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Dia. 3

No. White has completely surrounded two separated liberties. If black attempted to play on either point inside the white enclosure his stone would have no liberties, while white would still have one liberty. The invading black stone would be smothered as soon as it touched the board. The white stones cannot be surrounded completely (outside and inside) because black cannot occupy white's inside liberties.

To Escape or Not to Escape...!

Stones that retain one or more liberties but have no hope ultimately of keeping any liberties are said to be dead as they stand, or simply dead. Stones that are dead as they stand remain on the board as long as they retain even one liberty (unless the game is finished, in which case dead stones will be removed as prisoners).

Problem: Do the black stones appear to be dead as they stand in the diagrams below?

Dia. 4

Answer:
Yes. There is no escape for this black stone, yet it remains on the board because it has one liberty.

Dia. 5

Answer:
No. Black can add more stones to these connected stones in order to guide them toward the open area of the board, where they may be able to enclose territory. (With his turns, white may well attempt to block black's access to new liberties).

Dia. 6

Answer:
Yes. These black stones are very well enclosed. Black cannot surround any points or capture any white stones. However, white can fill black's four liberties without endangering any white stones.

Thus, we see that stones can die from being loosely surrounded even if they are not absolutely smothered. Stones die when all their liberties can be taken, whether they are taken immediately or not.

Problem: How many black stones appear to be dead as they stand on the following abbreviated boards? (Hint: Count the liberties of each unit involved. The one with more liberties overpowers the one with fewer liberties.

Dia. 7

Answer:
One. The black stone in the upper left corner is trapped and white need only fill two liberties to remove it. Adding another black stone to it will not increase its liberties or help it escape.

Dia. 9

Answer:
Three. The two black stones in the upper left have no prospect either of escaping or of enclosing territory. Also, the black stone near the center of the board has only one liberty, while the two enclosing white stones beside it have two liberties.

Problem: In each of the two diagrams above, how many white stones are dead as they stand?

Answer: Diagram 7
Three. The single white stone in the lower right corner has only one liberty. The two connected white stones in the lower right corner have only one liberty. Each black unit has more than one liberty.

Answer: Diagram 8
Three. Black's liberties overwhelm those of white in the lower right corner and in the upper right corner. White can neither escape nor surround safe liberties there.

Two Eyes

A point fully enclosed by one color is called an eye. A group of points fully enclosed by one color is also an eye. Stones live by shaping an enclosure of two eyes; stones that can form only one eye, or none at all, eventually come into atari. Enclosures with two eyes always have at least two liberties and thus cannot be captured.

The following examples show some formations with two eyes and some without.

Problem: Is white alive or dead in each case below?

Dia. 9

Answer:
Alive. This formation has two eyes, one enclosed area of two points and one enclosed point in the lower right. Even if all the outside liberties are filled by black, white will never come into atari.

Dia. 10

Answer:
Dead as they stand. White has one eye and no escape route. If necessary black can fill points A, B, and C to remove the white stones.

Dia. 11

Answer:
Alive. White has two eyes; black cannot occupy either of the white liberties without placing a stone on the board that would have no liberties after the play is completed.

Dia. 12

Answer:
Dead. Black has wisely placed inside white's single eye a stone that occupies the only point by which white could have separated the enclosed area into two eyes. If white plays at either A or B he will leave his stones with only one liberty, in atari. Confirm that black can bring white into atari by adding another black stone at A or at B. If white then captured the two black stones, black would simply place another stone inside white's eye, finally leaving white inescapably in atari.

Of course, if white had played first on the point occupied by the single black stone, then white would have two eyes.

Dia. 13

Answer:
Alive. If an enclosed area is large enough, then it can be separated into two distinct eyes anytime it is necessary. In this case white has enclosed a single area that can be separated into two eyes with a white stone either at A or at B. If black took one of these points and white took the other, then black could not place another stone inside the white enclosure due to a shortage of liberties.

If, however, white allowed black to occupy both A and B, then white could no longer make two eyes and would die:

Dia. 14

In attempting to approach the two black stones now, notice that white would have to place his own stones into atari. Black can bring white into atari at any time by adding another black stone, allowing white to capture three stones, and then occupying white's vital point as in Diagram 12.

So we see that in order for his stones to keep liberties, a player must enclose at least two eyes, or enclose an area large enough to be separable into two eyes despite opposing effort. As you play, the concept of eyes will become clear.

Congratulations! You have now learned the alphabet of go. The principle of liberties is the basis for the whole game.

Chapter Three

Ending the Game

There are four goals in go: (1) surround territory, (2) reduce your opponent's territory, (3) capture enemy stones, and (4) protect your own stones. The winner, on balance, has always accomplished these goals more efficiently than the loser.

Tying Up the Loose Ends

The game is ended by a pass of turn by each player in sequence. Saying "I pass" means that you see no opportunity to further any of the four goals above. Passing presumes that all the claimed territories are completely surrounded (all fence sections are in place), and no stones are in atari along the borders formed by the opposing stones.

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