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 2-4 probe against a low corner enclosure for an example of how it may form.

Attacks

Attacks: overview  

We will explore the following lines of attack for white:

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

First attack: block

[01]

First attack (block) response  

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

Follow-up 1  

If blocks, then lives.

Follow-up 2  

If makes a placement here, then hanes. and are miai for life.

Follow-up 3  

The descent at is answered by as well.

Follow-up 4  

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

Follow-up 4, alternative  

If captures, then and lives by oshitsubushi as well.

Mistake after follow-up 4  

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

Mistake after attack 1  

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

Second attack: push down

[02]

Second attack: push down  

The second attack is at . Black should respond with

Second attack  

The second attack is much easier.

Second attack  

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

Tenuki  

If plays elsewhere, then and can create a ko.

Reference  

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.

Reference  

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

Third attack: 1-3 placement

[03]

Third attack (placement)  

The third attack is at and is normally answered by .

If Black answers at a he still lives but only with a double ko – see below.

Third attack: key move  

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

Third attack: crush 1  

Subsequently, if , then Black can live with and by oshitsubushi.

Third attack: crush 2  

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

Third attack: double ko  

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

Third attack: double ko  

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

Third attack: can White crawl?  

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

Third attack: White crawls out  

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

Surrounding stones

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.

Surrounding stones  

In this case, when there is the stone, then and can kill. Black is dead after .

Surrounding stones  

Again, for the case when is present, can kill. falsifies the eye on the side.

The tripod group with the extra leg

Tripod group with extra leg  

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

Tripod group with extra leg  

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

Practical application

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.

Invasion  

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

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

• More discussion on the tripod group
• Tripod Group with Extra Leg
• Life and death