Impressive analysis Bill . One question:

Click Here To Show Diagram Code

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

Black doesn't actually have to respond to this move, as white is not actually threatening to capture the four black stones. However, white can then fill in in sente:

Click Here To Show Diagram Code

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

This result is -3. So, if black were to play like this, white would have gained -3/2 points with each move. Since this is worse than the result you showed for black, black should have captured rather than let white protect it in sente. Is my analysis correct?

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The sequence -- White takes two stones, Black takes back, White plays atari, Black connects on the second line, White takes ko --, should be considered as a unit (except for ko threats). This happens frequently, the hane-connect is a common example. I do not know of a go term for this, but the CGT term is reversal. Yes, considered as individual plays the capture and recapture each gain 1 2/3 points, but that just takes us back to where we began, in terms of points.

So you are right, Black should take back.

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At some point, doesn't thinking have to go on?
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Visualize whirled peas.

Everything with love. Stay safe.

Yes, I think you are right, I wasn't very thorough. {sigh}

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Many thanks.

OK, let's try again. Here I assume AGA territory scoring, which is equivalent to Chinese scoring. (I also include notes on Japanese scoring.) The difference lies in the value of the seki. By AGA scoring White gets two points in the seki and Black gets one point. By Japanese scoring seki is worth 0.



There are some cute plays in there, I think.

Edit:

Hmmm. Where does that "Black to play" come from?

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.