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BentFourInTheCorner
BentFourInTheCorn...

 

Old Bent Four In The Corner
   

[Diagram]
Diag.: White is alive

If a group has an eye space of 4, it is usually alive as in this diagram. If which invades at 1, white responds with 2 and makes two eyes. (1 and 2 are miai)


[Diagram]
Diag.: Straight 4 is alive in the corner

Even in the corner, a straight line of 4 is alive (the points 'a' and 'b' are miai).


[Diagram]
Diag.: Bent 4 in corner

However, with a bent four in the corner, if the defending shape has less than two liberties on the outside, black can prevent unconditional life for White's group by playing 1. White responds with an atari at 2.


[Diagram]
Diag.: Bent 4 in corner

But black can capture with 3, and since white can't respond at the marked space due to ko, the fate of the group is decided by a ko fight.

If white plays 4, she puts her stones into atari and black captures her stones right away with 5 (otherwise if white plays at the marked space capturing the two inner stones she creates life).


[Diagram]
Diag.: Bent 4 in corner

If white has an extra liberty on the outside, however, ...


[Diagram]
Diag.: Bent 4 in corner

... black 5 doesn't kill white. So, white plays 6 (capturing two stones) and creates life.

The bent four in the corner is not a simple shape.



See also Beginner Exercise 5 for a similar problem on bent four in the corner. --unkx80


More often the term 'bent four in the corner' refers to the situation like this.

[Diagram]
Diag.: Situation with a potential bent four.

Bent four appears after black plays at 'a'. Since white cannot play there black can fill the outside liberties first before playing 'a'. As we know this starts a ko. So, naturally, black could wait to make sure that there are no ko-threats left. -HolIgor

It is not so simple though. Sometimes eliminating ko-threats takes too many moves in own territory, some ko-threats cannot be eliminated at all. The result depends on the rule set, area or territory counting, suicide rule etc. This is a big headache of people concerned with rules of the game.

By Japanese rules white group here is considered dead and is removed without playing any ko. By Chinese rules the ko should be played.

Sorry, if I am not precise, rules are not my forte. -HolIgor

A small correction here: That eliminating ko-threats takes moves in the own territory does not matter. This kind of moves do not have to be played, just like you do not have to fill in the liberties of dead stones. However, under Chinese rules, or under rulesets where life and dead have to be proven rather than be decided, unremovable ko threats can make a difference. -- AndreEngels


[Diagram]
Diag.: unremovable ko threat

Unremovable ko threats sometimes occur in seki positions, here is an example. White has a ko threat here at 'a', black cannot remove it. Note that playing this ko threat does cost points for white - as it is, black lives without territory (or both have one point, depending on the ruleset), while after capturing black will have 7 points of territory. However, white will of course well be willing to sacrifice these 7 points to live in the bent four situation shown above. -- AndreEngels


[Diagram]
Diag.: Bent Four

Another bent four diagram.

KarlKnechtel: It's not immediately obvious to me why this would also be called a 'bent four' - there are five spaces underneath the black group, after all. My understanding is that white can eventually AlmostFill the space with a bent four, which if captured by black reverts to the first "Bent 4 in corner" diagram. (If black plays inside first, white AlmostFills with a bent three, which is dead even if not in the corner.)



Have a look [ext] here for an easy problem involving a bent four in the corner.



This is a copy of the living page "Old Bent Four In The Corner" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.