Life In 19x19

I have a yose question about a frequent yose position. Below is an easy-to-understand tesuji for white:

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[go]$$B
$$ --------------------
$$ . . . . 2 1 . . . .
$$ . . X X X O W . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

However, if we remove the marked stone, and assume the area on the right is white's territory, which is the better move for white: a or b?

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[go]$$B
$$ --------------------
$$ . . . . b 1 a . . .
$$ . . X X X O . . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

With 'a', the game will obviously go like this:

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[go]$$W
$$ --------------------
$$ . S S S 2 X 1 T T .
$$ . S X X X O 3 T T .
$$ X X O O O O T T T .
$$ . . . . . , . . . .[/go]

Counting the squares as positive points for black and the triangles as negative points for black, we get a tally of -3.

However, the throw-in seems more complicated:

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[go]$$W B4 elsewhere
$$ --------------------
$$ . . . . 1 X 2 . . .
$$ . . X X X O . 3 . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

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[go]$$Wm5
$$ --------------------
$$ . . . 2 . X X 1 . .
$$ . . X X X O . O . .
$$ X X O O O O . a . .
$$ . . . . . , . . . .[/go]

Let's say that white does not need to worry about getting cut at 'a'. The value of playing first in this position seems rather low, so both players will probably play elsewhere. However, eventually this position will become the biggest place to play, and I can't figure out exactly what the value of this position is. It seems both players have too many options for whether to respond to their opponent's move or not. I'm still learning miai counting, and this position just blows me away.

So, can anyone show me which move (the block or the throw-in) produces a better result for white?

Didn't a similar position appear in a Malkovich game about a month ago?

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[go]$$Wm5
$$ --------------------
$$ . . . 2 5 X X 1 . .
$$ . 4 X X X O 3 O . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

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[go]$$Wm5
$$ --------------------
$$ . . . X 8 6 7 O . .
$$ . X X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

This seems like the best white could possibly get this way and by my count is one point worse than simply blocking.

final answer... below is the correct move.

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

and usually throwin will yield better result for white.

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

If we assume the area on the right is white's territory, then W should be able to capture the B stones without a geta, since B runs out of liberties when he eventually hits some W stones or runs into the edge of the board:

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[go]$$B
$$ --------------------
$$ . . . . 2 1 3 5 . .
$$ . . X X X O 4 6 . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

But if B simply captures the W throw-in, W cannot block without risking ko:

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[go]$$B
$$ --------------------
$$ . . . 3 . 1 4 . . .
$$ . . X X X O 5 . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

Assuming W is unwilling to risk this ko, this will be the result. The last two moves can be played later, but can be assumed sente for B. This result is several points better for W than the reference position, where W blocks immediately.

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[go]$$B B has captured 1 stone
$$ --------------------
$$ . . . 3 . 1 6 . . .
$$ . 5 X X X O 4 . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

B actually does better to sacrifice a second stone:

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[go]$$B
$$ --------------------
$$ . . . 5 . 1 3 6 . .
$$ . . X X X O 4 . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

This is the likely final position, after each side captures two stones. The final point count is the same as the reference position, where W blocks immediately.

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[go]$$B
$$ --------------------
$$ . . . X X X O O . .
$$ . X X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

Reference position:

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[go]$$
$$ --------------------
$$ . . . . X X O . . .
$$ . . X X X O O . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

Suppose B just descends, presumably in sente. The final result is two points worse for B than the reference position.

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[go]$$
$$ --------------------
$$ . . . . 1 2 . . .
$$ . . X X X O . . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

Conclusion (unless I am missing something) -- B should hane, W can either block or throw-in. If W throws-in, B should sacrifice two stones.

Thanks everyone! Chew Terr - I vaguely recall something like that, but I haven't followed Malkovich games for a long time, so I don't know for sure.

mitsun wrote:

$$B
$$ --------------------
$$ . . . X X X O O . .
$$ . X X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .

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[go]$$B
$$ --------------------
$$ . . . X X X O O . .
$$ . X X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

This diagram is wrong. There is one white stone too much:

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[go]$$B
$$ --------------------
$$ . . . X X X O O . .
$$ . X X X X O O . . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

Therefore, this is one point better for White.

mitsun wrote:This is the likely final position, after each side captures two stones. The final point count is the same as the reference position, where W blocks immediately.

$$B
$$ --------------------
$$ . . . X X X O O . .
$$ . X X X X O O W . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .

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[go]$$B
$$ --------------------
$$ . . . X X X O O . .
$$ . X X X X O O W . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

Where did the marked stone come from?

OC, play depends upon the details of White's territory. This agrees with mitsun's analysis.



White's reverse sente gains 3 2/3 points.

Harleqin wrote:This diagram is wrong. There is one white stone too much ...

Thanks for the correction. The correct play makes more sense now -- B should hane, W should throw in, B should give up 2 stones. I refuse to count 1/3 points, so I will trust Bill on the value of the position

Small note:

It does not matter whether Black throws away two stones, three stones, or more, the final score will be the same.

Not so small note:

If Black captures the throw-in stone immediately, she should be able to win the ko. Therefore White should avoid the ko, and then the score will be the same as when Black extends instead. (Yose books generally assume that Black can win such kos. In this case, however, the loss of the ko is huge for Black. That is why extending is optimal for Black. The immediate capture assumes that Black can win the ko and that White will make a mistake.

Larger note:

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[go]$$W B4 elsewhere
$$ --------------------
$$ . . . . 1 X 2 . . .
$$ . . X X X O . 3 . .
$$ X X O O O O . . . .
$$ . . . . . , . . . .[/go]

If is correct, then is wrong. White should atari at 2 instead.

Chew Terr, You may be thinking of this position in my game vs tj86430:

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[go]$$Bc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . . X O O O . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

In the game, play went this way:

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[go]$$Wc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . 2 X O O O . . . . |
$$ | . . . . . . . . . . 4 1 5 . . . . . . |
$$ ---------------------------------------[/go]

If I understand the thread correctly, it doesn't exactly fit this situation, because of the atari, as dusk eagle pointed out in my game:

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[go]$$Wc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . 3 X O O O . . . . |
$$ | . . . . . . . . . . . 1 2 . . . . . . |
$$ ---------------------------------------[/go]

So it seems the best play there was this:

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[go]$$Wc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . 2 X O O O . . . . |
$$ | . . . . . . . . . . . 1 4 . . . . . . |
$$ ---------------------------------------[/go]

emeraldemon wrote:Chew Terr, You may be thinking of this position in my game vs tj86430

That's the one, thanks! Not being able to remember was going to bother me. =) Now, to compare the two and try to see how much I can internalize to actually use. Endgame is hard.

Dusk Eagle asks about the value of this position:

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[go]$$W
$$ --------------------
$$ . . . X . X X O . .
$$ . . X X X O . O . .
$$ X X O O O O . a . .
$$ . . . . . , O O O O[/go]

I have added some stones to make it clear that White has territory to the right and that there is no threat of a cut at "a".

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[go]$$B Black first.
$$ --------------------
$$ . . . X 3 X X O . .
$$ . 1 X X X O 2 O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

Let's count the final score as 0.

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[go]$$W White first
$$ --------------------
$$ . . . X . X X O . .
$$ . . X X X O 1 O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

is gote.

Now from this position suppose that Black plays first.

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[go]$$B Black first
$$ --------------------
$$ . . . X 2 B X O . .
$$ . 1 X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

takes back.

The final score is -1, i. e., 1 point for White.

Now suppose that White plays first:

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[go]$$W White first
$$ --------------------
$$ . . . X 1 B X O . .
$$ . . X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

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[go]$$W Continued
$$ --------------------
$$ . . . X W 2 3 O . .
$$ . 4 X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

takes the ko.

If Black wins the ko the result is -1, if White wins the ko it is -2.

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[go]$$W White follower
$$ --------------------
$$ . . . X . X X O . .
$$ . . X X X O O O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

So the count of this position is -1 1/3. A play gains 1/3 point.

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[go]$$W Original position
$$ --------------------
$$ . . . X . X X O . .
$$ . . X X X O . O . .
$$ X X O O O O . . . .
$$ . . . . . , O O O O[/go]

And the count of the original position is -2/3. A play gains 2/3 point.

Here is what I get for the interesting position in emeraldemon's game:

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[go]$$Wc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . 2 X O O O . . . . |
$$ | . . . . . . . . . . . 1 . . . . . . . |
$$ ---------------------------------------[/go]

is a 4 1/6 point sente (assuming that Black cannot stand the ko).

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[go]$$Bc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . X X O O O . . . . |
$$ | . . . . . . . . . . . O 1 . . . . . . |
$$ ---------------------------------------[/go]

Next, (or a White play at 1) gains 1 5/6 points.

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[go]$$Wc
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . . . . . . O X . . . . . . . . X . . |
$$ | . . O . . . O X . . . . . . . . . X . |
$$ | . . . , . . O X . , . . . . . X X O . |
$$ | . . . O . O X . . X . . X X X O O O . |
$$ | . . . . O . X . . . X X O O O . . . . |
$$ | . . . . . . . . . . . O X 1 . . . . . |
$$ ---------------------------------------[/go]

Next, (or a capture by Black) gains 1 1/3 points.