Eye versus No Eye Capturing Race
In a fight where one group has one eye and the other group has not, seki is not possible and in the majority of cases the group with one eye wins. We calculate the capturing race as follows:
The group with eye counts its outside liberties, its eye liberties and the inside liberties. The group without eye counts its outside liberties. The threshold thus becomes
- OL1 + EL1 + IL = OL2
If the numbers are equal, the one who has sente kills the other. If one number is larger, the other party is dead already. The reason why eyes win semeais is that all inside liberties go to the group with the eye.
At first glance Black seems to have more liberties than White (6 against 5). When we apply the theory, however Black cannot win the race even if playing first. a + b + circled points yields 5. The c points yield 4.
There is a second way in which eyes influence semeais, less well-known (and in general also less important). The following diagrams show how it works. Black and White both have four dame.
Black has an eye and White does not, but at first sight that does not seem to matter, because there are no shared liberties. Nevertheless, White is not able to win the capturing race, as this diagram shows.
The reason for this is the approach move that White has to make, with . At first sight, Black has a similar approach move problem at a. However, this problem does not worry Black, who can simply solve it by making b the last liberty that Black fills up. White, on the other hand, is forced to play the eye as the last move - so White has to make the approach move first. Stating this as a rule:
- If there are no shared liberties in a semeai, each player can omit the necessary approach moves for one liberty, but not if his/her opponent has an eye.
A complicating factor is that when there are big eyes (four spaces or more), the number of liberties also is higher than a naive count would suggest. See Four Is Five And Five Is Eight And Six Is Twelve or counting liberties for this effect.
See also the pages in the Eyes Collection.
Authors: Morten Pahle (10 kyu), Arno Hollosi (1 dan), Andre Engels (2 dan), Dieter