Why only after two black moves is white dead?

[paullik]

I was reading about ko, and ko threats at Sensei's Library and I found this diagram:



If I take it in isolation and consider this paragraph:

In this diagram black can play at a. White must respond at b. If white neglects to respond black will kill all the white stones by playing at b himself.

Well, isn't white already dead? Since he's surrounded and cannot make eyes?
Why should black play at a and b in order to consider white dead? Or is this just for illustration purposes for the entire article?


Original article:
http://senseis.xmp.net/?Ko

[leichtloeslich]

its a simple seki

[paullik]

I cannot see it...

[Abyssinica]

Even though white has no eyes, when the liberties on the outside get filled, black cannot fill in the liberties on the inside to capture white without making it so that white will be able to live.

Simple example:

In order for white to capture black, white would have to play a move inside. Yet if white plays a move here, it creates a straight 4 shape, black captures, and then black has the 4 space eye shape to live with. If black wants to capture white well then that's self-atari and he dies.

$$c Seki
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O O O O O O O O O . . . . . |
$$ | . . . . . O X X X X X X X O . . . . . |
$$ | . . . , . O X . O O O . X O . , . . . |
$$ | . . . . . O X X X X X X X O . . . . . |
$$ | . . . . . . O O O O O O O . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$c Seki
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O O O O O O O O O . . . . . |
$$ | . . . . . O X X X X X X X O . . . . . |
$$ | . . . , . O X . O O O . X O . , . . . |
$$ | . . . . . O X X X X X X X O . . . . . |
$$ | . . . . . . O O O O O O O . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

[xed_over]

I cannot see it...

well then... let's play it out...

$$B Ko threat
$$ -------------------
$$ | . X X X . b 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Ko threat
$$ -------------------
$$ | . X X X . b 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

Black makes the ko threat.
If White ignores the threat to win the ko (elsewhere on the board, and not shown), then black plays again to kill the white stones.

$$B White ignores the Ko threat
$$ -------------------
$$ | . X X X . 3 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B White ignores the Ko threat
$$ -------------------
$$ | . X X X . 3 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

Now there is no way for white to make two eyes here. Black will just continue to fill in all the liberties until he can capture all of white's stones.

However, if White responds to the threat, white is alive in seki.

$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

Once all the outside liberties are filled, neither side want to play at a or b. Seki.

$$B Seki
$$ -------------------
$$ | a X X X b O X X .
$$ | O O O O O O O X .
$$ | 7 O 1 X X X X X .
$$ | X O O 3 X . . . .
$$ | X O X X X . . . .
$$ | 5 X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Seki
$$ -------------------
$$ | a X X X b O X X .
$$ | O O O O O O O X .
$$ | 7 O 1 X X X X X .
$$ | X O O 3 X . . . .
$$ | X O X X X . . . .
$$ | 5 X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

If black plays at a or b, then white can live with territory.
If white plays at a or b, then black can capture all of whites stones for lots of territory.

[paullik]

well then... let's play it out...

[...]

However, if White responds to the threat, white is alive in seki.

$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

Ok, so the seki is after white responds to the threat, that makes more sense.

Thanks for the clarifications.

[Bill Spight]

One more point about this position.

$$W
$$ -------------------
$$ | . B B B . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ -------------------
$$ | . B B B . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

If White plays the stones are dead.

[paullik]

One more point about this position.

$$W
$$ -------------------
$$ | . B B B . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ -------------------
$$ | . B B B . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

If White plays the stones are dead.

Since they are inside white's territory, right?

[skydyr]

One more point about this position.

$$W
$$ -------------------
$$ | . B B B . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W
$$ -------------------
$$ | . B B B . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

If White plays the stones are dead.

Since they are inside white's territory, right?

Yes, in a sense, but do you understand why it's white's territory now and not before?

[paullik]

Since they are inside white's territory, right?

Yes, in a sense, but do you understand why it's white's territory now and not before?

Because it's only now that the are surrounded.

[skydyr]

Since they are inside white's territory, right?

Yes, in a sense, but do you understand why it's white's territory now and not before?

Because it's only now that the are surrounded.

Well...

$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

In this diagram, black's three stones are also surrounded, but they're alive in seki. So what's the difference between the this one and the following that makes it different?

$$W White lives outright
$$ -------------------
$$ | . X X X . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W White lives outright
$$ -------------------
$$ | . X X X . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

[paullik]

Well...

$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

In this diagram, black's three stones are also surrounded, but they're alive in seki. So what's the difference between the this one and the following that makes it different?

$$W White lives outright
$$ -------------------
$$ | . X X X . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W White lives outright
$$ -------------------
$$ | . X X X . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

The number of liberties of the white stones, which in fact lead to seki or to killing the three black stones.

[skydyr]

Well...

$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Seki
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

In this diagram, black's three stones are also surrounded, but they're alive in seki. So what's the difference between the this one and the following that makes it different?

$$W White lives outright
$$ -------------------
$$ | . X X X . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W White lives outright
$$ -------------------
$$ | . X X X . . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

The number of liberties of the white stones, which in fact lead to seki or to killing the three black stones.

Well, if black plays here:

$$W White lives outright
$$ -------------------
$$ | . X X X 2 . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W White lives outright
$$ -------------------
$$ | . X X X 2 . 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

Isn't the number of liberties the same as before? White has 5 liberties in this and the other diagram.

[Joaz Banbeck]

http://senseis.xmp.net/?DeadEyeshapes

[gowan]

In this diagram

$$W White lives outright
$$ -------------------
$$ | a X X X 2 b 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W White lives outright
$$ -------------------
$$ | a X X X 2 b 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

White has three "outside" liberties so white can play at a and b (if necessary) so in the end the shape will be

$$W White lives with territory
$$ -------------------
$$ | O . . . . O O X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$W White lives with territory
$$ -------------------
$$ | O . . . . O O X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

The empty points inside White's group make four in a line which is alive.

If Black plays first as in the next diagram, White lives in seki, as do the three surrounded black stones.

$$B White lives in seki (no territory)
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B White lives in seki (no territory)
$$ -------------------
$$ | . X X X . 2 1 X .
$$ | O O O O O O O X .
$$ | . O . X X X X X .
$$ | X O O . X . . . .
$$ | X O X X X . . . .
$$ | . X . . . . . . .
$$ | . X . X . . . . .
$$ | . . . . . . . . .[/go]

So in either case, White lives. In one case White gets points, in the other no points, but White lives in both cases.