Humans love to conquer. To deepen their insight into military warfare, Chinese generals in the past played go and actively used its strategies to gain the upper hand. The urge to conquer is still alive and kicking in the business world. The Japanese way of doing business often drew on excluding others by increasing market share-that, rather than short-term profits, was a formula for success until recently, when Japan finally opened its economy and realized that inefficiencies must be worked out of the system.

But the success formula of market share expansion is the reason why go has received a lot of attention from businesspeople, both in Japan and overseas. Playing go is an excellent way to exercise the brain in areas where it is used for business. It offers a kind of virtual-reality excitement and relaxation at the same time, as players chase, deceive, threaten and kill without hurting a soul.

We have learned some technical rules for capturing stones and are ready to discuss the most important aspect-how to win.

Concept of territory

Diagram 1 : Each of the groups of stones in the upper right, upper left and lower right have encircled some points. We call these areas "territories." In this example, the black group in the upper right has nine points, the one in the lower right has five and the white group in the upper left corner has eight points.

Note: Notice that all groups here consist of seven stones. Obviously, the group in the upper right uses stones most efficiently, while the one in the lower right is the least efficient in making territory.

Diagram 2 :This is a sample game-In all of the 53 moves, no stones were captured. This made counting easy.

Diagram 3 :This is the end result. How many points do Black and White have each ?

Black : Upper Left's nine points plus Lower Right's six points equals 15 points
White : Upper Right's six points plus Lower Left's seven points equals 13 points

According to this system of counting, Black would win by two points. Usually though, White receives compensation for Black playing the first move. The compensation depends on an agreement between the two players or is in accordance with tournament rules. This compensation is called "komi" and usually amounts to five to seven points. While physically impossible to prevent draws (jigo), the komi often is set at 5-1/2(harf).

If we follow this komi system, then the game shown here would have been won by White by 3-1/2(harf) points.

Diagram 4 : In fact, territory is not the only thing that is counted-captured stones are counted as well. In this example, the three white stones can be captured at any time by Black. For example, even if White moves first, these stones have no chance. At the end of the game, Black doesn't need to spend an extra move to capture these stones as they are dead already and the three white stones are taken off the board.

Diagram 5 : This is the end situation with the captured stones removed. Black has seven points in territory plus three captured stones, making a total of 10 points.

Diagram 6 : Here, the premise is that the three white stones can be captured at any time. But who decides whether stones are dead or alive? And ultimately, the question is, what is territory? In this diagram, some may argue that the white stone in the corner can be captured at any stage and therefore should be proclaimed dead. Others may insist that it is the black group of four stones that is dead as it has no chance to escape. So what is the truth ?

Diagram 7 : Let's assume it is Black's turn. Indeed, he can capture one stone now by playing at 1.

Diagram 8 : However, that is not the end of it, because now White can capture five black stones by playing at 2. Do not confuse this with ko, where a situation is repeated endlessly if played. In this diagram, the situations after each move (black 1 and white 2) are different.

Diagram 9 : This diagram shows a more complex version where the white stones in Diagram 7 are also surrounded. Let's assume it is Black's turn. Who is dead and who is alive here ?

Diagram 10 : Let's try to solve the puzzle layer by layer. First of all, Black captures one white stone.

Diagram 11 : Next White captures five black stones.

Diagram 12 : In the last step, Black plays at 3 and captures all of White's stones. We will look at this situation in detail next week. However, before that, try to figure out how White can capture the black stone, but in the end will be captured by correct play by Black.

Solutions to last week's problems

Solution 1A : White can only hope to win by freeing the marked stones. Using the technique we learned about last week, White starts a ko with 1. Black can capture (no repetition), but White first has to play somewhere else to recapture. White 3 threatens to capture one black stone. Connecting with 4 is natural, but..........

Solution 1B : White can recapture the marked black stone with 5. Black 6 needs a response at 7 (otherwise White cuts there), and.......

Solution 1C : Black captures the marked stone again with 8. White 9 threatens to kill the whole black group and forces Black to respond with 10.......

Solution 1D : White 11 takes the marked black stone. Black plays a ko threat at 12. But it is too small.

Solution 1E : White connects the ko by playing at 13. He has thus saved his stones in the upper left. After black 18, there are still a few moves left to play. Close all the holes in the various territories and try to play the game to the end. Also try to find out what the approximate score would be.

Solution 2A : White can start a ko with 1. Black captures first, but White has a ko threat at 3. If Black compromises by taking the two marked stones with 4, white 5 captures two stones while threatening the black upper left corner. Therefore, Black has to defend with 6. We can now envision the end game moves through black 16.

Black has 14 points in territory, plus he has captured 3 white stones, which leaves him with 17 points. White has 19 points in territory plus 2 prisoners, leaving him with 21 points. Including komi, White easily wins.

Solution 2B : As Black loses in the previous variation, he may want to resist with 4 and 6. But White captures the marked black stone with 5 and then three more black stones with 7. Try to count what the score is by filling the holes in the territories.

New Problems

Problem 1 : How does White respond to black 1 ?

Problem 2 : Look at Diagram 12 and figure out why White will be captured in the end. (Hint: Fill the liberties first from the outside.)

Problem 3 : Look at Solution 1E and figure out the score.

Problem 4 : Look at Solution 2B and figure out the score.