10 practice problems (capturing, escaping, living)

The two white stones at the top center have only one liberty: the point to their right on the top line. They are in atari, so playing there captures both. Their worried faces give it away.

The black stone's only liberty is the point above it. Extending there connects it to the three black stones above, making a group with plenty of liberties. It can no longer be captured right away.

The six white stones running from the center to the bottom left form a big group, but they have only one liberty, at the top. However big a group is, it can be captured when it has just one liberty. Black 1 also puts the white stone in the top left and the two white stones in the top right in atari.

Black 1 joins the four black stones on the left to the black stones on the right. At the same time, the four white stones at the top are left with a single liberty at the top: they are in atari. White cannot escape there, because a white stone played on that point would have no liberties, so the move is not allowed. Next, Black plays there and captures four stones.

The stone in atari has only one liberty, the point above it. Extending there connects it to both the black stone above and the black stone to the right, giving it plenty of liberties. When you escape, heading toward your own stones is the safest direction.

The black stone in atari has one liberty, below it. That point is also the last liberty of the two white stones next to it. So Black 1 is both the escape and a capture: the captured stones leave empty points that become Black's liberties, and Black is safe. Whenever you are in atari, check whether your opponent is in atari too.

The two white stones have two liberties, both below them. The lower-right liberty is next to a white friend, so block that side when you give atari. If White runs to the lower left, it is surrounded by black stones there and gains no liberties. Block the side where their friends are.

The black group has three connected empty points inside, in a bent shape. Black 1 leaves two separate points, one above it and one to its left: two eyes. With two eyes, this group can never be captured. If White takes the vital point first, Black cannot make two eyes, has no liberties outside either, and will eventually be captured.

This is a snapback (also explained in “Capturing and escaping”). The three white stones had two liberties: the point where Black 1 goes and the point below it. After Black 1, White 2 can capture it, but the resulting four-stone group has only one liberty, the point where Black 1 stood. Playing there again with Black 3 captures all four. If White does not capture Black 1 and plays elsewhere, Black plays the point below and captures three stones.

The white group has two empty points inside, but they are next to each other, so they make only one eye. The danger is the worried-looking black stone on the left: it is in atari, and if White captures it, White's inside grows and it can make two eyes. Black 1 captures the single white stone and moves inside, which also saves that black stone. Even if White 2 puts the black stone in the top right in atari, Black 3 captures White 2, and White has nowhere to make a second eye. Once its outside liberties are all filled, this white group is captured.