Life In 19x19 :: Ladder study

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Ladder study http://www.lifein19x19.com/viewtopic.php?f=15&t=17889	Page 1 of 1

Author:	lightvector [ Tue Nov 24, 2020 7:08 pm ]
Post subject:	Ladder study
A fun position I found. The upper right is the outcome of one possible variation of a 3-4 large knight probe joseki ((https://online-go.com/joseki/30931), the bottom left is a familiar joseki that everyone knows. White just played the marked move to capture a black stone in a ladder. Black to play. What is the best that black can do? Click Here To Show Diagram Code [go]$$Bc Black to play $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . W X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go]

Author:	Kirby [ Tue Nov 24, 2020 8:20 pm ]
Post subject:	Re: Ladder study
Not a solution: I thought it might be this at first: Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . 7 O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . 5 . . . . . . . . . . . . . . . . . \| $$ \| . 2 3 . . . . . . . . . . . . . . . . \| $$ \| 4 1 O O O X . . . , . . . . . X . . . \| $$ \| 6 X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] But I don't know what to do in this sequence: Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . W . . . . . . . . . . . . . . . . \| $$ \| . O X . . . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Maybe something along these lines? Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . 5 . . . . . . . . . . . . . . . . \| $$ \| . . O 3 . . . . . . . . . . . . . . . \| $$ \| . O 4 2 1 . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go]

Author:	dany [ Wed Nov 25, 2020 5:06 am ]
Post subject:	Re: Ladder study
Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . 4 7 . . . . . . . . . . . . . . . \| $$ \| . 2 3 5 6 . . . . . . . . . . . . . . \| $$ \| . 1 O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go]

Author:	Kirby [ Wed Nov 25, 2020 7:10 am ]
Post subject:	Re: Ladder study
dany wrote: Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . 4 7 . . . . . . . . . . . . . . . \| $$ \| . 2 3 5 6 . . . . . . . . . . . . . . \| $$ \| . 1 O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Initially, I didn't think that this worked since after white connects, the ladder doesn't seem working: Click Here To Show Diagram Code [go]$$Wc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . 5 4 2 O O O O X X . \| $$ \| . . . . . . . . O X X 3 . O X X . X . \| $$ \| . . O . . . . O X X O . . . . O X . . \| $$ \| . . . . . . O X X O . . . . . . . . . \| $$ \| . . . . . O X X O . . . . . . . . . . \| $$ \| . . . . O X X O . . . . . . . . . . . \| $$ \| . . . O X X O . . , . . . . . , . . . \| $$ \| . . O X X O . . . . . . . . . . . . . \| $$ \| . . . X O . . . . . . . . . . . . . . \| $$ \| . . . O . . . . . . . . . . . . . . . \| $$ \| . 1 O X . . . . . . . . . . . . . . . \| $$ \| . O X X O . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] So maybe black can do this ladder first... Click Here To Show Diagram Code [go]$$Wc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . a O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . X C . O X . . \| $$ \| . . . . . . . . . . . X O O . . . . . \| $$ \| . . . . . . . . . . X O O X . . . . . \| $$ \| . . . . . . . . . X O O X . . . . . . \| $$ \| . . . , . . . . X O O X . . . , . . . \| $$ \| . . . . . . . X O O X . . . . . . . . \| $$ \| . . . . . . X O O X . . . . . . . . . \| $$ \| . . . . . X O O X . . . . . . . . . . \| $$ \| . 1 O X 2 5 O X . . . . . . . . . . . \| $$ \| . O X X O 3 4 . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Then if black plays the marked move, above, black can come out at 'a'. But is that worth it? Maybe there's a subtler way. Thinking along those lines, I guess this works in response to white's connection: Click Here To Show Diagram Code [go]$$Wc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . 2 . . . . . . . . . . . . . . \| $$ \| . 1 O X . . . . . . . . . . . . . . . \| $$ \| . O X X O . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] So I think dany's idea seems somewhat solid...

Author:	lightvector [ Wed Nov 25, 2020 8:01 am ]
Post subject:	Re: Ladder study
@dany and Kirby - good idea, but... Nice sequence by black! Yep this does break the ladder. However, white can play like this: Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . . O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . 9 . . . . . . . . . . . . . . . \| $$ \| . 0 4 7 8 . . . . . . . . . . . . . . \| $$ \| . 2 3 5 6 . . . . . . . . . . . . . . \| $$ \| . 1 O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Black escapes the ladder, but white is not dissatisfied: Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . , . 1 O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . 2 O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . X . . . . . . . . . . . . . . . \| $$ \| . O O X O . . . . . . . . . . . . . . \| $$ \| . O X X O . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] The problem is that black's exchanges in the lower left are a little costly. For example, if black simply takes a stone now white gains a lot in the lower left in compensation and White's top side group is still doing fine, getting the pleasant forcing moves at at 2 and 4: Click Here To Show Diagram Code [go]$$Bc White is fine $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . 1 O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . 5 3 X O O O O X X . \| $$ \| . . . . . . . . . . 4 2 . O X X . X . \| $$ \| . . O . . . . . . . . . . . O O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . X 6 . . . . . . . . . . . . . . \| $$ \| . O O X O . . . . . . . . . . . . . . \| $$ \| . O X X O . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Similar this way: Click Here To Show Diagram Code [go]$$Bc White is also fine $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . 5 O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . 9 7 X O O O O X X . \| $$ \| . . . . . . . . . . 8 6 . O X X . X . \| $$ \| . . O . . . . . . . . . . . O O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . X 1 3 0 . . . . . . . . . . . . \| $$ \| . O O X O 2 4 . . . . . . . . . . . . \| $$ \| . O X X O . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Because White hanes on top are so pleasant, Black may be better off to fight, which is of course playable, but the lower left exchanges are still costing black a little. Click Here To Show Diagram Code [go]$$Bc Fight $$ --------------------------------------- $$ \| . . . . . . . . . . . 3 . . . . . . . \| $$ \| . . . . . . . . . 2 4 O X X . . . . . \| $$ \| . . . . . . . . . . O X O X X X O . . \| $$ \| . . . O . . . . . . . X O O O O X X . \| $$ \| . . . . . . . . . . . 1 . O X X . X . \| $$ \| . . O . . . . . . . . . . . O O X . . \| $$ \| . . . . . . . . . . . 5 . . . . . . . \| $$ \| . . . . . . . . . . . . . . . 6 . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . X . . . . . . . . . . . . . . . \| $$ \| . O O X O . . . . . . . . . . . . . . \| $$ \| . O X X O . . . . . . . . . . . . . . \| $$ \| . X O O O X . . . , . . . . . X . . . \| $$ \| . X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] Can black do better?

Author:	Kirby [ Wed Nov 25, 2020 8:24 am ]
Post subject:	Re: Ladder study
If we have to take into account bad exchanges and not just capturing something, maybe this? Click Here To Show Diagram Code [go]$$Bc $$ --------------------------------------- $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . O X X . . . . . \| $$ \| . . . . . . . . . . O C O X X X O . . \| $$ \| . . . O . . . . . , . 4 O O O O X X . \| $$ \| . . . . . . . . . . . . . O X X . X . \| $$ \| . . O . . . . . . . . . . . . O X . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . , . . . . . , . . . . . , . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . . . . . . . . . . . . . . . . . . \| $$ \| . . 3 . . 9 . . . . . . . . . . . . . \| $$ \| . 2 5 . 7 . . . . . . . . . . . . . . \| $$ \| 6 1 O O O X . . . , . . . . . X . . . \| $$ \| 8 X X X O X . . . . . . . . . . . . . \| $$ \| . O O O X . X . . . . . . . . . . . . \| $$ \| . . . . . X . . . . . . . . . . . . . \| $$ ---------------------------------------[/go] It's hard for me to evaluate how good or bad black is in a position like this. Nothing got captured, but black made a position on the outside? I feel like i'm just guessing at this point, so I'll wait for more discussion.

Author: dany [ Wed Nov 25, 2020 1:09 pm ]

Post subject: Re: Ladder study

lightvector wrote:

Can black do better?

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

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

Author: lightvector [ Fri Nov 27, 2020 1:50 pm ]

Post subject: Re: Ladder study

Yep, that's just about right.

Based on analysis from Kata, below is the exact correct order of moves. Although Kata does *not* solve the ladder breaker/maker tactics all correctly without help, I believe it is fairly trustworthy for evaluating the whole-board positions *after* the ladder is resolved, which is what I'm using it for.

The theme of this position is "ladder magnification", which I've seen come up in many other positions too. Breaking a ladder sometimes involves moves that are costly. However, if your ladder breaker is far more heavy for the opponent to ignore than letting you escape from the ladder, then you should run out from the ladder one or more times first, to make it similarly heavy for the opponent. That way, either the opponent backs down right away and you never have to pay the cost at all, or else the opponent plays a broken ladder out several times and you get much more.

The correct order of moves in this problem is very interesting.

Firstly, Black should make one bad exchange early, to make sure White is heavily committed to the lower left. If Black starts to run out with "a" first, then White might accept the bigger ladder capture and then later with :b1:

give way with :w2:

at "b". (Actually, Black can run with "a" exactly once first, but that's the almost only deviation from this order of moves that is possible if Black wants the best result).

Click Here To Show Diagram Code: [go]$$Bc First, push $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . a O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . b . . . . . . . . . . . . . . . . | $$ | . 2 . . . . . . . . . . . . . . . . . | $$ | . 1 O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Side variation:

If White sees the big trouble that they're about to get into, then White could plausibly try to back off immediately:

Click Here To Show Diagram Code: [go]$$Bc White tries to dodge $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . . O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 2 . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 1 O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Fascinatingly, if Black simply accepts the profit with :b3:

below, then in KataGo's judgment, this is actually a slight success for White compared to what is to come! Black lets White get away too easy:

Click Here To Show Diagram Code: [go]$$Bc Black lets White get away too easy. $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . 6 O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 4 O . . . . . . . . . . . . . . . . | $$ | . 3 a . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | 5 O O O X . X . . . . . . . . . . . . | $$ | . C C C . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The problem above is that white remains fairly solid in the lower left. "a" is White's sente, and Black will have to fill a few more points in the endgame to finish the capture. Instead, Black should play as below:

Click Here To Show Diagram Code: [go]$$Bc Tesuji! $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . . O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 3 . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If White finishes the ladder as before, then because of :b3:

, White is unable seal Black in:

Click Here To Show Diagram Code: [go]$$Bc White cannot block at "a" due to the marked stone. $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . 4 O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . B . . . . . . . . . . . . . . . | $$ | . O O 6 . . . . . . . . . . . . . . . | $$ | . X 5 7 a . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

So we get this result:

Click Here To Show Diagram Code: [go]$$Wc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O . O X X X O . . | $$ | . . . O . . . . . . . O O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 3 . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . B . . . . . . . . . . . . . . . | $$ | . W W W 1 . . . . . . . . . . . . . . | $$ | . X X X 2 . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

With the extra captures and no longer needing to fill-in, Black's territory is about 14 points larger than without the tesuji. White gains an extra move at :w3:

, but this is offset by the fact that White's remaining 4-stone outside group alone is noticeably weaker than before. Black's cut-off tesuji stone even still has a bit of aji.

Alternatively, if White responds to Black's tesuji by taking back the corner, Black simply escapes from the ladder.

Click Here To Show Diagram Code: [go]$$Bc Black is happy $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . 5 O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . B . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . 4 . . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Via tewari, we can see that black has gotten a ladder breaker very cheaply. In the below tewari, the exchange of :b3:

ladder break for the extremely passive :w4:

below is obviously highly pleasant for Black, so Black is more than satisfied with this.

Click Here To Show Diagram Code: [go]$$Bc Tewari $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . 5 O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 3 . . . . . . . . . . . . . . . | $$ | . . 4 . . . . . . . . . . . . . . . . | $$ | . 2 . . . . . . . . . . . . . . . . . | $$ | . 1 O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Next, Black should magnify the ladder by running out twice.

As we saw earlier in this thread, it is relatively cheaper for White to let Black escape from the ladder compared to other options. Therefore, Black should make the ladder heavier for White before anything further. Black can afford to do this because "a" in the diagram below is so strongly forcing against White. With white having invested the marked stone, White cannot allow the lower left to collapse, even in exchange for a turtle shell or a "super turtle shell" on the top.

Click Here To Show Diagram Code: [go]$$Bc Next, magnify the ladder twice $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . 4 3 1 O O O O X X . | $$ | . . . . . . . . . . . 2 . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . W a . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Side variation:

Cutting at :b1:

below before magnifying the ladder would be a slight mistake in move order. White responds immediately at :w2:

Click Here To Show Diagram Code: [go]$$Bc Black fails to maximize the profit $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . . O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O 1 . . . . . . . . . . . . . . . . | $$ | 2 X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Black can get a ladder break this way and this is still an overall reasonable result for black, but Black has still made more bad exchanges in the lower left than they needed to in order to make the ladder escape work. Black's two stones have some outside worth, but Black has lost forcing moves like "a" and endgame value at "b".

Click Here To Show Diagram Code: [go]$$Bc Black is okay, but not as good as the main line $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . . . 5 O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 3 . . . . . . . . . . . . . . . . . | $$ | . O 1 . a . . . . . . . . . . . . . . | $$ | 2 X O O O X . . . , . . . . . X . . . | $$ | 4 X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . b . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Now that the ladder is heavy for white, black can cut to activate the ladder breaker sequence. White has nothing better to do than follow along - even the 3-stone ladder capture is not worth losing the entire lower left.

Click Here To Show Diagram Code: [go]$$Bc Now begin ladder break $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . . . O . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 2 . . . . . . . . . . . . . . . . | $$ | . O 1 . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If it seems surprising to you that it could be good for Black can sacrifice so many stones in the ladder, that White can't even afford to take them see here:

Consider that as a baseline, White would normally be getting this anyways, if Black is getting an extra move in the lower left:

Click Here To Show Diagram Code: [go]$$Bc Baseline $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O . O X X X O . . | $$ | . . . O . . . . . . . O O O O O X X . | $$ | . . . . . . . . . . . . . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . |[/go]

So we're only talking about the difference between that and capturing two more stones, rather than getting a thick 3-stone capture out of nothing. Also, just looking at the whole board as a fresh position, it's not hard to see why Black could be ahead if the entire lower left collapses.

Click Here To Show Diagram Code: [go]$$Bc Whole board judgment $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O . O X X X O . . | $$ | . . . O . . . . . O . . O O O O X X . | $$ | . . . . . . . . . . O O . O X X . X . | $$ | . . O . . . . . . . . . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . X . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Black ultra-thickly owns the whole lower left. That counterbalances with White being ultra thick on top, but Black still owns the upper right corner too and is not even enclosed there. Black has two big corners secure and the upper hand on a third and is not behind on overall board thickness, while White only has one corner and sente. So Black is winning.

At this point, Black magnifies the ladder one more time, and then continues the lower left.

Click Here To Show Diagram Code: [go]$$Bc One more $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . . 3 O . O X X . X . | $$ | . . O . . . . . . . 4 . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . O X 5 6 . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Side variation:

Black should cut before investing the fourth stone in the ladder. If Black gets the order wrong, then White will switch gears and play like below:

Click Here To Show Diagram Code: [go]$$Bc Black gets the order wrong $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . . 1 O . O X X . X . | $$ | . . O . . . . . . . 2 . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 8 . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 5 6 4 . . . . . . . . . . . . . . . | $$ | 7 O 3 . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The 4 ladder stone capture is just enough to make up for the damage in the lower left, because the remains of white's outside group avoid coming under serious attack and still cooperate with white's upper side framework. Therefore, Black needs White to completely commit in the lower left before investing the fourth stone in the ladder.

One interesting tactical detail here is that Black can try to get ahead of White here with a ladder maker:

Click Here To Show Diagram Code: [go]$$Bc Black tricky ladder maker $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . c X O . O X X . X . | $$ | . . O . . . . . . . O . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 7 . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X O O . . . . . . . . . . . . . . . | $$ | a O X b . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

White "a" and "b" are not good enough, since then Black gets away at "c". And neither is White "c" good enough, since then Black goes back and captures "a" and White is worse off compared to the diagram above, since :b7:

is now ahead of White's group on the left, putting it under serious attack.

White's correct answer is this funny-looking empty triangle ladder maker :w1:

below, and when Black descends to rebreak the ladder, White :w3:

is a surprising tesuji to remake the ladder once and for all. All Black can do is capture at "a", and White gets to connect at "b". Black still made a lot of profit, but White again gets all 4 stones in the ladder without their lower left group coming under serious threat.

Click Here To Show Diagram Code: [go]$$Wc White pulls out some more tesuji! $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . . X O . O X X . X . | $$ | . . O . . . . . . . O . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . 3 . . . . . . . . . . . . . . . | $$ | . 2 X b . . . . . . . . . . . . . . . | $$ | . . 1 . . . . . . . . . . . . . . . . | $$ | . X O O . . . . . . . . . . . . . . . | $$ | a O X . . . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

These tesuji seem to be the key reason why Black must cut before investing the fourth stone in the ladder.

And finally we get this result. With White having been forced to play a broken ladder many times, this more than compensates the cost of Black's moves on the lower left. Black has a good position, and far better than playing all the moves in the lower left first.

Click Here To Show Diagram Code: [go]$$Bc Result $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . 5 X O . O X X . X . | $$ | . . O . . . . . . . O . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 3 . . . . . . . . . . . . . . . | $$ | . 4 O 1 2 . . . . . . . . . . . . . . | $$ | . O X X O . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

A result like this would also be good for Black - the lower left is a a big enough disaster for White to more than balance the huge top side capture, so Black is ahead.

Click Here To Show Diagram Code: [go]$$Wc Even better $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . 1 X O . O X X . X . | $$ | . . O . . . . . . . O . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 2 O X . . . . . . . . . . . . . . . | $$ | . O X X O . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Lastly, there is this fascinating detail, involving a ladder going the other way. What if white connects directly here as below? If you read carefully, you'll find that the ladder at "a" actually is not broken yet - it is still working for White, barely. And, the ladder at "b" does not immediately work for Black either:

Click Here To Show Diagram Code: [go]$$Wc What if white tries to save everything? $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . a X O . O X X . X . | $$ | . . O . . . . . . . O . . . . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 1 O X b . . . . . . . . . . . . . . | $$ | . O X X O . . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

In this case, Black goes ahead and plays the non-working ladder anyways. Because if White tries to run, Black has the massively forcing ladder maker at :b4:

Click Here To Show Diagram Code: [go]$$Wc Ladder maker $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . O X O X X X O . . | $$ | . . . O . . . . . O X X O O O O X X . | $$ | . . . . . . . . . . X O . O X X . X . | $$ | . . O . . . . . . . O . . 4 . O X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O O X 2 . . . . . . . . . . . . . . | $$ | . O X X O 3 . . . . . . . . . . . . . | $$ | . X O O O X . . . , . . . . . X . . . | $$ | . X X X O X . . . . . . . . . . . . . | $$ | . O O O X . X . . . . . . . . . . . . | $$ | . . . . . X . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Which seems like a fitting end to this problem.

(edit: a few typo fixes)

Author:	lightvector [ Fri Nov 27, 2020 1:59 pm ]
Post subject:	Re: Ladder study
I don't know if the above tactical judgments would be within the range of human pros (pros can be quite amazing with time to read) - but some easier takeaways for us amateurs: * In general, if your ladder breaker is extremely severe and forcing, whereas the ladder that it breaks is not so severe, it is surprisingly often a good move to run out the ladder a little bit first and magnify its value. Then, either the opponent backs down and you get to escape without even having to play your ladder breaker, or else the opponent has to give up a lot more by playing out a broken ladder for some distance. * Just as a good thing to know - the 3-3 point invasion double-hane joseki in particular seems to have very severe ladder-breaking aji against it. Depending on the precise diagonal lane that the ladder is coming in on, there are multiple possible sequences that will either break the ladder or make the corner collapse.

Author:	Uberdude [ Sat Nov 28, 2020 12:14 am ]
Post subject:	Re: Ladder study
Great post, thanks lightvector. lightvector wrote: I don't know if the above tactical judgments would be within the range of human pros (pros can be quite amazing with time to read) See https://lifein19x19.com/viewtopic.php?p=222978#p222978 for some crazy pro double ladder breaking and making.

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