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Offline Bill Spight
 Post subject: Opening problems for AI: Problem 35
Post #1 Posted: Tue Jul 21, 2020 12:29 pm 
Honinbo

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White to play.

White made a big blunder, losing 47% to par, according to Elf. Assume komi, as always.

Click Here To Show Diagram Code
[go]$$Wcm24 White to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X O O . . . . . . . . . . . . . . |
$$ | . O O X . . . . . . . . . . . . . . . |
$$ | . X X , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Enjoy! :)

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

Visualize whirled peas.

Everything with love. Stay safe.
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Offline Uberdude
 Post subject: Re: Opening problems for AI: Problem 35
Post #2 Posted: Tue Jul 21, 2020 1:31 pm 
Judan

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This is one of the textbooks I have read. What on earth could White have realistically chosen that is so much worse? Don't think a human pro would tenuki to close the lower right corner like the gospel days if you ignore the urgent fight on left side. Maybe cut with 24 at 25?

Click Here To Show Diagram Code
[go]$$Wcm24 White to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X 7 . . . . . . . . . . . . . . . |
$$ | . 5 3 . . . . . . . . . . . . . . . . |
$$ | . 4 X O O . . . . . . . . . . . . . . |
$$ | 6 O O X 1 . . . . . . . . . . . . . . |
$$ | . X X 2 . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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Offline HermanHiddema
 Post subject: Re: Opening problems for AI: Problem 35
Post #3 Posted: Tue Jul 21, 2020 1:51 pm 
Gosei
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There's this, with a working ladder. It feels like an overplay, but perhaps it isn't?

Click Here To Show Diagram Code
[go]$$Wcm24
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . 2 . . . . . . . . . . . . . . . . |
$$ | . 1 X O O . . . . . . . . . . . . . . |
$$ | . O O X 4 9 . . . . . . . . . . . . . |
$$ | . X X 3 . . . . . , . . . . . , . . . |
$$ | . 5 6 7 . . . . . . . . . . . . . . . |
$$ | . . 8 . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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Offline Shaddy
 Post subject: Re: Opening problems for AI: Problem 35
Post #4 Posted: Tue Jul 21, 2020 3:55 pm 
Lives in sente
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I bet this is the game variation and Uberdude's variation is the suggestion...
Click Here To Show Diagram Code
[go]$$Wcm24
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . 2 . . . . . . . . . . . . . . . . |
$$ | . 1 X O O 6 . . . . . . . . . . . . . |
$$ | . O O X 4 . . . . . . . . . . . . . . |
$$ | . X X 3 8 . . . . , . . . . . , . . . |
$$ | . 5 7 9 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


edit

looking at it again, this is actually not bad for white. the solution?

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Offline Knotwilg
 Post subject: Re: Opening problems for AI: Problem 35
Post #5 Posted: Tue Jul 21, 2020 3:58 pm 
Oza
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I first looked at the problem and then checked the answers. I concur with Uberdude.

After the two way forcing sequence, Black is still not alive and White is super thick.

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Offline Bill Spight
 Post subject: Re: Opening problems for AI: Problem 35
Post #6 Posted: Wed Jul 22, 2020 9:32 am 
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Click Here To Show Diagram Code
[go]$$Wcm24 White to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X O O . . . . . . . . . . . . . . |
$$ | . W W X . . . . . . . . . . . . . . . |
$$ | . X X , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

For human and bot alike, the question boils down to this. Should White sacrifice the :wc: stones or save them? Saving them involves a well known tesuji.

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— Winona Adkins

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Offline Bill Spight
 Post subject: Re: Opening problems for AI: Problem 35
Post #7 Posted: Wed Jul 22, 2020 11:12 am 
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The game is GoGoD 2010-08-19i between Iyama Yuta (W) and O Meien.

Iyama chose to save the two White stones.

Click Here To Show Diagram Code
[go]$$Wcm24 Save Our Stones
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . 2 . . . . . . . . . . . . . . . . |
$$ | . 1 X O O . . . . . . . . . . . . . . |
$$ | . W W X 4 5 . . . . . . . . . . . . . |
$$ | . B B 3 6 . . . . , . . . . . , . . . |
$$ | . . . 7 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:w24: added a dame to the :wc: stones in sente. After :w30: O Meien had the choice of sacrificing the :bc: stones or losing 3 stones in a ladder.

Click Here To Show Diagram Code
[go]$$Bcm31 Game continuation
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
$$ | . 9 8 O . . . . . , . . . . . X . . . |
$$ | . c . . 6 . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . X . 4 b 0 . . . . . . . . . . . . |
$$ | . O X O O 3 . . . . . . . . . . . . . |
$$ | . O O X X O 5 . . . . . . . . . . . . |
$$ | . X X O X 1 . . . , . . . . . , . . . |
$$ | . a 2 O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

O Meien saved his three stones, and even got in a ponnuki. For :w32: Elf prefers a, but only by 0.1%. For :w36: Elf prefers b by ½%, a difference that may be attributed to noise. For :w40:, however, Elf prefers c by 4½%, which is too large for noise, even if it is within Elf's margin of error.

Click Here To Show Diagram Code
[go]$$Wcm40 Variation for :w40:
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . 2 . . . . . . . . . . . . . . . . . |
$$ | . . X . 4 . . . . . . . . . . . . . . |
$$ | . X O O . . . . . , . . . . . X . . . |
$$ | . 1 3 . O . . . . . . . . . . . . . . |
$$ | . . X . 7 6 . . . . . . . . . . . . . |
$$ | . . X . O . . . . . . . . . . . . . . |
$$ | . O X O O X . . . . . . . . . . . . . |
$$ | . O O X X . X . . . . . . . . . . . . |
$$ | . X X O X X . . . , . . . . . , . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . 5 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

White makes territory on the left side in exchange for the top left corner and Black strength in the center, but White also gets the 3-3 invasion in the bottom right corner.

Now let's go back and see Elf's mainline variation for :w36:.

Click Here To Show Diagram Code
[go]$$Wcm36 Mainline variation for :w36:
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . 0 . . . . . . . . . . . . . . . . . |
$$ | . 6 5 7 . . . . . . . . . . . . . . . |
$$ | . . 4 O . . . . . , . . . . . X . . . |
$$ | . . . 2 3 . . . . . . . . . . . . . . |
$$ | . . B . . . . . . . . . . . . . . . . |
$$ | . 8 B . O 1 . . . . . . . . . . . . . |
$$ | . O B O O X . . . . . . . . . . . . . |
$$ | . O O X X . X . . . . . . . . . . . . |
$$ | . X X O X X . . . , . . . . . , . . . |
$$ | . 9 O O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

With :w44: this line transposes to Elf's mainline variation for :w32:. :) This way White lets Black save his :bc: stones and extend into the corner.

Click Here To Show Diagram Code
[go]$$Wcm46 Mainline variation for :w36:, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ | . X O O . . . . . . . . . 5 . . . . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . X X . O O . . . . . . . . . . . . . |
$$ | . O X O O X . 1 . 3 . . . . . . . . . |
$$ | . O O X X . X . . . . . . . . . . . . |
$$ | . X X O X X . . 2 , 4 . . . . , . . . |
$$ | . O O O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:w46: and :w48: attack Black's central stones, pushing them further into the center. Along with :w50: they build a large White sphere of influence on the top side.

Top choice: Give up the stones

Click Here To Show Diagram Code
[go]$$Wcm24 Sacrifice
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . B 7 . . . . . . . . . . . . . . . |
$$ | . 5 3 . . . . . . . . . . . . . . . . |
$$ | . 4 X O O . . . . . . . . . . . . . . |
$$ | 6 W W X 1 . . . . . . . . . . . . . . |
$$ | . X X 2 . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:w30: completes a standard pattern for sacrificing the :wc: stones. The :bc: stone still has a bit of aji left.

Click Here To Show Diagram Code
[go]$$Bcm31 Mainline, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . 5 . 4 . 3 . . . 2 . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . O O . . . . . . . . . . . . . . . . |
$$ | . X X O O . . . . . . . . . . . . . . |
$$ | X . . X O . . . . . . . . . . . . . . |
$$ | . X X X . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , 1 . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:b31: encloses the bottom right corner. Then :w32: approaches the top right corner. :w32: - :b35: make an amusing flow of the stones. ;)

This is a question of judgement. My own feeling, going back to when I was an SDK, is that the sacrifice is a clear way to cash in on the White thickness in the lower left, while capturing the 2 Black stones leaves White overconcentrated on the left side. So I am not surprised that Elf prefers the sacrifice. I am surprised, even knowing of Elf's extreme views, that it prefers it by a whopping 47%! :shock: I expect that other top bots will also prefer the sacrifice. It would be interesting to see by how much. :)

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

Visualize whirled peas.

Everything with love. Stay safe.
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Offline yoyoma
 Post subject: Re: Opening problems for AI: Problem 35
Post #8 Posted: Wed Jul 22, 2020 12:03 pm 
Lives in gote

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My Katago:

Sacrifice: Black 44.6%, -0.6 points
Save (game): Black 86.9%, 6.1 points
Swing: 42.3pp, 6.7 points

So it agrees with Elf -- White made a huge mistake. Later it also generally agrees with Elf.

About continuation of the Sacrifice line:
It also wants to play bR4 next.
Then Kata slightly prefers R17 invasion to O17 approach (0.8pp, 0.1 points). For the next amusing sequence, Kata mostly agrees with, although there are other choices slightly higher.
For the bF17 re-pincer move, Kata thinks of the submarine invasion bF18 first. When forcing Kata to play bF17 instead though it thinks it's basically the same.

I just like the bF18 idea. :cool:

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Offline Joaz Banbeck
 Post subject: Re: Opening problems for AI: Problem 35
Post #9 Posted: Wed Jul 22, 2020 1:37 pm 
Judan
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When I look at Uberdude's answer, I see this influence map.

Click Here To Show Diagram Code
[go]$$Wcm24
$$ ---------------------------------------
$$ | ? ? ? ? ? ? ? . . . . . . . . . . . . |
$$ | ? ? ? ? ? ? ? . . . . . . . . . . . . |
$$ | ? ? ? ? ? ? ? ? . . . . . . . . . . . |
$$ | ? ? ? O ? ? ? ? . , . . . . . X . . . |
$$ | ? ? ? ? ? ? ? ? . . . . . . . . . . . |
$$ | ? ? X 7 ? ? ? ? . . . . . . . . . . . |
$$ | . 5 3 ? ? ? ? ? . . . . . . . . . . . |
$$ | . 4 X O O ? ? . . . . . . . . . . . . |
$$ | 6 O O X 1 . . . . . . . . . . . . . . |
$$ | ? X X 2 . . . . . , . . . . . , . . . |
$$ | ? ? ? ? . . . . . . . . . . . . . . . |
$$ | ? ? . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X , . O O O . , . . . . . , . . . |
$$ | . . . X . X X . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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Offline Uberdude
 Post subject: Re: Opening problems for AI: Problem 35
Post #10 Posted: Wed Jul 22, 2020 1:54 pm 
Judan

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KGS: Uberdude 4d
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f18 is nice, setting up miai like this one:

Click Here To Show Diagram Code
[go]$$W Weon Seongjin 7p (black) vs. Han Chongjin 6p
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . 1 . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . , . . . . . , . . . . . X O . . |
$$ | . . . . . . . . . . . . . X X O O . . |
$$ | . . . . . . . . . . . . . . O X O . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . X , X . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]

http://ps.waltheri.net/database/game/46994/

This post by Uberdude was liked by: Bill Spight
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Offline dhu163
 Post subject: Re: Opening problems for AI: Problem 35
Post #11 Posted: Mon Dec 26, 2022 7:13 am 
Lives in gote

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KGS: mathmo 4d
IGS: mathmo 4d
Speculatively:
Current position:
1. Overall other than the fight, this looks even other than the misplaced lower right.
2. From experience, the fight looks like an overplay next to W's strong wall.
3. B12 works well to win the capturing race while surviving in the centre, however it gives up a ponnuki which reduces W's wall and W may be overconcentrated, and in the upper side, W's cutting stones are in terrible shape.
4. E12 is a standard alternative to take the corner and force B to live smaller, getting a big corner, so I guess it is the better move? The centre potential remains and W's shape is cramped but not too bad.

Opp to play
1. B12 is first instinct, but I can't see a way to punish C13, so it is very tempting.

Past:
1. I feel that W should be slightly ahead even if the lower right was well placed. The lower left seems slightly better for B though.

Check:
1. Correct, but I have a vague memory of reading this thread already.
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