Two liberties
In my games, I've noticed that nearly as important as atari is when a group has just two liberties. What kind of liberties they are determines whether they're safe.
When a group has just two liberties, unless both are eyes, it is one move away from being in Atari. In all of the below discussion, I assume that the groups don't have two eyes.
Make sure that your group can be saved, even if either liberty is taken.
Basic Example
This group has two liberties, a in the northwest and b in the south.
Black can defend an attack from the northwest...
... but not from the south. The black stones die, because if Black tries to escape with , White can capture with
.
More Examples
Three examples are inspired by my own games:
The stones are dead. My kosumi was half-cut by the
stone, and cut by
. If White responds at a, Black will capture at b.
After , the white stones are dead. If White plays at a, Black will capture at b. (See shunt.)
W moves at . What happens if Black moves at a?
Black loses eight pieces, because he lacks liberties.
Ladders and Nets
Many situations are related to having just two liberties.
In a ladder, an attacker repeatedly reduces a group of stones from two liberties to one liberty.
A simple net keeps the number of liberties to two or less.
White has two liberties. If white moves to either a position, black will reduce white's liberties by moving to the nearest b position.
Double atari
A double atari can occur when two groups with just two liberties share a liberty that's not an eye.
Ko threats
Every group with just two liberties (not both eyes) can be used as a ko threat.
Auto-atari
Auto-atari can only happen when your group had two liberties, you move into one liberty, and you gain no more liberties. In this diagram, I chased after , only to discover...
... that I hadn't counted my liberties.
Same shape, different order.
A snapback is a specific kind of auto-atari.
See also:
Alex Weldon: Even three is not enough, quite often.
Here, White can be captured in geta with a Black move at a.
In fact, see Five liberties for tactical stability.