Sunday, February 14, 2010

Ladders, Cutting, Keimas and One Point Jumps

One of the first two topics in go introductory books are ladders and nets.

So this is fundamental stuff, right? At 12-10kyu, or whatever I am now, it should be old news, right?

For a long time, I thought ladders and nets were relatively rare -- either would only enter my thoughts 0-2 times per game.

This is before I really analyzed cutting, and started to look at every connection and cut point carefully, reading each one out several moves.

Once I did this, two things happened:
1) I suddenly jumped 1-3 stones in effective skill level.
2) I started seeing ladders 50-100 times during a game (they just rarely showed up on the board)

For example, every time I see a keima (my own or opponents, played or potentially playable), I consider the two possible ladders involved in it's cut, and whether or not they will work. This alone makes ladders suddenly an integral part of my games now.

This directly stemmed from the first chapter in Lessons in the Fundamentals of Go, an interesting and hilarious (possibly unintentional) book that I hope to get around to reviewing in more detail. The ladder portion was basically telling you to practice to learn to read ladders, and that you are a ass-clown if you do not. Basically. This book is strange.

What in the hell is going on in the picture on the cover of this book?

Do I want to know?

Cutting the Keima

The ubiquitous keima connection always involves two ladders.
First, let's look at how to cut one.

You have to start at either a or b in the diagram. These are miai, meaning if the opponent want to maintain the connection (and he will), he must play the other point.

After the opponent blocks, you must play either c or d depending on whether you played a or b -- you would not have started the cut (one would hope) without intention to follow through.

The first move forces the next two moves, and you have the choice of two sequences (attacker chooses):

Which you choose depends on the cuttability of each pair of points.
The cuttability of the first point requires, at the minimum, that the ladder works.

Here are the two ladders possible, one for each starting point:

The ladder failing is necessary for the cut to succeed, but far from sufficient -- there are many ways for a cutting stone to be captured besides a direct ladder.

The basic summary of cutting a keima is: any of the two pairs of cutting points must work

In creating and maintaining your own keimas, ensure that the above does not become true.

Cutting the One Point Jump

The one point jump is rarely cut. The reason is that there are four potential cutting points, and the defender gets to choose which one it is! This means that all four cutting points must be cuttable! This stems directly from the flexibility of the connection -- the defender gets to choose the cut point from four available, so if just one of the four is not cuttable, the entire connection is safe. On top of that, at the end of the 5 move sequence, the defender has grown a lot of thickness (qb).

OPJ Cutting Points -- defender chooses, so all four must be cuttable to allow connection to be cut.

That's a pretty high requirement, which is why OPJs are so rarely cut.

Let's look at it in detail.
  1. Cut begins on center point.
  2. Defender gets to choose one of two sides to block from.
  3. Attacker's extension is forced.
  4. Defender can patch one of the two cutting points
  5. Attacker can now cut that one point.

Here are the four cut sequences, and remember: defender chooses!

Nets and Cuts

Oddly enough, I seem to have recently had a blind spot for nets. I'm not sure why. I'll have to focus on that next.

Let's look at this example:

Without the ladder breaker, this would be non-cuttable.
With the ladder breaker, it IS cuttable.

In case you forgot how ladders work.

In case you forgot how ladder breakers work (now white can choose from several double-ataris)

With just a slightly longer 'backboard', you can now utilize a net even though the ladder still fails. This is the trap I've fallen into recently because I'm so excited that the ladder works, that I jump in and cut, only to be caught in a net.

In case you forget how nets work...

Cutting Other Connections

As far as cutting two-point jumps and ogeimas, that's for another time. I think ogeima cutting is similar to keima cutting, but I haven't looked at it in detail.


A big thing being glossed over here is cuttability. I'm not sure there's a magic answer here, just do some reading.

Reading Ladders

After reading the first chapter in the book mentioned, I took the author's advice and started trying to read large ladders better. It's not really that difficult, and it's saved me a few times in games since.

I tend to try to find the nearest star point to the start of the ladder, then find the nearest one to a side or potential ladder breaker, and start the zig-zag pattern at that point in the same direction. Works pretty well for me.

Because ladders now affect the game so much more for me, my whole board game has become much more intriguing. Now, whenever I see a cut point that involves a ladder, now the other side of the board affects the cuttability of that cut point. Ideally, if I can place a ladder breaker across the board (preferably in sente), I've turned a uncuttable point into a cuttable one, and all the consequences that entails.

Drawn Out Ladders

One of the high drama situations in a game. It is the go equivalent to going 'all in' in poker. It doesn't happen too much in high skill games though (unlike the other high-drama situation in go -- high stakes ko fights, which also draws parallels to poker).

If a ladder is being drawn out, it means either:
1) Each player is reading the ladder differently, and betting (often the entire game) that the other player is wrong. Since one must be wrong, that means they cannot read (some) ladders, which is why you don't see this (rare exceptions) in high level games.
2) One player is a beginner who can't read ladders.

I know I've drawn out a ladder one move by accident before I've realized it was a ladder, even recently. But when you see it drawn out like 10 moves, it's usually the game determiner.

And there's nothing quite as fun as winning due to a long drawn out ladder because you read it correctly and your opponent did not. I'm also amused by the occasional 'am I crazy?' pauses when a ladder is being drawn out -- it doesn't take much thinking to figure out the next move in a long ladder, so it's normally "snap-snap-snap-snap", but occasionally one player or the other pauses to re-read it to ensure they aren't nuts.

At least, I know I do.


  1. Wow... very useful, humbling and entertaining tutorial on some very important concepts that I really never took the trouble to isolate. I am sitting and doing problems at 10 to 12 kyu (like you said) right now and I totally realized how much I neglected basics.

    FYI I think you did a very eloquent description of the charged "moment of truth" that takes place in an actual ladder in a 15k or better game. The waiting as the players take turns to try to figure out if they are the unfortunate soul who misread it.

    Put out a 2-point jump and ogeima article! This is VERY good stuff.

  2. Glad you found it useful. Not only did I use to post to this blog but the older ones were actually mildly useful. Don't really have the time for it any more, I'm afraid, but I do still play on OGS ( as 'antinoun' if you ever want to hit me up for a game.