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 Post subject: Re: This 'n' that
Post #621 Posted: Sat Jun 08, 2019 11:37 am 
Honinbo

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A difficult endgame position.

Click Here To Show Diagram Code
[go]$$
$$ ------------------------
$$ . X . . . . . . O . . . .
$$ . X . O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


The outside region is Black's territory.

Enjoy! (If you can. :lol: )

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 Post subject: Re: This 'n' that
Post #622 Posted: Sun Jun 09, 2019 8:23 am 
Lives with ko

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Since Bill said this was difficult, I'm guessing this might not be it for some reason, but it's still something?

Click Here To Show Diagram Code
[go]$$B main line?
$$ ------------------------
$$ . X . 1 3 4 2 . O . . . .
$$ . X . O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


Click Here To Show Diagram Code
[go]$$B white only does this with a ton of ko threats
$$ ------------------------
$$ . X 4 1 2 . 3 . O . . . .
$$ . X 5 O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


This post by lightvector was liked by: Bill Spight
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 Post subject: Re: This 'n' that
Post #623 Posted: Sun Jun 09, 2019 9:09 am 
Dies with sente

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If I read it correctly, I'd call this a tsumego problem.

Click Here To Show Diagram Code
[go]$$B kill in ko?
$$ ------------------------
$$ . X 4 3 2 . 1 . O . . . .
$$ . X 5 O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


White cannot connect:

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[go]$$W white fails
$$ ------------------------
$$ . X O 1 O 2 X . O . . . .
$$ . X X O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


So it bocomes a ko:

Click Here To Show Diagram Code
[go]$$W white fails
$$ ------------------------
$$ . X O 2 O . X . O . . . .
$$ . X X O . O 1 O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]

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 Post subject: Re: This 'n' that
Post #624 Posted: Sun Jun 09, 2019 9:20 am 
Dies with sente

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My previous answer was wrong, white can live:

Click Here To Show Diagram Code
[go]$$B live
$$ ------------------------
$$ . X . 2 4 3 1 . O . . . .
$$ . X . O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


So 2 seems to be the vital point and I now think that lightvector's answer is correct (white gets 3 points less in his solution).


This post by gennan was liked by: Bill Spight
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 Post subject: Re: This 'n' that
Post #625 Posted: Sun Jun 09, 2019 10:20 am 
Honinbo

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This is a modification of a position from a game, where White had one fewer dame and Black to play could kill. I realized that giving White a dame would make an interesting endgame position. :)

The main difficulty comes from the ko evaluation, depending on who is komaster. You may think of the komaster as having just enough sufficiently large ko threats to win the ko or kos that may arise in the position. :)

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At some point, doesn't thinking have to go on?

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 Post subject: Re: This 'n' that
Post #626 Posted: Mon Jun 10, 2019 10:42 am 
Honinbo

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Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . . . . O .
$$ . O X O O . . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


Outside stones are safe.

Evaluate the position.

This is an ambiguous position, a 2 move distant sente where each move gains 1 pt. Its count is -7.

What is the best play by each side?

Click Here To Show Diagram Code
[go]$$B
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . 4 2 . O .
$$ . O X O O 3 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


OC, since the position is ambiguous, :b1: and :b3: are not sente. The result is a local score of -7.

Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . . 3 . O .
$$ . O X O O 1 2 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


The sequence, :w1: - :w3:, gains one pt., for a local score of -8.

----

What about the other plays? Let's use difference games to compare plays. :)

Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 2 . X X .
$$ . X O . . 3 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 6 4 . O .
$$ . O X O O 5 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


:b1: is the recommended play, :w2: is the other play in the mirror position. We can stop play after :w6: because the local temperature has dropped below 1. Black has 6 + 1¼ = 7¼ pts. and White has 7 pts., for a net result of ¼. Black is ahead and has the move, so Black wins.

Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 6 2 X X .
$$ . X O . . 4 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 3 . . O .
$$ . O X O O 1 . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


We can stop after :w6: because the left sides are mirrored and the right sides have temperatures less than 1. The left sides are miai and equal. Black has 1 pt. on the right and White has ½ pt., for a net result of ½. Black wins.

Since both moves result in a win for the first player, They should be incomparable. In which case, which to play depends upon the rest of the board. But actually, :b1: in the second game is a mistake, unless the ko situation makes it a good ko threat or there is some other ko consideration. We have actually run across this kind of problem before in this thread, with the mistake that Dieter (Knotwilg) discovered in Sakata's Tesuji and Anti-Suji of Go. The point is that :b1: in the second diagram reverses. (See https://senseis.xmp.net/?Reversible ) That is, White has a local play that produces a position that is at least as good for White as the original position.

Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X . . X X .
$$ . X O . . . . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 2 . . O .
$$ . O X O O 1 . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


In this case, :w2: is just such a play. :) How can we tell that this position is at least as good for White as the original position? Well, the original position is mirrored on the top, so we already have a difference game set up. If Black to play cannot win, then this position is at least as good for White as the original. (Remember, the original difference game is worth 0.)

Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 3 4 X X .
$$ . X O . . . 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 2 . . O .
$$ . O X O O 1 . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


We can stop after :b5: because the local temperature is below 1. Black has 8 pts. and White has 7¼, for a net result of ¾. But White to play can round down to 0, so Black does not win.

When a play reverses the rule is to keep going locally. In the worst case that means playing inside territory or simply giving up 1 pt.

Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 6 4 X X .
$$ . X O . . 7 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 2 . . O .
$$ . O X O O 1 3 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


So :b3: makes a local play in the bottom position, after which White plays first in the mirror position. The net result is ½, which White to play can round down to 0. Because :b1: reverses, Black does not win. :)

Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 4 . X X .
$$ . X O . . 5 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 6 2 . O .
$$ . O X O O 3 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


It turns out that :b1: in this diagram also reverses. :) After :w6: the net result is ¼. Black wins.

So :b1: in the last diagram is correct, and the other play is not. :) We could have reached the same conclusion by noticing that the wrong play is a losing sente. But I wanted to revisit reversal with difference games. :)

Now what about White's play in the original position?

Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 3 2 X X .
$$ . X O 8 7 5 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 9 6 . O .
$$ . O X O O 1 4 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


If :b4: plays at 5, :w5: plays at 4 and wins. After :w9: the net result is -1½. Black can round that up to -1, but White wins.

Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 2 3 X X .
$$ . X O . . 7 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 6 . . O .
$$ . O X O O 4 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


After :w7: the left side is miai, and the net result is -½, which Black can round up to 0. White does not win.

So :w1: in the first diagram dominates :w1: in the second diagram. However, it turns out that both plays reverse, so with correct play we get this comparison.

Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 5 4 X X .
$$ . X O . . 6 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . . 3 . O .
$$ . O X O O 1 2 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


So with correct play we get this diagram, which is a jigo.

Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 4 5 X X .
$$ . X O . . . 6 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 3 . . O .
$$ . O X O O 2 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]


And this diagram, which is also jigo.

So both plays are correct, as long as White recognizes that each one reverses and continues locally. OC, White could make a mistake. The difference game compares the mistakes and prefers the play with the smaller mistake. Did you notice the reversal? Neither did I. ;) (OC, we would have in a game after :b2:. :))

_________________
There is one human race.
----------------------------------------------------

The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

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