# Maximum unfillable points in seki question

How might we construct a 'single' seki to maximize the number of points that neither player wants to play in? (Note for example that a simple no-eye seki may have more than two shared liberties to start out with, but either player may reduce the count to 2 without danger, so I count this as a "score" of 2 regardless)

We need some terminology here:

"string" has the usual formal meaning.

I will use "dangerous point" to mean one of the liberties which causes the seki to be seki: i.e., a point such that, if filled by either player, renders one or more of the second player's strings alive at the expense of some string(s) of the first player.

By "single" seki I mean one such that a play at any dangerous point, followed by its response, renders every string in the seki either dead, or alive with points.

Then I see the single seki with the maximum number of dangerous points. I am aware of a 4-point example, see at bottom of cutting seki. Can we do better? The example on seki example 1 is not single as it is possible to sacrifice some of your groups while having others remain in seki.

Challenge offered by Karl Knechtel.

Warfreak2: Arbitrarily many, as long as the board is big enough to hold them. Repeat the pattern as many times horizontally as you like (equivalent seki can be constructed on more normal board sizes). By your above definition, this is a single seki (although intuitively, it is two).

Bass: In Warfreak2's example no chain has more than two liberties, and no chains share more than one dangerous liberty. Robert Pauli appears to have invented a way to construct a multi-way seki so that both of these numbers also approach infinity. It may also be possible that the liberties are not dangerous, but that is yet to be proven :-)