Is the 3-3 double hane switcheroo ponnuki joseki ever good?

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Is the 3-3 double hane switcheroo ponnuki joseki ever good?

Post by Uberdude »

Prompted by viewtopic.php?p=255156#p255156, quoted below, I thought I'd take a look at some pro games with this joseki and see if bots ever approve of it.
Uberdude wrote:
Bill Spight wrote:
Yes, but! Why :w4:?
Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . 8 . . X O . . . . . . . . . . . . . |
$$ | . 6 X X O . . . . . . . . X . . . . . |
$$ | . 1 O O 4 . . . . , . . . . . X . . . |
$$ | 7 2 3 . . . . . . . . . . . . . . . . |
$$ | . 5 . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]
White gets a big corner. :)
Indeed, bots nearly always say this is terrible for black so this is a joseki for the bin. I don't recall ever seeing it suggested, maybe it's possible to construct a position where it's okay: White invested a lot in building left and top boring.
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Re: Is the 3-3 double hane other ponnuki joseki ever good?

Post by Uberdude »

First test, Gu Li 9p (white) doing it against Gu Lingyi 5p in 2010.

There's a few questions to answer:
1. Once you have played 3-3 and opponent decided to block the side they did and double hane, is taking the "other side" ponnuki better than the normal ponnuki?
2. Should opponent have followed sequence with outside connect and allowing other ponnuki joseki or resist with the atari on top (book answer is generally 'yes if they had a stone on 3rd line at or closer than middle of side' but pros probably know this so selection bias against seeing it)
3. If yes to 1, is it equal to or better than the position before the 3-3 invasion? ie maybe it was ok given the 3-3, but something other than 3-3 was better way to start.

Initial position before the 3-3, LZ 15b224trained gives white 66% if he doesn't do anything in top left and instead plays to settle approach stone at top right.
Screen Shot 2020-03-29 at 10.29.18.png
Screen Shot 2020-03-29 at 10.29.18.png (567.91 KiB) Viewed 15647 times
3-3 and 'other ponnuki' finishing with Gu Li's gote move at h17 (LZ at first preferred one to the right at j17 but very close) is down to 50%.
Screen Shot 2020-03-29 at 10.37.00.png
Screen Shot 2020-03-29 at 10.37.00.png (474.78 KiB) Viewed 15647 times
How about if take the normal ponnuki? LZ thinks this is considerably better, at 70%. One key difference is it's generally sente, though here you can see LZ thinks spending a move with the big d14 push is worth it (here it threatens cuts of g13 as well as e15 hane) with playing first at top right another good idea.
Screen Shot 2020-03-29 at 10.39.57.png
Screen Shot 2020-03-29 at 10.39.57.png (578.04 KiB) Viewed 15647 times
So conclusion here is the switcheroo ponnuki was 20% worse than normal one. White would have done better not to invade at all, and given he did black actually made a mistake to double hane because if white took the normal ponnuki that was better than the starting position (black should have extended or one-point jump to get sente to play important top right first).
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Re: Is the 3-3 double hane other ponnuki joseki ever good?

Post by Uberdude »

2nd game, http://ps.waltheri.net/database/game/65192/, invading white is Kono Rin 9p vs Yuki Satoshi 9p in 2010 Tengen. Picked this one because early opening and black has side extensions of equal distance from the corner, but the top j17 has a 2-space extension so stronger than lonely r9 so I can understand Kono's intention of making the switcheroo ponnuki on the right creating a follow up of approaching around q5 to isolate and attack r9 (and indeed the game went like that).

Initial position, LZ gives likes 3-3 at 63% but q5 approach maybe better at 64%, so 3-3 is fine.
Screen Shot 2020-03-29 at 12.14.59.png
Screen Shot 2020-03-29 at 12.14.59.png (639.71 KiB) Viewed 15626 times
LZ agrees with black blocking right and double hane, and best for both is white to take the usual ponnuki so ends at the same 63%, with next good moves all predictable big places of q5 approach, e17 kick and o16 push.
Screen Shot 2020-03-29 at 12.18.42.png
Screen Shot 2020-03-29 at 12.18.42.png (631.03 KiB) Viewed 15626 times
How about the switcheroo ponnuki? That drops white down to 46% (-17%), and that was with black making the 5% mistake of s18 extension instead of r18 atari (which prevents white sabaki technique of o17 cut later). So switching was a bit more than a 20% mistake if black punished optimally, a bit less in the actual game.
Screen Shot 2020-03-29 at 12.22.59.png
Screen Shot 2020-03-29 at 12.22.59.png (634.67 KiB) Viewed 15626 times
P.S using KataGo to put a point(*old KG so score mean) value on the mistake, it says white leads 3.3 points with the normal ponnuki (7.5 komi), black leads 1.2 with the game line, a difference of around 4 and a half points! And black would be 2.9 with r18 atari which is a wooping 6+ points difference. Pros making mistakes the size of komi in the first 20 moves is quite shocking. It rather spoils the "pros abandoned the old large avalanche variations because Go Seigen's inside turn innovation made a 2 point yose gain and pros are so sensitive to mistakes of that magnitude they can't play it anymore" story.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Bill Spight »

Here is a recent game that I found on Waltheri (ps.waltheri.net) between Cho Chikun and Seo Bongsoo with the switcheroo ponnuki joseki. (Wonderful name, Uberdude! :)) There are some earlier variations of interest, as well.



Edit: Added rollout data. :)
Last edited by Bill Spight on Sun Mar 29, 2020 12:05 pm, edited 1 time in total.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Uberdude »

3rd game, between 2 top Chinese pros in mid-2017 so after AG arrived but unsure how much AI knowledge of this shape disseminated at the time: Mi Yuting 9p white vs Tuo Jiaxi 9p. http://ps.waltheri.net/database/game/75560/. This analysis with KataGo.

Initial position black (Tuo) 3-3 invades at 47%, a good move though KG says an unsettling slide on the right corner is slightly better at 49%.
switcheroo3.1.PNG
switcheroo3.1.PNG (952.1 KiB) Viewed 15588 times
Double hane by white is a little mistake (rare example where, given first hane, bot thinks extend is better than double hane) and black should take the normal ponnuki in sente then take the key slide on right for 53%, so that's a 5% improvement on white's best response to 3-3 (the normal modern joseki of 1-point jump at f3)
switcheroo3.2.PNG
switcheroo3.2.PNG (523.61 KiB) Viewed 15588 times
Game line with switcheroo ponnuki is again about a 20% drop (on a different bot) and loses about komi. KG also wants to play the atari not extend.
switcheroo3.3.PNG
switcheroo3.3.PNG (273.97 KiB) Viewed 15588 times
This game also soon featured the e5 attachment as a resource for black to settle his ponnuki when he tenukid and white attacked it, so we can get a concrete variation to show the superiority of the corner atari over extend. In the game black slid at 1, white attacked the ponnuki at 2 (key point to note is this attack is more powerful than trying to attack the normal ponnuki, because in that one the aji of the 2 corner stones means pushing out gives white liberty problems in the corner). KG says the extension of 6 was soft and white should atari and bravely fight the ko (this is true whether white defended with b2 extend or c2 atari)
Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . 1 . . . . . . . |
$$ | . . . . . O . . . . . . . X X . . . . |
$$ | . . . O . . . . O , . O . O . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . X O X . . |
$$ | . . 8 . . . . . . . . . . X . X X . . |
$$ | . . . , . . . . . , . . . X X O . . . |
$$ | . . . . . . . . . . . . . . O O . . . |
$$ | . 2 . . . . . . . . . . . . . X O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . X . . . 5 9 . . . . . . . . . . . . |
$$ | X . X 7 3 4 6 0 . . . . . . . O . . . |
$$ | . X O O O . . . . , . . . . . O X . . |
$$ | . O X X O . . . . . . . . . . . X . . |
$$ | . O . . X O . . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
So what happens if white resists 5? We end up with this ko:
Click Here To Show Diagram Code
[go]$$Wcm6
$$ | . . . , . . . . . , . . . X X O . . . |
$$ | . . . . . . . . . . . . . . O O . . . |
$$ | . O . . . . . . . . . . . . . X O . . |
$$ | . . . 5 4 . . . . . . . . . . . . . . |
$$ | . X . 2 3 X . . . . . . . . . . . . . |
$$ | X . X 1 X O . . . . . . . . . O . . . |
$$ | . X O O O . . . . , . . . . . O X . . |
$$ | . O X X O . . . . . . . . . . . X . . |
$$ | . O . . X O . . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
With B2, KG thinks black should (by a slim margin) ignore the threat (black is around 25% here) and connect the ko, white pushes through to follow up on the threat, black jumps to save (part of) the corner and then white defends at g5. That last part is crucial, because black g5 is sente for f3 which captures all the white stones and turns the corner black.
Click Here To Show Diagram Code
[go]$$Bcm11
$$ | . . . , . . . . . , . . . X X O . . . |
$$ | . . . . . . . . . . . . . . O O . . . |
$$ | . O . . . . . . . . . . . . . X O . . |
$$ | . . . O X . . . . . . . . . . . . . . |
$$ | . X . X 3 X . . . . . . . . . . 5 . . |
$$ | X . X O 1 O 6 . . . . . . . . O . . . |
$$ | . X O O O . . . . , . . . . . O X . . |
$$ | . O X X O . . . . . . . . . . 2 X . . |
$$ | . O . . X O . . . . . . . . X 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
Compare to if white had played atari, now black winning the ko no longer has the lovely sente atari at g5 as a followup, so this ko is easier for white to lose. White wouldn't defend at g5 but keep pressing the lower right corner
Click Here To Show Diagram Code
[go]$$Bcm11
$$ | . . . , . . . . . , . . . X X O . . . |
$$ | . . . . . . . . . . . . . . O O . . . |
$$ | . O . . . . . . . . . . . . . X O . . |
$$ | . . . O X . . . . . . . . . . . . . . |
$$ | . X . X 3 X . . . . . . . . . 6 5 . . |
$$ | X . X O 1 O . . . . . . . . . O . . . |
$$ | . X O O O . . . . , . . . . . O X . . |
$$ | . O X X O . . . . . . . . . . 2 X . . |
$$ | . . W . X O . . . . . . . . X 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
Indeed KG recommends black to not ignore the threat this time. Black is around 20% rather than 25% in these lines.
Click Here To Show Diagram Code
[go]$$Bcm11 17 ko at 11
$$ | . . . , . . . . . , . . . X X O . . . |
$$ | . . . . . . . . . . . . . . O O . . . |
$$ | . O . . . . . . . . . . . . . X O . . |
$$ | . . . O X . . . . . . . . . . . . . . |
$$ | . X . X 4 X . . . . . . . . . . . . . |
$$ | X . X O 1 O . . . . . . . . . O . . . |
$$ | . X O O O . . . . , . . . . . O X . . |
$$ | . O X X O . . . . . . . . . . 2 X . . |
$$ | . . W 5 X O . . . . . . . . X 3 8 9 . |
$$ | . . . . 6 . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Bill Spight »

Another recent game at Waltheri, between Lee Sedol and Weon Seongjin. :)



Edit: Added rollout data.
Last edited by Bill Spight on Sun Mar 29, 2020 12:34 pm, edited 2 times in total.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Bill Spight »

A third recent game on Waltheri, between Ke Jie and Yang Dingxin.



Edit: Added rollout data.
Last edited by Bill Spight on Sun Mar 29, 2020 12:50 pm, edited 1 time in total.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Kirby »

Probably doesn't make a difference here in terms of the conclusions we're drawing, but I forgot what the consensus was on the number of playouts we feel comfortable with in drawing conclusions. When I do stuff in my journal, I'm content with a low number of playouts, since I suck and I'm OK with getting a sense for the bot's intuition.

But I was a little surprised to see the first few examples with under 10k playouts. I'd suspect that it doesn't make a difference here, but I was just curious, since I thin folks discussed meaningful playout count before (but I forgot what folks thought makes it meaningful).
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Knotwilg »

Kirby wrote:Probably doesn't make a difference here in terms of the conclusions we're drawing, but I forgot what the consensus was on the number of playouts we feel comfortable with in drawing conclusions. When I do stuff in my journal, I'm content with a low number of playouts, since I suck and I'm OK with getting a sense for the bot's intuition.

But I was a little surprised to see the first few examples with under 10k playouts. I'd suspect that it doesn't make a difference here, but I was just curious, since I thin folks discussed meaningful playout count before (but I forgot what folks thought makes it meaningful).
I was reminded of that when I left an analysis where I was at 50% to have dinner and found on my return I was actually leading by 65%.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Bill Spight »

Kirby wrote:Probably doesn't make a difference here in terms of the conclusions we're drawing, but I forgot what the consensus was on the number of playouts we feel comfortable with in drawing conclusions. When I do stuff in my journal, I'm content with a low number of playouts, since I suck and I'm OK with getting a sense for the bot's intuition.

But I was a little surprised to see the first few examples with under 10k playouts. I'd suspect that it doesn't make a difference here, but I was just curious, since I thin folks discussed meaningful playout count before (but I forgot what folks thought makes it meaningful).
Despite the fact that the Elf commentaries are a year and a half old, and bots are getting better all the time, they use a lot of rollouts, more than I might take the time to generate on my own. I edited the SGF files to include the number of rollouts used to estimate the winrates for each option, and most of them are around 30k. One is as low as 15.5k, and a number are more than 100k. :)
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Uberdude »

Yes, more playouts makes the results more reliable, though I'd be surprised for this 20% difference to disappear. The first 2 games were posted from my laptop in bed :) . I'm guessing Knotwilg had a complicated position in which positional judgement intuition was not a good judge because deep reading along sharp lines was needed to discern something almost working and being great and not quite working and being crap. Whereas here the generalised positional knowledge of the network about one ponnuki vs the other is a good first estimate.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Uberdude »

Example 4, finally found one where the switcheroo ponnuki was actually better! Though don't take this as evidence that "about 1 in 4 times pros play it it's good" because I checked a few others that were bad, and didn't even bother checking quite a few examples in Chinese openings similar to game 2. The white player using it well is Park Yeonghun 9p against Baek Hongseok 7p in 2009, http://ps.waltheri.net/database/game/56707/. It's quite a developed middlegame position, but the key points are:
- black is very strong around q11 so the r14 area is boring
- top side is urgent following black's f17 approach

In the initial position white is around 32% with various choices in the top left. Top right 3-3 only gets a few playouts, but barely loses 1% when played, and KataGo agrees with black's blocking the top and double hane choice.
switcheroo4.1.PNG
switcheroo4.1.PNG (922.4 KiB) Viewed 15505 times
Following the switcheroo joseki (and this time KG agrees with the extend not atari in the corner, presumably with white's central thickness in support black doesn't have a realistic attack on the white ponnuki so the better yose choice wins) white started off with slightly MORE than 32% but with more playouts this drops to around 32%, essentially the same as before. Park presumably saw this as making some top side strength in sente to help support his kick and pincer plan (which KG also approved of, well done Park!).
switcheroo4.2.PNG
switcheroo4.2.PNG (479.74 KiB) Viewed 15505 times
The normal ponnuki is really bad here (in fact so bad after atari it's better to connect at s16 and live in the corner with an L+2 group), down to 18%. White's played on the useless right side in a small space it's still weak, and didn't get support on the important top side.
switcheroo4.3.PNG
switcheroo4.3.PNG (482.55 KiB) Viewed 15505 times
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Bill Spight »

Here is one where Elf prefers the usual play, but the switcheroo is within the margin of error. White invades the corner at move 68. Black is strong in the vicinity.

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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Gomoto »

Thanks for sharing. Interesting variations.
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Re: Is the 3-3 double hane switcheroo ponnuki joseki ever go

Post by Bill Spight »

Another game where Elf prefers the usual ponnuki to the switcheroo. However, it does not prefer the usual ponnuki, either. It prefers to sacrifice the corner. :)

First, the game record.
Click Here To Show Diagram Code
[go]$$Bcm69 Fan Yunruo, 6 dan (W) - Xiao Zhenghao, 9 dan, 2017-10-14
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . 5 6 . . . . . . . . . . . . . |
$$ | . . 1 3 4 . . . . . . . . O . O O O . |
$$ | . 7 2 O 0 . . . . , . . . . X X X O . |
$$ | . 8 9 . . . . . . . . . X . . . X X . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . O X . X . . . |
$$ | . . . . . . . . . . . O . O X X . . . |
$$ | . . . , . . . . . , . . . . O , X . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . O . . . . . . |
$$ | . . . . X . . . . . . . . . . X . X . |
$$ | . . O . . . . . . . . . . . O X . O . |
$$ | . . O X . . X . . X . . . . X O O . . |
$$ | . . O X . X O X . , . X . . X , . . . |
$$ | . . O O X . O X O O X . . . . X O . . |
$$ | . . . X O O O O X X . O . . . . O . . |
$$ | . . . . . . . X . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Bcm79 Game Record, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . 4 . . X O . . . . . . . . . . . . . |
$$ | . 2 X X O . . . . . . . . O . O O O . |
$$ | . X O O O . . . . , . . . . X X X O . |
$$ | 3 O X . . . . . . . . . X . . . X X . |
$$ | . 1 . . . . . . . . . . . . . . O . . |
$$ | . 7 6 . . . . . . . . . . . X . . . . |
$$ | . 9 8 . . . . . . . . . O X . X . . . |
$$ | . . 0 . . . . . . . . O . O X X . . . |
$$ | . . . , . . . . . , . . . . O , X . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . O . . . . . . 5 . O . . . . . . |
$$ | . . . . X . . . . . . . . . . X . X . |
$$ | . . O . . . . . . . . . . . O X . O . |
$$ | . . O X . . X . . X . . . . X O O . . |
$$ | . . O X . X O X . , . X . . X , . . . |
$$ | . . O O X . O X O O X . . . . X O . . |
$$ | . . . X O O O O X X . O . . . . O . . |
$$ | . . . . . . . X . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Bcm89 Game Record, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O . . X O . . . . . . . . . . . . . |
$$ | . O X X O . . . . . . . . O . O O O . |
$$ | . X O O O . . . . , . . . . X X X O . |
$$ | X . X . . . . . . . . . X . . . X X . |
$$ | . X 3 . . . . . . . . . . . . . O . . |
$$ | . X O . . . . . . . . . . . X . . . . |
$$ | . X O . . . . . . . . . O X . X . . . |
$$ | . 1 O . . . . . . 4 . O . O X X . . . |
$$ | . 2 . , . . . . . , . . . . O , X . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . O . . . . . . X . O . . . . . . |
$$ | . . . . X . . . . . . . . . . X . X . |
$$ | . . O . . . . . . . . . . . O X . O . |
$$ | . . O X . . X . . X . . . . X O O . . |
$$ | . . O X . X O X . , . X . . X , . . . |
$$ | . . O O X . O X O O X . . . . X O . . |
$$ | . . . X O O O O X X . O . . . . O . . |
$$ | . . . . . . . X . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Now, Elf's mainline variation.
Click Here To Show Diagram Code
[go]$$Bcm73 Black cuts!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 9 8 2 . . . . . . . . . . . . . . |
$$ | . 5 X X O . 0 . . . . . . O . O O O . |
$$ | . 3 O O 1 . . . . , . . . . X X X O . |
$$ | . 4 6 . 7 . . . . . . . X . . . X X . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . . . . . . . . . . O X . X . . . |
$$ | . . . . . . . . . . . O . O X X . . . |
$$ | . . . , . . . . . , . . . . O , X . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . O . . . . . . |
$$ | . . . . X . . . . . . . . . . X . X . |
$$ | . . O . . . . . . . . . . . O X . O . |
$$ | . . O X . . X . . X . . . . X O O . . |
$$ | . . O X . X O X . , . X . . X , . . . |
$$ | . . O O X . O X O O X . . . . X O . . |
$$ | . . . X O O O O X X . O . . . . O . . |
$$ | . . . . . . . X . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Click Here To Show Diagram Code
[go]$$Bcm83 And sacrifices the corner.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | 6 . X O O . . . . . . . . . . . . . . |
$$ | 0 X X X O . O 2 . . . . . O . O O O . |
$$ | . X O O X . 1 . . , . . . . X X X O . |
$$ | 9 O O . X . . . . . . . X . . . X X . |
$$ | . 8 . . . . . . . . . . . . . . O . . |
$$ | . 4 7 3 . . . . . . . . . . X . . . . |
$$ | . 5 . . . . . . . . . . O X . X . . . |
$$ | . . . . . . . . . . . O . O X X . . . |
$$ | . . . , . . . . . , . . . . O , X . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . O . . . . . . |
$$ | . . . . X . . . . . . . . . . X . X . |
$$ | . . O . . . . . . . . . . . O X . O . |
$$ | . . O X . . X . . X . . . . X O O . . |
$$ | . . O X . X O X . , . X . . X , . . . |
$$ | . . O O X . O X O O X . . . . X O . . |
$$ | . . . X O O O O X X . O . . . . O . . |
$$ | . . . . . . . X . . . . . . . . . . . |
$$ ---------------------------------------[/go]
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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