# Eye liberties

Keywords: Tactics

Chinese: 眼气 (yǎn qì)
Japanese: 呼吸点 (kokyuten)
Korean: -

A group involved in a capturing race may have an eye. The liberties provided by that eye are called eye liberties. Here, "liberties" is used in its capture metric liberty meaning.

Small eyes (one to three points) have as many eye liberties as their number of empty spaces, less the number of opposing stones inside. See small eye liberties.

Big eyes (four to seven points) have more eye liberties than their number of empty spaces. See big eye liberties.

The player who knows the sequence for liberties as a function of eye size (1, 2, 3, 5, 8, 12, 17) has an advantage over a player who has to read the capturing race. The general formula for an eye of size n (for 2 <= n <= 7) is

L(n) = {n(n-3)}/2 + 3

Subtract the enemy stones inside to determine the number of eye liberties remaining.

Instead of using that formula it might be easier for some players to remember: “3 is 3, 4 is 5, 5 is 8, 6 is 12”. The first number is the size of the eye in question; the second number is the amount of liberties it is worth before(!) an enemy stone is placed inside. To memorize this read it out loud repeatedly.

Another possibly easier way to remember the number of eye liberties in an empty big eye is:

The smallest big eye (4 points) has 1 extra liberty, total 4 + 1 = 5.
The next big eye (5 points) has 1+2 = 3 extra liberties, total  5 + 3 = 8 .
The next big eye (6 points) has 1+2+3 = 6 extra liberties, total 6 + 6 = 12 .
The largest big eye (7 points) has 1+2+3+4 = 10 extra liberties, total 7 + 10 = 17.