Spiral ladder problem from a real game

Uberdude · #1

I had a rather nice spiral ladder problem in a random online game recently. The backstory: black has just captured the marked ko, should white look for a ko threat (not much on this board) or connect and if connect what happens if black then connects the ko? Can the white stones escape?

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

Black stubbornly connects at 2, obviously bad shape so white throws in and squeezes. Black has 4 liberties, white has 3 so has to try to break out.

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

White ataris to break out, 14 can't block or a and b are sente and then cut is a ladder. So black has to extend again, and then white cuts with 3 liberties inside and has to capture something to survive and thus kill the big black group inside.

Click Here To Show Diagram Code: [go]$$Wcm9 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . b . . . . . , . . . | $$ | . . . . . . . . . a 2 O O O O O . . . | $$ | . . . . . . . . . 1 X O X X O X . . . | $$ | . . . . . . 9 6 4 X O X X X O X O . . | $$ | . . . . . . 8 7 5 3 O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

First, some simple failures for black. If atari from above with 18 white squeezes and captures in a ladder: thanks to the big squeezy wall white can run it along there before going diagonally so it misses the top right black corner.

Click Here To Show Diagram Code: [go]$$Bcm18 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . p . . | $$ | . . . . . . . . . . . . . . . l o . . | $$ | . . . . . . . . . . . . . . h k m n . | $$ | . . . . . . . . . . 8 0 b d g i j . . | $$ | . . . , . . . . . 6 7 9 a c e f . . . | $$ | . . . . . . . . 4 1 X O O O O O . . . | $$ | . . . . . . . 2 3 5 X O X X O X . . . | $$ | . . . . . . O X X X O X X X O X O . . | $$ | . . . . . . X O O O O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Sometimes black playing the net-but-not-a-net shape point is a tesuji to avoid bad shape squeezes (e.g. https://youtu.be/ZAoSBbPyG5U?t=15m23s) but here white uses 19 and 21 in sente for that ladder, and 23 in sente for capturing cutting stone, and then 25 captures black with only 2 liberties to white's 3.

Click Here To Show Diagram Code: [go]$$Bcm18 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . 5 . . . . . . . . | $$ | . . . , . . . . . 4 3 . . . . , . . . | $$ | . . . . . . . 8 1 2 X O O O O O . . . | $$ | . . . . . . . . . O X O X X O X . . . | $$ | . . . . . 6 O X X X O X X X O X O . . | $$ | . . . . . . X O O O O O X X X O O . . | $$ | . . . . . . 7 X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

So black's best try is to simply extend with the empty triangle, saving 3 stones for now and trying to avoid white's forcing moves to either side setting up a capture with 2 or fewer liberties. For example using the same sente moves as before white can set up a net with 25 from which black can't escape, but he has enough liberties to win the capturing race at a (this is still a good result for white to squeeze on the outside in sente, but kill everything is even better!)

Click Here To Show Diagram Code: [go]$$Bcm18 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . 5 . . . . . . . . | $$ | . . . , . . . 0 . 4 3 . . . . , . . . | $$ | . . . . . . 8 9 . 2 X O O O O O . . . | $$ | . . . . . . . 1 . O X O X X O X . . . | $$ | . . . . . 6 O X X X O X X X O X O . . | $$ | . . . . . . X O O O O O X X X O O . . | $$ | . . . . . . 7 X X a . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

So white needs to capture black without him getting 3 libs, a more forceful approach is needed. 21 is a classic shape tesuji. If black captures then white ataris on the outside, f7 is sente and then it's a ladder (and black answering f7 at f6 to take a lib doesn't change that). So black extends out, white takes the f7 sente and then h9 is the shape point. Black pushes out to avoid shapback, and then the fun starts...

Click Here To Show Diagram Code: [go]$$Bcm18 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . 5 2 . . . . , . . . | $$ | . . . . . . . 8 4 3 X O O O O O . . . | $$ | . . . . . . 9 1 . O X O X X O X . . . | $$ | . . . . . 6 O X X X O X X X O X O . . | $$ | . . . . . 7 X O O O O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm27 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . 9 . . . . . . . . . . . | $$ | . . . . . . 0 8 5 . . . . . . . . . . | $$ | . . . . . . 7 6 4 1 . . . . . . . . . | $$ | . . . , . . . 3 2 X O . . . . , . . . | $$ | . . . . . . . O O X X O O O O O . . . | $$ | . . . . . . X X . O X O X X O X . . . | $$ | . . . . . O O X X X O X X X O X O . . | $$ | . . . . . X X O O O O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm37 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . 7 . . . . . . . . . . . . . | $$ | . . . 9 8 6 3 . . . . . . . . . . . . | $$ | . . . . 5 4 2 O . . . . . . . . . . . | $$ | . . . . . 1 X X O . . . . . . . . . . | $$ | . . . . . . O X X O . . . . . . . . . | $$ | . . . , . . . O X X O . . . . , . . . | $$ | . . . . . . . O O X X O O O O O . . . | $$ | . . . . . . X X 0 . X O X X O X . . . | $$ | . . . . . O O X X X O X X X O X O . . | $$ | . . . . . X X O O O O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

etc

Click Here To Show Diagram Code: [go]$$Wcm47 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . 1 O . . . . . . . . . . . . . | $$ | . . . O X X O . . . . . . . . . . . . | $$ | . . . . O X X O . . . . . . . . . . . | $$ | . . . . . O X X O . . . . . . . . . . | $$ | . . . . . 9 O X X O . . . . . . . . . | $$ | . . . , 0 8 5 O X X O . . . . , . . . | $$ | . . . . 7 6 4 O O X X O O O O O . . . | $$ | . . . . . 3 X X X 2 X O X X O X . . . | $$ | . . . . . O O X X X O X X X O X O . . | $$ | . . . . . X X O O O O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

hyperpape · #2

Impressive. Also:

1. Who was which color?
2. Can any bot read that?

lightvector · #3

One little detail: White doesn't actually need to read all of this to be completely winning.

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . . . . . . . , . . . | $$ | . . . . . . . . . . . O O O O O . . . | $$ | . . . . . . . . . . X O X X O X . . . | $$ | . . . . . . . . 2 X O X X X O X O . . | $$ | . . . . . . . . a 1 O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . 3 . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Just pushing at W1 gains a liberty, so now white wins the capturing race without needing any reading.

Of course, if you can read it out, pushing again at "a" is *better*, but white is easily 30+ points ahead just like this unless there was an absolutely monster reverse komi.

Uberdude · #4

hyperpape,
1. I was white. I actually made a mistake and played k10 before the g7 cut but my opponent kindly returned the favour by pushing through at k9. Then you can get the ladder to the north east to the edge of the board, capture in middle and then north west ladder.
2. I tried a bit with LZ 231 and it didn't find it. It was happy enough to do things like letting inside stones die ans squeeze with that 3 lib net. White is 99% that way too. Looking at the expected lines when it does play the right moves it is through local shape intuition rather than reading the ladders to the end. With 100k at g7 cut time MiniGo cormorant thinks black j9 net shape saves the day as it doesn't see the ladder starting at l11 working (it looks at the net that way a bit, not using the wall to push ladder along enough to avoid top right).

lightvector, hah! I missed that in my excitement. I hadn't found the spiral ladder when I connected the ko, but figured 3 inside liberties was enough to capture something on the outside for a fun challenge.

lightvector · #5

Having ladders as an input feature, KataGo seems to handle this position okay, but not perfectly.

So, firstly, if taking the position as given, KataGo's score maximization instinct is nowhere near strong enough to prevent it from backing down and simply accepting a 99+% win rate. Either backing out at the point at my earlier post...

...or in any number of variations where white *does* try to push out and where black tries to play some struggling moves on the white lower right group like shown, or even running out the ladder at 'a':

Click Here To Show Diagram Code: [go]$$Wcm1 $$ | . . . , . . . . . . . . . . . , . . . | $$ | . . . . . . . . . . . O O O O O . . . | $$ | . . . . . . . . . . X O X X O X a . . | $$ | . . . . . . . . . X O X X X O X O . . | $$ | . . . . . . . . . 1 O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O 3 2 O . | $$ | . . . . . . . . . . . . . O . . . 4 . | $$ ---------------------------------------[/go]

... and where KataGo lets black get away with having a ko, or other things!

Because, White still ends up (in its estimation) 40+ points ahead in these variations with 99+% winrate. Its score maximization instinct is nowhere near strong for it to seek *even more* score given all these easy ways out that lead to a game already ahead by so much for white. So it's happy to let black get away with something.

In some lines (including where white goes back down to 3 liberties), the fact that black is trying all of these distractions suggests that black knows that trying to resist directly won't work. So presumably it has an idea of the tactics, it's just that white is sort of indifferent to accepting them to simplify the game given how far ahead white is, so it's hard to actually see the relevant variations that have been rejected.

So let's modify the position to make white unable to afford to accept any of these simplifications to get more clarity on the tactics.

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . B . . B . . . B . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . . . . . . . , . . . | $$ | . . . . . . . . . . . O O O O O . . . | $$ | . . . . . . . . . . X O X X O X . . . | $$ | . . . . . . . . . X O X X X O X O . . | $$ | . . . . . . . . . . O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

We give black 3 more free stones AND a reverse komi of -25 points. Now, white actually wants to play sharply. Running for a few thousands to tens of thousands of playouts from this position, here's roughly the tactic that KG is seeing through the entire time (sometimes it wastes some ko threats for black in the lower right, but ignoring those):

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . X . . X . . . X . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . 8 . . . . . . . . | $$ | . . . , . . . . . 7 6 . . . . , . . . | $$ | . . . . . . . . 4 5 2 O O O O O . . . | $$ | . . . . . . . . 3 1 X O X X O X . . . | $$ | . . . . . . . . . X O X X X O X O . . | $$ | . . . . . . . . . . O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . X . . X . . . X . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . X . . . . . . . . | $$ | . . . , . . . . . O X . . . . , . . . | $$ | . . . . . . . . X O X O O O O O . . . | $$ | . . . . . . . 8 O O X O X X O X . . . | $$ | . . . . . . 7 4 2 X O X X X O X O . . | $$ | . . . . . . 6 5 3 1 O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . X . . X . . . X . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . X . . . . . . . . | $$ | . . . , . . . . . O X . . . . , . . . | $$ | . . . . . . . a X O X O O O O O . . . | $$ | . . . . . . . X O O X O X X O X . . . | $$ | . . . . 3 1 O X X X O X X X O X O . . | $$ | . . . . . 2 X O O O O O X X X O O . . | $$ | . . . . . . b X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . . O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

And now a and b are miai, so white breaks out while black kills the 4 center white stones. This looks like a legitimate way to break out that doesn't involve the spiral ladder. It also means that white's left side group is unattackable afterwards, but it makes black very thick in the center. With a -25 point komi, white is actually still behind.

If I give it 110K+ playouts on the original position, it finally searches Uberdude's move enough to realize it likes it even more, and by quite a bit more, 15% ish better.

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . X . . X . . . X . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . . . . . . . , . . . | $$ | . . . . . . . . . . X O O O O O . . . | $$ | . . . . . . . . . O X O X X O X . . . | $$ | . . . . . . . . . X O X X X O X O . . | $$ | . . . . . . . . . 1 O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . a O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

As soon as this move gets a few thousand playouts, the tactics are basically solved (although black still wants to waste ko threats in the lower right). You can see this in the ownership map in Lizzie here, for what regions it's expecting white to own.

Attachment:

fight.png [ 620.07 KiB | Viewed 4710 times ]

Example line from one of the displayed variations, skipping the ko-threat wasting moves:

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . X . . X . . . X . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . . . . . . . , . . . | $$ | . . . . . . . . . . X O O O O O . . . | $$ | . . . . . . . 8 . O X O X X O X . . . | $$ | . . . . . . 7 4 2 X O X X X O X O . . | $$ | . . . . . . 6 5 3 1 O O X X X O O . . | $$ | . . . . . . . X X . . O O X X X . . . | $$ | . . O O . O O X . X O . X O X X X X . | $$ | . O X O . X O O X X X X X O X O O X . | $$ | . X X X . X . . . . . a O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . X . . X . . . X . . | $$ | . . . , O . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . . 7 . . . . , . . . | $$ | . . . . . . . 5 . . B O O O O O . . . | $$ | . . . . . . 6 X . O B O X X O X . . . | $$ | . . . . . 1 O X X X O X X X O X O . . | $$ | . . . . 3 2 X O O O O O X X X O O . . | $$ | . . . . . . 4 X X . . O O X X X . . . | $$ | . . W W . W W X . X O . X O X X X X . | $$ | . W X W . X W W X X X X X O X O O X . | $$ | . X X X . X . . . . . a O O O . . O . | $$ | . . . . . . . . . . . . . O . . . . . | $$ ---------------------------------------[/go]

As you actually play down the line, KataGo starts getting better opinions about the order of moves it prefers, this is just what it sees from the initial atari.

Most of the slowness (still taking many thousands of playouts) in solving the position is due to the fact that black can interpose all sorts of moves in the lower right. If in Lizzie you have black waste all the ko threats in the lower right in advance, the solving the tactics in the center becomes very fast. Presumably the ladder solver input is doing a tremendous amount of work here to enable this.

Also, if you play down this line, KataGo realizes that it's even better than it thought, putting white ahead even with a -25 point komi instead of still behind. In many variations, white captures the marked black stones but black gets an attack against the marked white stones, but is not able to kill them, so white ends up fine.

So overall: solving the tactics seems easy enough, but KataGo has some trouble evaluating which tactics are the best way and how to optimize winning chances (when having a negative komi), particularly from the earlier positions.

Spiral ladder problem from a real game

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