Big P

    Keywords: EndGame

The Big P is a corner shape that can be turned into a ko or a seki because of the special properties of the corner.

[Diagram]
Big P  

At first glance, Black seems to have 6 points of territory. However, if there are no outside liberties then white+circle 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+circle. (Black has other ways of doing that, but black+circle leaves no ko threats.)


White's threat

[Diagram]
if B2 is elsewhere  

If Black ignores W1, then White's followup is W3, 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

[Diagram]
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

[Diagram]
possible seki  

white+circle makes seki. black+circle lives with 5 points under territory scoring, which is the same number as if Black had played B1 at W1. (Black playing at k also does that, but black+circle leaves no ko threats.)


if Black chooses k

[Diagram]
possible ko  

black+circle lives with 5 points under territory scoring, which is same the number as if Black had played B1 at W1. white+circle at-least-basically starts a direct ko.

[Diagram]
direct ko line  

If B6 is tenuki, then White chooses between playing W7 anyway, in which case Black got an extra move outside and it's White who needs to find the first ko threat, and playing W7 at B6, in which case White will eventually reduce Black's group to bent four in the corner.



Outside liberty

[Diagram]
ko threats  

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



Black's inferior attempt at ko

[Diagram]
what Black hopes for with i  

B2 hopes for this sequence, in which it's White who will need to find the first ko threat. However, White can do better.

[Diagram]
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 B6 is tenuki, then W7 at this diagram's B6 kills outright, without needing eventual reducibility to bent four in the corner to mean death. (In that case, W7 as in this digram does the same thing, but W7 at this diagram's B6 leaves no ko threats.)


Furthermore, B2 makes Black's threatened followups smaller, because:

[Diagram]
inferior move by Black  

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

[Diagram]
approach ko after inferior move by Black  

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


Big P last edited by RickyDemer on March 9, 2018 - 18:06
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