Life In 19x19

Idle ramblings based on a comment by ez4u that made me think.

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . |
$$ . . . . b O O . |
$$ . . 1 O O X X O |
$$ . . . a X . X . |
$$ . . O . X . . . |
$$ . . . . . . . . |[/go]

The idea is that 1 threatens a cut at a but works as a ladder breaker for the cut at b.

It's a beautiful move and I'd like to put it in my mind simplified to a more primary concept. I think the base is that ladder breakers can be outside of the ladder. I'll try to build examples:

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . a . . . |
$$ . . . . . b . . |
$$ . . . . . X X . |
$$ . . c X X O . . |
$$ . . . d O O . . |
$$ . . . . . . . . |[/go]

Even the minimal observation tells me I've never tried to find these ladder breakers. For some reason I've always looked for them in the path of the ladder itself.

So, if ladders are composed of base, side and starter (I think the names are self explanatory), from now on I'll count the liberties of all three elements and see if I can leave them at 3, 2, 2 (respectively) while threatening/doing something else.

In the diagram, c and d would leave the base at 3 and a and b the starter at 2. I'll make a diagram for leaving the side at 1:

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . |
$$ . . . . . O O e |
$$ . . . . . . X X |
$$ . . . . . X X O |
$$ . . . X X O O O |
$$ . . . . . O . . |
$$ . . . . . O . . |[/go]

Thinking about it now, for a ladder to work:
- The base needs 4 libs, as the ladder steals two.
- The side needs just 3.
- The starter needs 4, but it's usually a lone stone, so it just needs its full space.

Also, there are only two points that steal two of those libs with a single stone, as the stone that steals from all three ends up having a single one and entering the ladder:

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . |
$$ . . . . . . . . |
$$ . . . . . g . . |
$$ . . . . . X . . |
$$ . . . X X f . . |
$$ . . . . . . . . |
$$ . . . . . . . . |[/go]

Anything to add? A better diagram of ladder breakers?

Here's a similar suji in joseki.

http://www.josekipedia.com/#path:qdodoc ... iehbgbhale

This seems a very thorough treatment of something that was starting to form in my head.

In your second diagram,

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . a . . . |
$$ . . . . . b . . |
$$ . . . . . X B . |
$$ . . c X X O . . |
$$ . . . d O O . . |
$$ . . . . . . . . |[/go]

I have been thinking of "d" as ruining the ladder because executing the ladder puts the base (I like your terminology) in atari. Same with "c", but I hadn't thought that far yet.

I still think of the ladder "base", "side", and "starter" as a trailhead, but I like your decomposition and analysis.

One further thought that's been forming in my head is the reduction of problems based on their exposed surfaces, which is another way of simplifying liberty counting.

As an aside, I don't think the marked stone is required, but removing it makes the attack at b reduce the liberties of both the side and the starter.

Using d as a ladder breaker looks rather silly most of the time as it is pushing from behind and normally would prompt your opp to just extend which makes the previous ladder into a net unless my reading is off.

tchan001 wrote:Using d as a ladder breaker looks rather silly most of the time as it is pushing from behind and normally would prompt your opp to just extend which makes the previous ladder into a net unless my reading is off.

Any ladder breaker can be answered by just capturing the laddered stone (or connecting if it hasn't yet been played). The point is that they are forcing moves, long range atari.

I agree that 'd' doesn't look good, but It depends on the surrounding stones. Maybe 'd' is the perfect move for a nearby fight and it's good to know it might be sente because it breaks the ladder.

Maybe 'd' also breaks a different ladder in the other side of the board and extending the base to turn the first ladder into a net is miai with capturing the other ladder.

Move 89 in recent Ing cup game is similar.

http://www.go4go.net/go/games/sgfview/32365

Alguien wrote:
It's a beautiful move and I'd like to put it in my mind simplified to a more primary concept. I think the base is that ladder breakers can be outside of the ladder. I'll try to build examples:

$$Bc
$$ . . . . a . . . |
$$ . . . . . b . . |
$$ . . . . . X X . |
$$ . . c X X O . . |
$$ . . . d O O . . |
$$ . . . . . . . . |

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . a . . . |
$$ . . . . . b . . |
$$ . . . . . X X . |
$$ . . c X X O . . |
$$ . . . d O O . . |
$$ . . . . . . . . |[/go]

Even the minimal observation tells me I've never tried to find these ladder breakers. For some reason I've always looked for them in the path of the ladder itself.

So, if ladders are composed of base, side and starter (I think the names are self explanatory)...

This post deserves a like simply for the above diagram. Just to be sure though, you are calling the triangled stone the starter, the squared the side and the circled the base?

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . |
$$ . . . . Y . . . |
$$ . . . . O # # . |
$$ . . . B B O . . |
$$ . . . . O O . . |
$$ . . . . . . . . |[/go]

While I might quibble a bit about the terms base and side as a bit non-descriptive, I find the distinctions quite valuable. Another pair of useful terms in this context, I believe coined by John Fairbairn, are ladderer and ladderee.

The function of a ladder is to capture a cutting stone (the runner?). What the cutting stone cuts, to continue with your terminology, is the base from the side.

Click Here To Show Diagram Code

[go]$$Bc
$$ ? e ? . a . . . |
$$ ? ? ? . . b . . |
$$ . . . . Q X X . |
$$ . . c X X O . . |
$$ . . . d O O . . |
$$ . . . . . . . . |[/go]

It seems to me that there are three possible functions of a ladder breaker:

1. A ladderee's stone in the ladder's path (around e), allows the ladderee to gain enough liberties to exploit the ladderer's vulnerability (double ataris).

2. A ladderee's stone at a or b in your diagram assures that the ladder won't get off the ground because the single starter stone will immediately become ataried.

3. A ladderee's stone at c or d likewise endangers the two stones of the base.

It seems to me that the side's role is secondary, because it can only be captured after the runner has escaped. The only scenario where it's possible to capture the side before the runner has escaped is if playing the runner puts the side in atari like so:

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . |
$$ . . . . . O O . |
$$ . . . . r X X . |
$$ . . . X X O O . |
$$ . . . . O O . . |
$$ . . . . . . . . |[/go]

I'm having a hard time wrapping my mind around the rest of your post.

...Thinking about it now, for a ladder to work:
- The base needs 4 libs, as the ladder steals two.
- The side needs just 3.
- The starter needs 4, but it's usually a lone stone, so it just needs its full space.
...

It seems to me that in order for the ladder to work (to capture the cutting stone in a ladder) the base needs 4 libs, but since the starter is invariably played after the runner, it starts with three libs and needs all of them. Again, as to the side, it's libs can't be reduced without the runner escaping.