Ladder

  Difficulty: Introductory   Keywords: Tesuji, Go term

The term ladder may also refer to a ranking system used within clubs. See Club Ladder for details.

Chinese 1: 征子 (zhēng zǐ)
Chinese 2: 征 (zhēng);
Chinese 3: 扭羊头 (niǔ yáng tóu)
Japanese 1: シチョウ (shichō)
Japanese 2: 征 (shichō) (Rare)
Korean: 축/逐 (chuk)






A ladder is a technique for capturing stones. At each step the attacker plays atari (threatens capture on their next turn) and then the defender runs away, but can only gain one more liberty.[1] The process stops when the defender can run no further (is captured) or gets more than two liberties; in the latter case the ladder fails.

The term ladder is often thought of as applying to the well-known staircase of the first example, but is also used for any other sequence where the defender never has more than two liberties.

There are plenty of Ladder problems and exercises in Sensei's Library.

Table of contents Table of diagrams
Ladder
Playing out the ladder
A long ladder
A long ladder (cont'd)
A long ladder with ladder breaker
A broken ladder
More complicated ladder
Straight ladder

Example

[Diagram]
Ladder  

Black B1 starts a ladder to capture the white+circle stone.

[Diagram]
Playing out the ladder  

If White tries to escape, Black can at each time play atari and White will be captured.

Clearly White should see this and not play W2.

Longer ladder

[Diagram]
A long ladder  

Ladders may span a large part of the board. If for example Black captures the white stone in a ladder with B1, the ladder will cross the entire board if White tries to escape, resulting in the next diagram.

[Diagram]
A long ladder (cont'd)  

If White tries to escape, the ladder will continue in this way. This is a disaster for White.


Ladder breaker

[Diagram]
A long ladder with ladder breaker  

Suppose, however, that there is a stone in the path of the ladder, such as white+circle in this diagram,

[Diagram]
A broken ladder  

After W8, B5 is suddenly in atari. Now, black cannot continue with the ladder, because white could simply capture the B5 stone. The ladder is broken. Also, note that black's formation is full of cutting points each of which is a double atari that White can play. This is therefore a disaster for Black.

And so we can plainly see that a ladder is little more than a one-sided fight for one side or the other. Hence the proverb, "If you don't know ladders, don't play go".


Cost of playing if you lose

It is expensive to play in a ladder if you are going to lose it. Traditionally people talk of about 7 points per mistaken play (PJT: Just seen that [ext] here — any other views?). [ext] Here is a game on OGS where KataGo estimates that the mistaken plays up to resignation cost roughly 10, 8, 6, 6, 6, … 6, 3·5, 5·9, 1·6, 7·7, 1·1.

Theoretical ladder

Although ladders normally follow a zigzag pattern across the board, and indeed derive their name from this "stairway" like formation, any sequential series of ataris forcing the opponent's stones around is considered a ladder. Thus ladders may go straight, or bend, and still be considered ladders.

[Diagram]
More complicated ladder  

In this example, there are several white (white+circle) and black (black+circle) stones in the path of the ladder. The diagram shows that white cannot escape with W1. Had black followed the basic zigzag pattern by playing B4 at W5, white would have escaped. But by using his own additional stones for support, black is able to maneuver the ladder past white's stones.

[Diagram]
Straight ladder  

In the same vein, this pattern is also a ladder, though most people might not refer to it as such.


Linguistic note on Chinese

The Chinese term for "long march", 长征 (cháng zhēng), is often used as a metaphor for the Chinese term for "ladder", 征子 (zhēng zǐ). The idea is that if the ladder is played out fully, then it can be a very long sequence, like a long march.

According to John Fairbairn, the word 征 first appeared in Chapter 2 of Dunhuang Classic in the 6th century, well before Mao Zedong's time, and there is no reference there to marches. In the ancient, 征 refers to firmly attacking a rebellious state and had nothing directly to do with marching, but later it developed to another meaning of "(military) expedition".

Computational complexity of ladders

Marcel Crasmaru and John Tromp proved that the [ext] problem of computing ladders belongs to the class of [ext] PSPACE-complete, due to the possible twists and turns and other complications in the execution of a ladder. However, such complicated cases are quite rare in Go. The majority of the ladders can be easily read out by a beginner with some practice. (A similar comment applies to many such proofs. Indeed, they are "asymptotic" and really only apply to arbitrarily large boards. By themselves they say nothing about our good old 19x19 goban. Concrete bounds are needed for that.)


See also

Homonym

Notes

[1] The term, "ladder", though long in use, is also debatable. The term "stair" is much better to describe this form. (But... A stair and not a ladder, a thing and not a process? It's a reckless path to disaster, not a trip to the attic.)

Other languages

Chinese

下子后,打吃对方的棋子,对方长出时只有两口气,己方再迎头堵住,一直打到对方没有地方可逃,最后把对方的棋子吃掉,这种吃子的方法就叫作“征子”,也叫“征吃”,俗称“扭羊头”。 征子时要保持己方的全部棋子都有两口或两口以上的气。


Ladder last edited by PJTraill on December 29, 2023 - 17:53
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