Tripod Group

  Difficulty: Beginner   Keywords: Life & Death, Ko

The tripod group

[Diagram]
Tripod group  

The black group in this diagram is called the tripod group. It is one of the smallest shapes in the corner that is alive as it stands. Black needs to remember the correct reply to three white attacks. See probe for an example of how it may form.


Table of contents Table of diagrams
Tripod group
Attacks
First attack response
Follow-up 1
Follow-up 2
Follow-up 3
Follow-up 4
Follow-up 4, alternative
Mistake after follow-up 4
Mistake after attack 1
Second attack
Second attack
Second attack
Tenuki
Reference
Reference
Third attack
Third attack
Third attack
Third attack
White crawls out
White crawls out
Reference
Reference
Surrounding stones
Surrounding stones
Surrounding stones
Tripod group with extra leg
Tripod group with extra leg
Application
Invasion
Two points smaller corner

Attacks

#02 #03 #01
[Diagram]
Attacks  

We will explore the following lines of attack for white:

  • a : First attack.
  • b : Second attack.
  • c : Third attack.


First attack

[01]

[Diagram]
First attack response  

In response to the attack at W1, black should defend at B2. We will investigate some follow-ups from this position.

[Diagram]
Follow-up 1  

If W1 blocks, then B2 lives.

[Diagram]
Follow-up 2  

If W1 makes a placement here, then B2 hanes. W3 and B4 are miai for life.

[Diagram]
Follow-up 3  

The descent at W1 is answered by B2 as well.

[Diagram]
Follow-up 4  

W1 and W3 is probably the strongest attack, threatening a ko. The throw-in at B4 is necessary for life. The result is oshitsubushi.

[Diagram]
Follow-up 4, alternative  

If W5 captures, then B6 and B8 lives by oshitsubushi as well.

[Diagram]
Mistake after follow-up 4  

B4 here would be a mistake, because W5 turns the whole group into a ko.

[Diagram]
Mistake after attack 1  

The descent at B2 is a mistake, because W3 is the eye-stealing tesuji, making a placement and aiming at setting up a snapback at a. Black is dead.


Second attack

[02]

[Diagram]
Second attack  

The second attack is at W1. Black should respond with B2

[Diagram]
Second attack  

The second attack is much easier.

[Diagram]
Second attack  

Note that when White plays at W1, B2 is necessary for unconditional life.

[Diagram]
Tenuki  

If B2 plays elsewhere, then W3 and W5 can create a ko.

[Diagram]
Reference  

B2 here lives too, but it appears not to be the recommended move. Probably the reason is that a White descent at a becomes a definite sente, in the sense that White will get a unconditional kill if Black plays elsewhere. See Xuanxuan Qijing Unnumbered Problem 2 for the reason.

[Diagram]
Reference  

The crawl at B2 here may or may not be a good move, and depends heavily on whether the white+circle stone exists, and the White stones in the vicinity of white+circle. In this case, the clamp at W3 takes away all the eye space and kills. Therefore, in life-and-death problems, the main line always have B2 at W3.



Third attack

[03]

[Diagram]
Third attack  

The third attack is at W1 and is answered by B2.

[Diagram]
Third attack  

W1 and W3 aims for either a ko or a bent four in the corner kill, but with the key move of B4, Black can live.

[Diagram]
Third attack  

Subsequently, if W1, then B2 and B4 can lives by oshitsubushi.

[Diagram]
Third attack  

Similarly, if W1 captures, then Black lives by oshitsubushi as well.

[Diagram]
White crawls out  

RhysD: Suppose white eventually has a second-line stone in support; does black have an answer to the first-line crawl?

[Diagram]
White crawls out  

fractic: The second line stone needs to be a lot closer. Black can capture white with the sequence to B9. If now white plays a then black plays b and if white plays c then black plays a.

[Diagram]
Reference  

B1 lives too, but depending on the ruleset used, may give White an infinite supply of ko-threats.

[Diagram]
Reference  

White can aim for a ko with W1. To avoid a ko, B2 and B4 would be necessary. The rest is pretty much a one lane road, with B10 living unconditionally by a double ko.



Surrounding stones

[Diagram]
Surrounding stones  

Surrounding stones do matter for the status of the tripod group. For example, if there is a White stone at a or b, then the status becomes unsettled.

[Diagram]
Surrounding stones  

In this case, when there is the white+circle stone, then W1 and W3 can kill. Black is dead after W7.

[Diagram]
Surrounding stones  

Again, for the case when white+circle is present, W1 can kill. W7 falsifies the eye on the side.



The tripod group with the extra leg

[Diagram]
Tripod group with extra leg  

While the tripod group is unconditionally alive, Black should not make the exchange of B1 and W2.

[Diagram]
Tripod group with extra leg  

The reason is that after the exchange, W1 and W3 turns the whole group into a ko. See tripod group with extra leg for more detailed discussion for this.



Practical application

[Diagram]
Application  

This is a position from the final game of the 2000 German Championship, between Franz-Josef Dickhut (Black) and Christoph Gerlach (White). Black wanted to do something about the upper left corner.

[Diagram]
Invasion  

So he invaded at B1. White can play W4 one point higher, but then Black has a cut at W4, which he can use to isolate the two white stones at the top. Either way Black creates a nice position.

[Diagram]
Two points smaller corner  

From an endgame point of view, it is better for White to play like this diagram (1 replaces 8 above): Black will end up with two points less in the corner. However in the game White followed the previous diagram, probably because he didn't like the remaining weaknesses on the left side following this sequence at a.



See also


Tripod Group last edited by PeterHB on November 5, 2013 - 13:05
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