally, they make territory and take it away from White. The territory difference might only be 15 points or so, but the preceding four points have a strategic meaning. See Reference 1 for what happens if Black keeps attacking. After black 3, White has to choose: will he defend the stones marked with triangles, or will he defend A and the crossed stone? O decides that his bigger group is more important and plays at 4.
Reference 1: Many people probably would want to attack and play at 1, which makes some territory for Black. However, that would allow White to take the key point at 2. Black can now attack with 3 through 7, but after the exchange white 8 for black 9, White may counter with 10. This means that Black would come under attack, as White's position at the bottom (marked stones) is now strong. In the worst case, White can always play at A, followed by black B, white C, black D, white E, black F and white G, to ensure life.
Diagram 2: After white 4, Black invades at 5, which is also an attack as it splits White's position. White 6 and 8 form a good combination. These moves defend against an invasion at A (see Reference 2) while pressuring Black's marked stones. And, as an extra bonus, these moves make about 15 points of territory. Black 9 is a great move because White is forced onto the second line to connect. Usually that is painful. A rule of thumb for evaluating which player is leading is to count how many stones each player has on the second or, even worse, on the first line. The player with more stones on those lines is lagging behind. Another evaluation method is to count the total number of groups each player has. The person with fewer groups is leading. However, to make an accurate evaluation, you have to take into account the amount of territory each player can expect and how weak their stones or groups are.
Problem 1: Who do you think is leading? (White gets 5.5 points komi, or points compensating for Black having the first move.)
Problem 2: Now that Black has strengthened his marked stones, what should he do to fully exploit this development?
Reference 2: If White is not careful and plays elsewhere, Black will invade at 1. White would usually block at 2, forestalling a Black connection at that point. Black can then play at 3, and if White blocks with 4, Black can cut with 5 and 7. Without the marked stone, White can kill the black intruders with A, followed by black B, white C, black D, white E, black F and white G. Because of the presence of the marked stone, however, White has to save his two stones beneath 7 first, allowing Black to take the corner.
Diagram 3: As shown in Diagram 2, Black is strong on the right side. To fully use that power, attacking with black 1 is best. This deprives White of a potential base here, while scoring a lot of points by capturing the white stone marked with a cross in the sequence to 7. White has to take flight with the two stones marked with triangles so he has to play 8. Black 9 was a problem move.
By the way, the answer to Problem 1 is that Black is leading, although the territorial balance is about the same. Black is thick overall, and White has two fairly weak groups. Also, White has nine stones on the 1st or 2nd line while Black has only five.
Problem 3: Instead of 9, where should Black have played?
7-stone handicap
Diagram 4: This is the sixth article in a series of discussions on the 7-stone handicap game. We have been looking at the kakari (approach) of white 2 and several replies by Black. When playing with a handicap, it is important not simply to choose a joseki (standard corner exchange), simply because it is in a book. The most important thing is to think about the rest of the board, e.g. the marked stones, and consider how you should select a joseki to fully utilize those stones.
We started out with a White response at A, and looked at a double-kakari at 4. The pincer at 3 is a popular move.
Diagram 5: The moves shown here used to be a popular joseki. We already looked at the moves to 8 with a different answer by Black. In this case, Black resists with 9 and White cuts through with 10 and 12. Black should not try to save his corner stones. He should sacrifice them by playing at 13 and 15. After this move, White has two choices, playing at A or B.
Diagram 6: After black 15 in Diagram 5, White can play 16, followed by black 17, then defend with 18. Black can later play at B, followed by white C, black D and white E, or alternatively, Black can play at A to dominate the center.
Diagram 7: After Diagram 5, White can also play at 16 immediately, without exchanging A for B. Compared to Diagram 6, there are two differences to be considered. The first is that if the center becomes important, a White move at C becomes a good one. Next, he can play at D to put the two marked black stones in atari. In this variation, building influence is not Black's privilege anymore, as it was in Diagram 6. The second difference is described in Problem 4.
Problem 4: If Black plays at 1 (similar to B in Diagram 6), White should not block at 2. If he does, how should Black proceed? The answers to this problem and Problem 3 will appear next week.