Liberty
A liberty of an isolated stone or a group is an unoccupied cell adjacent to it. A stone or group with few liberties is generally weaker than one with many liberties.
Advice for players
Old advice
An older version of this page, dated 2005, contained the following advice:
- Do not play an isolated piece with three or fewer liberties. Such a move is always a bad move — it is always possible to find a better one.
The advice is not accurate. We now know that there are some situations where playing a stone with 3 liberties is the unique winning move (see here for an example). Nevertheless, it is still a useful guideline in most situations that arise in real games.
Updated advice
Below, we analyze groups with up to 3 liberties. Based on the analysis, we can formulate the following principle:
- Do not play a stone that creates an interior group with 2 or fewer liberties, or with 3 liberties when two of them are adjacent or bolstered.
Analysis of groups with up to 3 liberties
Definitions
By an interior group we mean a group of friendly stones that is not adjacent to an edge.
A liberty L of a group X is said to be bolstered if it matches one of the following patterns (up to rotation and symmetry):
Groups with one liberty
If an interior group has only a single liberty, the group is dead. It can never become part of a shortest winning path for the group's owner.
Examples:
In both cases, the red group has a single liberty and is dead.
Groups with two adjacent liberties
If an interior group has only two liberties, and these liberties are adjacent to each other, the group is dead.
Examples:
In both cases, the red group has two adjacent liberties and is dead.
Groups with two bolstered liberties
If an interior group has two non-adjacent liberties, and both of these liberties are bolstered, the group is captured. If the group's owner plays in one liberty, the opponent can play in the other, killing the group.
Examples:
Groups with two general liberties
If an interior group has two non-adjacent liberties that are not both bolstered, then the group is not in general captured. If one of the liberties is bolstered and the other is not, playing in the non-bolstered liberty dominates playing in the bolstered one for both players.
Examples: Both players prefer "a" to "b".
For all groups with two general liberties, if it is the opponent's turn, they can kill the group by taking away one of the liberties. Therefore, no player should play a move that creates an interior group with only 2 liberties.
Groups with three liberties
If an interior group has 3 liberties, it is not in general captured.
Examples: Three non-adjacent liberties, zero or one of which are bolstered.
However, if two of the liberties are adjacent or bolstered, then if it is the opponent's turn, the opponent can kill the group by playing in the remaining liberty. Therefore, no player should play a move that creates an interior group with only 3 liberties of which two are adjacent or bolstered.
Examples: Two of three liberties are adjacent or bolstered. Blue can kill the red group by playing at "a".
