Solution:

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[go]$$W White to play
$$ ---------------
$$ | . O O O . 1 . |
$$ | O . X . O O O |
$$ | O O O O O 4 5 |
$$ | 6 O X X X X X |
$$ | 2 O O 7 X 3 8 |
$$ | X X X X X X X |
$$ | . X . X X O 9 |
$$ ---------------[/go]

makes two points in the corner. prevents a White point on the left side. does not make a point difference, but guarantees the last move. Next the dame are played. As captures, and are played with red stones.

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[go]$$B Black to play
$$ ---------------
$$ | . O O O . O . |
$$ | O . X . O O O |
$$ | O O O O O X O |
$$ | X O X X X X X |
$$ | X O O O X . + |
$$ | X X X X X X X |
$$ | . X . X X . + |
$$ ---------------[/go]

We have now reached a scorable board. Black has 4 points, minus 2 for the group tax, and White also has 4 points, minus 2 for the group tax, for a net score of 0. Zero is a second player win, so Black to play loses.

----

Why is the three point White eye with the Black stone in the center worth 1 point (move) for White?

First, suppose that White plays first in the eye.

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[go]$$W White to play
$$ ---------------
$$ | . O O O . O . |
$$ | O 1 X 2 O O O |
$$ | O O O O O X O |
$$ | X O X X X X X |
$$ | X O O O X . + |
$$ | X X X X X X X |
$$ | . X . X X . + |
$$ ---------------[/go]

is a red stone, leaving this position.

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[go]$$ One point eye
$$ ---------------
$$ | . O O O . O . |
$$ | O O . + O O O |
$$ | O O O O O X O |
$$ | X O X X X X X |
$$ | X O O O X . + |
$$ | X X X X X X X |
$$ | . X . X X . + |
$$ ---------------[/go]

Plainly White has one point now in the eye, after zero net plays.

Now suppose that Black plays first.

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[go]$$B Black to play
$$ ---------------
$$ | . O O O . O . |
$$ | O 1 X 2 O O O |
$$ | O O O O O X O |
$$ | X O X X X X X |
$$ | X O O O X . + |
$$ | X X X X X X X |
$$ | . X . X X . + |
$$ ---------------[/go]

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[go]$$B Black to play
$$ ---------------
$$ | . O O O . O . |
$$ | O 3 4 + O O O |
$$ | O O O O O X O |
$$ | X O X X X X X |
$$ | X O O O X . + |
$$ | X X X X X X X |
$$ | . X . X X . + |
$$ ---------------[/go]

leaving

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[go]$$B One point eye
$$ ---------------
$$ | . O O O . O . |
$$ | O . + + O O O |
$$ | O O O O O X O |
$$ | X O X X X X X |
$$ | X O O O X . + |
$$ | X X X X X X X |
$$ | . X . X X . + |
$$ ---------------[/go]

Again we have a 1 point eye after zero net plays.

Now, what kind of play is ?

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[go]$$W White to play
$$ ---------------
$$ | . O O O . 1 . |
$$ | O . X . O O O |
$$ | O O O O O . . |
$$ | . O X X X X X |
$$ | 2 O O . X 3 . |
$$ | X X X X X X X |
$$ | . X . X X O . |
$$ ---------------[/go]

leaves a Black point plus a dame in the Black eye.

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

If Black plays there instead, Black also gets one point in the eye. So does not change the number of points in the eye. What it does in this case is to guarantee that White gets the last move before the players start reducing their own points. Like a dame, is an infinitesimal play. See http://senseis.xmp.net/?GoInfinitesimals for more about infinitesimals in regular go.

Gotta run.

{More later.}

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

Visualize whirled peas.

Everything with love. Stay safe.

Nice Thanks Bill.

_________________
finito ludos regula