Big P

Big P  

At first glance, Black seems to have 6 points of territory. However, if there are no outside liberties then threatens to leave Black with a group that White will eventually reduce to bent four in the corner, and Black's responses either let White-to-move make seki or let White-to-move make ko. To prevent both of those, Black can turn the corner into 5 points of solid territory with . (Black has other ways of doing that, but leaves no ko threats.)

White's threat

if is elsewhere  

If Black ignores , then White's followup is , after which the best Black can do is getting a group that White will eventually reduce to bent four in the corner.

Black's choices

i is inferior  

If Black plays the next move inside, then Black does so at s or k. i is an inferior way of limiting White to ko.

if Black chooses s

possible seki  

makes seki. lives with 5 points under territory scoring, which is the same number as if Black had played at . (Black playing at k also does that, but leaves no ko threats.)

if Black chooses k

possible ko  

lives with 5 points under territory scoring, which is same the number as if Black had played at . at-least-basically starts a direct ko.

direct ko line  

If is tenuki, then White chooses between playing anyway, in which case Black got an extra move outside and it's White who needs to find the first ko threat, and playing at , in which case White will eventually reduce Black's group to bent four in the corner.

ko threats  

If there is at least one outside liberty, then Black is alive with 5 points under territory scoring.

what Black hopes for with i  

hopes for this sequence, in which it's White who will need to find the first ko threat. However, White can do better.

correct direct ko after inferior move by Black  

If White does not want any complications, then White continues as if Black had chosen k. (The diagram's line of play transposes back to that ko line.) If is tenuki, then at this diagram's kills outright, without needing eventual reducibility to bent four in the corner to mean death. (In that case, as in this digram does the same thing, but at this diagram's leaves no ko threats.)

Furthermore, makes Black's threatened followups smaller, because:

inferior move by Black  

Black-to-move has no way to live outright without seki.

approach ko after inferior move by Black  

Although White will need one approach move, Black-to-move also can't win this ko outright.