As we saw last week, the value of ...

By Rob Van Zeijst

As we saw last week, the value of stones in a go game is dramatically different. Some have a huge value because they enable a group to live, while others barely make a contribution or even have a negative value, as in the case of stones that are dead but have not yet been captured. Naturally, players generally want to play moves that have a high value. Nothing wrong with that, but to become a stronger player, it is better to look for different types of move. A regular valuable move may be worth 10-20 points by itself, but a move that also enhances the value of the stones around it, is a gem. Such a stone can have a value of as much as 100 points. With the exception of stones that enable a group to live or to make it die, stones that serve multifunctional purposes are most important as they offer such a high return.

Diagram 1 (moves 51-66):Last week, we started this game between Masaki Ogata, 9-dan, and current Honinbo titleholder Shinji Takao to see how the value of moves changes.

We also introduced QARTS, a system that expresses quantitatively how much a weak group is worth. A weak group without eyes is worth about minus 20 points, while a weak group with an eye would be worth about minus 10 points. So reinforcing a weak group by making a base or rendering your opponent's group eyeless, is worth about 20 points. That is the reason why moves close to a weak group are so valuable--they have the potential to fulfill both of these functions and can be worth as much as 40 points. At this stage, both Black's and White's marked stones are weak. Black 1 and 3 safeguard the corner while keeping White weak. While black 7 defends, its main purpose is to take away White's eyes. Without a base on the right, White must move into the center with 8. Since neither player can make two eyes on the right, the escape route to the center becomes all-important. Black 9 is an important point. White 10, 12 and 14 make eyes and a few points, but black 9, 11, and 13 make some territory while building up center strength. Black 15 is a strong move (see Solution 2), while white 16 has a special purpose (see Reference 1).

Reference 1: White's marked stone aims at cutting with 9, 11 and 13. However, before doing so, a preparatory combination at the lower edge, such as 1 through 7, makes the split between Black's marked stones even more effective.

Diagram 2: As shown in Reference 1, Black should reinforce on the left, which he does with the moves through 23.

It is difficult to evaluate 24 and 26, but White is still aiming at Black's stones on the left. Exchanging black 29 for white 30 is worth a few points. Without this exchange white A would be a good move. However, if White plays at A after this exchange, Black can play at B, followed by white C and black 36. This takes away a lot of White's territory. However, White makes up for this by exchanging 36 for 37. Even if the territorial value is only slight, White now has definite eyes and is alive. This is worth a lot of points.

Solutions to last week's problems

Solution 1: Invading just anywhere on the right is not good enough.

White 1 is the ideal point because it spoils Black's eye shape and turns the marked stones into a target for attack. In a few moves, Black's stones have become weak while White's have a base and even make a few points in territory. According to the QARTS system, a success like this would be worth at least 40 to 50 points: 20 points for turning Black's stones into a weak group, 20 points for White building a strong group (as compared to a weak, eyeless invasion group), and about 10 points for the actual territory White makes. Since this result is so bad for Black, he will probably start a battle at A or B, rather than connect at 2.

Solution 2a: White should play at 1. This move has multiple purposes. First, it is an extension from the lower left. Second, it threatens to cut through with the sequence white A, black B, white C, black D and white E. If Black defends with the sequence 2 through 8 as in the game, White strikes with 9 through 13, the third raison d'etre for white 1. After this combination, White has built up a tremendous framework around the marked area, while Black's group in the lower right is still without two eyes.

Solution 2b: Black 1 is an extremely strong move--not because of the territory it makes around the marked spots, but because it prevents an attack on Black's group at lower right. It also aims at extending to A next, although Black can extend to B at this point. However, A and B are territorial moves, while 1 reinforces a weak group. Finally, black 1 is a good move because it indirectly defends against the sequence white C, black D, white E, black F and white G. After black 1, this cut has less of a sting.

Van Zeijst is a four-time European go champion and European representative at the Fujitsu World Championship.