<prev | next>

Problem: Is black ready to pass in the following diagrams?

Dia. 1

Answer:
No. White's wall is incomplete. Black can push into white's territory through the gap in white's wall. Also, the lowermost black stone is in atari; black can save it from capture by connecting it to the neighboring black stones. Black must decide which of these two plays is more valuable.

Dia. 2

Answer:
No. Two stones are in atari, one white and one black, and the walls formed by the stones are incomplete.

Dia. 3

Answer:
Yes. This example may look confusing at first since it brings together all the concepts discussed so far. We will simplify it by looking at it one step at a time:

Look at the two white stones in the upper left corner. They have two liberties, no eyes, and no hope of capturing any black stones, so they are dead.

Next look at the two black stones in the upper right corner. They also have only two liberties, no eyes, and no hope of capturing white.

Black's living stones are connected through the middle of the board. Black has an eye in the lower right corner and another in the upper left corner.

Notice that white has two enclosures, one in the upper right and one in the lower left. White's enclosures are not connected to each other through the middle of the board. Look to see that white has two eyes in each of these enclosures. In the upper right there is one eye in the area where the two dead black stones lie and one eye of two points just to the left of that. In the lower left corner, the single white stone divides that enclosure into two eyes.

Notice that no stones are in atari along the territorial borders. All the walls are complete, blocking out the opposing stones.

Problem: In each of the three diagrams above, is white ready to pass?

Answer, Diagrams 1 and 2: No.
Diagram 3?
Yes. The game in Diagram 3 is finished. If either side decides to fortify its defenses further, it will merely occupy its enclosed points with its own stones, thereby reducing the surrounded territory.

As the game progresses, outside liberties become less and less important and enclosed points become all-important. Often there remain between the opposing stones some vacant points called dame (dah meh), that neither side can exclusively enclose. Dame are neutral points, owned by neither side. The players continue filling dame in turn until all the points remaining on the board are completely enclosed by one side or the other.

Problem: How many dame are there in Diagram 3?

Answer:
One. Neither side can surround point X completely.

Reaching Agreement

After one opponent passes, the other may still play, in which case the turns continue until both pass in sequence. Then the players must agree with each other about the status of each unit on the board (whether it is alive or dead as it stands). If they cannot agree, then the play resumes until the situation becomes completely clear to both. In every case continued play will resolve any questions by steadily reducing the number of liberties. Eventually each unit will either lose all its liberties or it will enclose only safe points.

Another way to end a game is by resignation. A player voluntarily resigns a game that has become lopsided and uninteresting to his opponent. If you lose too many stones, simply resign and begin another game.

Scoring

Verify that all dame have been filled (with extra stones, not with prisoners). To count the score, remove from the board all stones that are dead as they stand and add them to the prisoner collections. Now count each vacant point as one point for the side that has surrounded it. Subtract one point from black's score for each black prisoner and subtract one point from white's score for each white prisoner. The winner is the player who has more points.

Problem: How many dame are there in the following completed games?

Dia. 4

Black has one white prisoner.

Answer:
Three. Confirm that either black or white stones may occupy the dame here without affecting the number of points either side has surrounded.

Dia. 5

Black has one white prisoner.
White has two black prisoners.

Answer:
One.

Problem: What is the final score in each of the two previous diagrams?

Answer, Diagram 4:
Black seven, white six. Black wins by one point.

Answer, Diagram 5:
Black fifteen, white nineteen. White wins by four points.

Now it is easy to see why enclosed points are vital -- not only do they enable stones to live, they determine the final score.

Chapter Four

The Rule of Ko

The word ko means eternity. In go, a ko refers to a common position that would allow an endless series of meaningless plays if there were no rule to cover the situation. The example below illustrates the ko position.

Dia. 1

Notice that the single black stone, separating the upper white stones from the lower white stones, is in atari. This situation is of considerable importance to both sides. The upper white stones are dead as they stand if they cannot connect to the lower white stones. However, if white can manage to connect, then black will relenquish three enemy stones and the points they occupy.

White can capture the single black stone by playing on point K and taking its last liberty.

Dia. 2

Now the single white stone is in atari and it is black's turn to play. It appears that black can recapture the white stone by playing on point O immediately. Then white can recapture by playing on K (first diagram). Then black can recapture, then white, then black, and so on. In order to prevent this meaningless sequence, a player may recapture in ko only after making at least one play elsewhere. After he has played on another point he may place a stone on the ko point. This simple rule prevents a possible stalemate.

Problem: In the diagram below, assume that black has just captured a white stone from point K.

Dia. 3

Problem: Can white recapture with his next move?

Answer:
No.

Problem: Where must white play?

Someplace else on the board.

Problem: What could happen if the rule of ko were not in effect?

Answer:
The game could not proceed if both players insisted on capturing and recapturing and neither would play elsewhere.

The concept of ko will become clear as you play. Now you are ready to apply your knowledge of go in a real game.
Go for it!

<< prev | next >>