If neither side has any eyes, then only the side with more outside liberties can win. The side with fewer outside liberties must hope for seki. The side with fewer outside liberties gets to add the shared liberties – 1.
In this example, black has 5 outside liberties, while white has only 2. However, white can add the 5 – 1 shared liberties, to give a total of 6. This means that white is winning the capturing race 6-5, and can safely tenuki (in other words, even if black plays first, white can still get a seki).
One eye vs no eye
In the situation where one group has one eye, and the other group has no eye, seki is not possible. In this situation, the group with the eye counts all the shared liberties.
In this example, white has the eye, and thus has 7 liberties. Black has 7 outside liberties. In this case, whoever moves first wins the capturing race.
Eye vs Eye
In the case of an eye vs an eye, the shared liberties belong to the side with the biggest eye. Very important: a one space eye, a two space eye, and a three space eye all count as equivalent size. Note also that if the eyes are differently sized, there can never be a seki.
There is also a set of counting rules for counting the additional liberties of large eyes. The rule is as follows:
1 space eye, 2 space eye, 3 space eye – no extra liberties
4 space eye – 1 extra liberty
5 space eye – 3 extra liberties
6 space eye – 6 extra liberties
In this example, black has 12 liberties (3 inside the eye, plus an additional 6 because it is a 6 space eye, as well as the 3 shared liberties, which belong to black because black has the bigger eye). White has 11 liberties (3 inside the eye, plus an additional 3 because it is a 5 space eye, as well as the 5 outside liberties). So if it is black’s turn, black can tenuki.