Two step ko - Two stage ko - Discussion

  Difficulty: Expert   Keywords: Ko, Go term

This discussion is mainly of historic interest. It was the reason why on SL we talk about stage ko and approach ko, but not about step ko.

Bill: Proposal for an edit.[2]

10 December[, 2002]:

I wonder if a two stage ko (one player needs to win 2 ko depending on each other) just a variant of an approach ko or a beast of its own kind. Should two stage ko get their own page or should they just be referred to the ApproachKo page? --Confused

It's a different notion. Charles Matthews

See TwoStepKo. -- Bill

That page is awfully incorrect. What is shown there is a two stage ko. A two step ko 'is' the same as an approach move ko (with one approach move). -- Andre Engels

Bill: Cut it out, Andre. Nidan ko = 2-step ko. Ni = 2. Dan = step. It is *not* the same as a 1 move approach ko (itte yose ko). In fact, there is such a thing as a 2-step 1-move approach ko. :-)

Apparently there is a bad translation somewhere, but that is no reason to perpetuate the error. In a recent note in, Simon Goss recommends saying two-step iterated ko, three-step iterated ko, etc. There was some discussion about whether to talk about 2-stage kos. That seems ambiguous to me, since there are 2 stages to a 1-move approach ko. Equitable ko threats are larger in the second stage.

Charles Matthews My favoured approach now to cyclic positions taxonomy doesn't solve problems of nomenclature (yet).

I don't care what the translation of "dan" is. The English go term means what the go term is used for in English, not what the translated go term means in Japanese. -- Andre Engels

It depends how widespread the use is. I guess many of us were bred with James Davies. It is not guaranteed that future generations and other nationalities read Davies. Therefore, if translations and interpretations lead to ambiguity, we can overrule what has been common use. Dieter

John F. If I've understood this correctly, I think Bill is out of step, to coin a phrase, with most people on this, because - as he often tells us - he doesn't read the English literature. The rest of us do and respect the work of Davies, so it's no surprise we often follow his terms (even rabbity six, no matter that it's always said apologetically and the accompaniment of groans). But it's easy to see where Bill is coming from. Maybe therefore we need to try for different words altogether. Maybe a 2-stage ko (Davies sense) could be called a two-phase ko or two-part ko.

On the other hand, I think Bill is being too rigid in saying "two-stage" is an error. Dan does mean step, but it means quite a few other things, too, such as a column of text or a scene in play. Nidan is very, very common in technical words and nearly always is rendered as two-stage (as in two-stage carburettor) or double. Indeed, the Japanese standards give two-stage as an official equivalent of nidan. So maybe the right approach is to shoot Bill down on this (in the nicest possible way, of course) and tell him to get on with calling it what the rest of us call it and what professional technical translators would call it.

Bill: Actually, John, the mistake I was referring to was calling a yose ko a two step ko. In the past I may have said that calling a nidan ko a two stage ko was a mistake, but I think that all I said was that I did not prefer it. In any event, the latest Go Players Almanac uses approach ko and two stage ko, and I recommend that usage here on SL.

John F. Thanks for the clarification, which I can agree with entirely (and, for others, what I think we are agreeing on is yose ko = approach ko and nidan ko = two-stage ko). But can Andre now explain where he differs? I suspect much of the confusion is simply due to the SL effect. Apart from stuff being all over the place and edited arbitrarily, it seems to matter what order you read things in.

Bill: Actually, Andre agrees, too. He and I collaborated on the current Two Step Ko page, which asks people not to use that term. :-)

As for the SL effect, a lot of the material here was moved here from the Message Board page or something. I think there are actually four different discussions merged on this page from different times and about related but different topics. That has to be confusing. ;-)

11 December[, 2002]:

Bill and Andre Engels, would it be possible to merge the pages TwoStepKo and TwoStageKo? They look awfully similar and I have the impression, that the definitions are very closely related. Wouldn't it make sense to define TwoStageKo as an alias to TwoStepKo and add the difference to that page? It also would help, if you could add an example of the type "This is a two step ko but not a two stage ko" (or the other way round) for weaker players like me who have trouble grasping the difference.

Another possibility would be to move the whole content to a page Nidan Ko and have both TwoStepKo and TwoStageKo refer to it as aliases.


14 February[, 2003]:

Bill: Happy Valentine's Day%%%

I do not mind if the local dialect avoided using two step ko entirely, given the unfortunate ambiguity in prior English usage. However, the paragraph comparing unfavorable "two step kos" and "two stage kos" is poorly written, at best, if not downright misleading. I say, cut it.

April 30, 2003

DougRidgway Looks like the toplevel pages haven't converged yet. For anyone interested in reading discussion, here's a link to the 2002 rgg thread on this topic:

[ext] thread

November 12, 2003

Two-something ko  

Bill: The question of what to call this ko has arisen again on Andre Engels home page. As it turns out, last week I took a look in the 2001 edition of the Go Players Almanac, where this ko is called a two stage ko, and the approach ko is called an approach ko. As two step ko has caused confusion, I propose that we go with the usage in the Almanac, and avoid the term, two step ko altogether.

DougRidgway: My vote would be to always include either iterated or approach: with step or stage alone, I'm never sure what is meant, there's too much usage going both ways.

Bill: You only need to use stage with an approach ko if it is a compound ko. E. g., a two stage one move approach ko. The phrase that caused the current confusion, on the Carpenters Square page, was a mistake. The ko is a three move approach ko. Not even close. Otherwise, two stage ko had an unusual usage here for a ko where one player can make a bent-four shape and create a new ko from that. Quite arguably, that is a two-stage ko. :-) However, it is also a rogue ko, and I went ahead and changed the references. In no case did I find anyone using two stage ko for a one move approach ko, unlike has happened with two step ko. So I do not think that there is as much confusion over that term.

Andre Engels: I agree that the best strategy would be to not use the term 'two step ko' at all. As far as I know, the terms 'one move approach ko' and 'two stage ko' are unambiguous. My proposal would be to write a small bit on the controversy on Two step ko, plus references to Approach ko and Two stage ko, and a remark to readers that if they find a page linking to it, it would be better to change the link to refer to one of those pages.

Andre Engels: Hmmm... Seeing below that there are people actually _swapping_ the meanings compared to Davies, maybe it would be better to rename two stage ko as nidan ko as well.

Bill: I am not as nihongophobic as Charles, but I think we shouldn't go with nidan ko, even if it is unambiguous. Do we expect people to learn to count in Japanese, so they can say, rokudan ko?

I dislike n-stage ko because, as an English speaker, calling each ko capture a stage seems weird to me. Wrong metaphor. But I think that it is good to have standards, and the latest Almanac is good enough.

December 12, 2003

Robert Pauli: Sorry, but I really feel that SL is going in the wrong direction here. The terms two-stage and two-step (ko) certainly are easy to confuse, no doubt about that, but the picture I have in mind helps me to keep them apart:

  • (itte) yose ko: a ko fight stages twice on the same spot
  • nidan ko: a ko fight steps (or shifts) from one spot to a second

Exactly this assignment is used in Go Terminology by Jim Davis (= James Davies??) in Go Review, Winter 1974. You can also find this use in the book Fighting Ko by Jin Jiang (translated by Dr. Sidney W.K. Yuan).

I read the mentioned RGG thread, but ... what was it again :-) At least one thing: Bill claims that current SL use - calling yose kos approach kos and nidan kos two-stage kos - follows the 2001 Go Players Almanac.

Unfortunately I don't posses it. However, I know that it includes a section about the [ext] 1989 Japanese Rules of Go, and my copy of this rules includes the following two relevant life and death examples:

LD10: approach-move ko  
LD24: filling dame to obtain territory - two-stage ko  

plus a double-ko seki somewhere else

Is this the source of confusion?

Bill: The source of confusion is an old translation calling a yose ko a two step ko.

LD10 no doubt is a yose ko, and calling it approach(-move) ko is fine with me. But LD24 is a yose ko as well as a nidan ko, depending on which side you take.

Bill: LD24 is not a yose ko.

For Black it's a nidan ko, shifting from the corner to the edge, and for White (going second) it's a yose ko, having to fill at the edge after winning and fight it once again.

Bill: This possibility arises in other nidan kos, as well. It is just not necessary, as here. White's filling the first ko is not an approach move; it does not make the second ko more valuable.

Since the whole example is about White wanting to claim three points by keeping the situation as is (not four because 1989 post-end analysis renders the single white stone at the top as dead (in no territory :-)), I strongly feel that this was called two-stage ko from White's perspective! (By the way, White's claim fails as he has to fill both kos (you know what I mean) to get rid of dame, but that's another story...)[1]

So, how about that.

If we want to avoid confusion, we shouldn't use either of those two terms. However, we should keep their original meaning as a reference.

I would suggest to call yose kos indirect kos (since we already have direct kos) and to call N-dan kos shifting kos, but of course you have to decide ;-)

Charles I know that James Davies now regrets the earlier terminology (personal communication). I prefer direct ko for the simple two-state ko, only; and indirect ko therefore for all others. I don't think there is a satisfactory terminology available that takes into account the precedents.

Bill: You can do what you want, Robert. I do not think that anyone is dictating usage here on SL. :-) However, completely unambiguous terms already exist: approach ko for yose ko, and iterated ko for dan ko. The latter is not in wide use, however.

December 15, 2003

Robert Pauli: Before this discussion gets totally out of hand (

  • I still think LD24 is a yose ko, Bill
  • I don't want to do what I want (to dictate)
  • LD24 isn't really about life or death, but about filling dame to avoid technical seki
  • I don't need another page, because ignoring one ko type causes the confusion
  • summing up both ko types under "indirect ko" seems sound - ok, Charles

) let me focus on the point:

I don't want nidan kos to be called two-stage kos, period.

Why? Because traditionally (at least to my belief) they were (and are) called two-step kos (which, by the way, fits to their "one step forth, one step back" reversable nature and also to how some translate "nidanbane").

As long as we don't have a better new term (like in the yose ko case with approach(-move) ko - fine, Bill), we should stick to what we have: two-step ko.

So, expect me in the future to exchange each "two-stage" tagged to a nidan ko by a "two-step" - should no reason why not show up here.

(BTW, why do I get no preview of this page??)

Bill: Robert, I'll drop the side details, except to refer you to the text of the Japanese rules commentary for LD24. We'll just disagree for the moment. :-)

I happen to agree with you about two step vs. two stage. I think that two step ko is clearer English for nidan ko. However, the tradition is to use two stage ko for nidan ko, contrary to what you have found. (If Davies wrote what you say in Go Review, he soon switched. Maybe you misread him.) Sticking to what we have is using two stage ko.

A while back I changed the two step ko page to refer to nidan ko. Andre Engels objected strongly because many Engish speakers learned to call a yose ko a two step ko. That is a tradition that is dying out, thank goodness!

Meanwhile, using two step ko causes confusion, and that is why I am recommending that we not use it here on SL. Andre agrees, as does John F. As do I. --DougRidgway

December 17, 2003

Robert Pauli:
Ok, Bill, so let it be that some believe that the prevailing term for yose ko is "two-stage ko" while others believe that it's "two-step ko". Maybe even both are in use. Conclusion:

We should use neither for either type (that's, "two-stage" isn't free for nidan kos either)

(I wasn't really arguing for "two-step ko" to be used for nidan kos - Doug, Andre, John F. - but to let it be till something better shows up. However, I learn from Bill that this isn't status quo. If you think "two-step" is confusing, you shouldn't keep "two-stage" either.

By the way, could anybody point to any publication that actually uses both (repeat: both) terms in the switched sense (that's, "two-stage" for nidan and "two-step" for yose ko)?)

So, we need a new term for nidan ko. You're telling me that there's already one - "iterated" - but, sorry, I have to reject it. Why? Because it could be applied to both types as well, starting the next ambiguity (we should have learned something from the past). Therefore I still suggest "shift".

Let me put this into a broader picture:

There's a ko running. Either I started it (I), or he (H). For the purpose of classification relative to my perspective I'll ignore each of his ko threats, of which we both have plenty. Each time I do, there are three cases:

  • I settle and win the ko (W)
  • I shift to a neighboring ko (S)
  • I do some approach move (A)

All in all that's

(H|I) {A|S} W

(bar indicating alternatives and curled braces repetition)

Summing up neighboring A's or S's and going to absolute colors we get

<Starter> { <Number of shifts> <Number of approaches> } <Winner>

Skipping trailing zeros and separating with '-' we get

B-B          direct ko     for Black, started by Black
W-B          direct ko     for Black, started by White
W-1-B        1-approach ko for Black, started by White (itte yose ko)
W-0-1-B      1-shift ko    for Black, started by White (nidan ko)
W-2-5-1-B    2-shift 5-approach 1-shift ko for Black, started by White (academic, OC)

Those with numbers being called "indirect" kos (BTW, is that status quo?).

Note, however, that each ko can be tagged from either perspective (...-B, ...-W):

Black starts (no captives, no komi)  

In above's terminology the ko in the upper left corner is a B-1-B as well as a B-W, that's

  • 1-approach ko for Black, started by Black
  • direct ko for White, started by Black

Now (asking everybody)

  • does this make sense?
  • isn't LD24 a B-1-W as well as a B-B (and even a B-0-1-B), very similar to the example?
  • may I replace each "two-st..." tagged to a nidan ko by a "1-shift" (there shouldn't be any "two-st..." tagged to a yose ko around, hopefully)?

(Still getting no preview of this page ??)

Bill: Quick comments.

I think that any of Davies' books would be a good place to find two step ko used for yose ko. He consistently uses two stage ko for nidan ko. Also the first edition of the Go Player's Almanac, I think.

OC your classification scheme makes sense. But it is also confusing and cuts across current classification, both in Japanese, which is unambiguous, and in English. Sure, LD24 is similar to your example, which has special peculiarities under the Japanese rules. As for replacing two-stage by one-shift, I would protest. AFAIK, two stage ko is used for yose ko in only one place in the go literature, otherwise, it is used for nidan ko. Anyone who knows the term nidan ko can guess that two-stage ko refers to it. What they would think of one-shift ko, God only knows. SL does not exist in a vacuum. We should be intelligible to new readers who already know some go terms.


BTW, your example is a sente ko. White's winning the ko is sente, and if Black takes the ko, White's taking the ko back is also sente.

As for shift ko, if you start using the term in your writing, and others take it up, particularly outside of SL, then switching from stage ko might be a good idea. :-)

And I have question for everyone. Given the controversy, should we make nidan ko basic, with two stage ko as an alias?

Charles What I'd like - without great hopes of getting it - is the first line of naming to be something like mediated ko?. So that indirect kos are divided into approach kos and mediated kos first (could overlap); and then if we need to quantify as N-(quantifier) mediated ko the chosen quantifier isn't carrying an attribute burden as well. Neither nidan ko nor two stage ko rings any bells with me, any more. Perhaps something more vivid, such as seesaw ko. But to the extent that Robert's point is that the current English usage is broken, I tend to agree with him.

John F. I think this note by Charles sums up, advertently and inadvertently, a lot of pitfalls. Yes, the English terms introduced by Davies have been around a long time without being used much, and desuetude and confusion have taken their toll. But Charles's English terms are worse, in my view. Mediated is totally meaningless to me. All kos are seesaws to me - indeed I recall considering whether to call kos seesaws once. But worst of all, I think he is calling a nidan-ko an indirect ko. To me it is as direct as you can get - it's here, now, you've got to deal with it straightaway. It may be incomplete, or some other in-word, but not indirect - to me; I accept mathematicians have a funny way with words :) Maybe this is a case where we should accept the Japanese words as the primary choice until someone has completed a catalogue of all kos and their characteristics.

Rafael: I don't get your reaction to calling nidan-ko an indirect ko. Do you take it as a suggestion by Charles? It goes back to Davis. Kos are either direct (I suppose this corresponds to honko) or indirect. In direct kos, either side can finish the ko by ignoring one ko threat. Every other kind of ko is indirect.

Charles I'm mainly suggesting getting away from translating the Japanese. I know enough Japanese to ask for two slices of toast, or two rail tickets, as nimae - 'two flat-ones': I can quite see why nidan is OK for a Japanese speaker. As a mathematician I see kos in terms of the underlying graph theory: draw out the possible repeating positions and you get (a) two connected by a two-way edge (direct ko), (b) a system with an irreversible transition in it (approach ko - it's a commitment to make the approach move), or (c) a system of reversible edges, with something in the middle. It's only case (c) where I feel the need of a term. I'll call it a graph ko, privately, then, the point being that there are no directed edges.

John F. Responding mainly to Rafael. One of Charles's main points seemed to be that lack of use of the terms over time meant their meanings were hazy. Therefore, when the terms are raised again we have to grope for the meaning. He suggested using more vivid terms, but that's a thing for the future. When I read the terms direct and indirect and had to grope for the meaning, I didn't come up with what some others apparently came up with me. To me, there's an element of movement/direction in the words. So what floated up in my kind was the idea of approach moves being indirect - and all other kos as direct.

When you translate go, you often use words that you would not have chosen yourself, because you try to stick with what people have been used to previously. I don't think I would have ever said direct ko for honkou - maybe I'd have chosen true ko.

The involuntary images that are summoned up in your brain by a particular word (direct, here, for me) are very hard to shift. There is another example by someone else here. They were (I think) arguing that a nidankou was a two-step ko because a dan is a step, and in their mind they saw it as taking one step forward and one step back. Trouble with that is a dan is a step only in the sense of a rung on a ladder or a part of a staircase. It is a static object. does NOT refer to a step movement made by a person.

Charles. What is not clear from the above is whether you are recommending not **translating** from Japanese but **using** (some) Japanese terms, such as hane. Or are you deprecating any Japanese connection? And/Or are you just referring to this specific instance? It is certainly true that Japanese terms create more trouble than they are worth once they are put under the microscope. (PS it's nimai).

Charles In this case, my problem with starting at the Japanese end is that it encourages the quantitative thought (how many plays?) ahead of the qualitative (what kind of thing do we have here?).

Bill: John, I sympathize with your confusion over direct ko. It made sense to me according to the sense of direct as immediate. After taking the ko, each player can win it on the next play. That is as immediate as a ko gets. Then Charles's idea of a nidan ko as mediated makes sense, too. :-)

Charles, there is a saying that taxonomy is the death of science. You are right: Just classifying kos for the sake of classification is not very important. Theory matters.

But graph theory is not enough for a meaningful classification of kos. You have to take temperature into account. For instance,

                     /     \
                    C---D   x
                   /     \
                  y       z

(The capital letters are go positions, the small letters are scores.)

A-B looks like an approach ko. However, we do not have enough information to tell. We have to know the values of x, y, and z.

To take a couple of abstract examples,

                     /     \
                    C---D   0
                   /     \
                  2       1

is not an approach ko. If Black plays from A to C, the local temperature drops from 5/9 to 1/3, and White may well tenuki, playing a 0.5 point move, for instance.

                     /     \
                    C---D   0
                   /     \
                 22       1

is an approach ko. If Black plays from A to C, the local temperature rises from somewhere around 4 or 5 (depending on the ko threat situation) to 7. White will almost surely take the ko.

The Japanese classification of kos, while incomplete, does take both graph features and temperature into account. It's a good start for a more comprehensive taxonomy.

Charles Unfortunately, a taxonomy would do less for my playing level, than removal of some more obvious errors in handling kos. But my need for terms is not related to that, so much as being able to handle queries in the club. Half the time I know it's going to be a mannenko before I look at the position properly. I just want a good term, such as approach ko, to describe the type of animal to people. If I carried a whiteboard with me, I could get into finer detail, doubtless ...

December 18, 2003

Robert Pauli:

  • Ok, I'll change nothing (frustrated, really)
  • I just can't believe that James Davies reversed his terms from his article in Go Review, Winter 1974, or was that someone else (I neither can believe :-)
  • Bill, OC I don't agree that to prefix "ko" with some N-approach" and/or "N-shift" is in any way confusing, it's plain simple (boys, tell him :-)
  • your protest against "one-shift" instead (the to me false) "two-stage" really sounds a bit preoccupied: "I'm not used to it, forget it" - OC it's a new term, and it's English
  • (Bill:) "AFAIK, two stage ko is used for yose ko in only one place in the go literature, otherwise, it is used for nidan ko" - hmm, and what about the two places I pointed out on this very page (and both certainly don't use them by accident)??
  • Bill, what did you mean with "As for shift ko, if you start using the term in your writing, and others take it up, particularly outside of SL, then switching from stage ko might be a good idea. :-)" - I'm OC proposing to get rid of both "two-st..." (in SL and else)
  • yes, Bill, the Japanese terms should be basic, the English alias, but OC the latter to be used
  • John F., after doing all the approaches and shifts - it's (oh wonder) direct (therefore Bill's protest against "one" instead of "two" is deeply wrong)
  • and last but not least, I fully agree with Charles not to depend on translating the Japanese - why shouldn't our terms be better ??
  • now I'll relax again ;-)

Charles I think the attempt to get consensus tends to end like this. My point, entirely. On terminology, I think SL should (i) accept that taking the 80 for 20 saves time, if it also misses the finer points, and (ii) be less worried about the 'guild' or enforcing minimum standards approach.

DougRidgway And even if we could obtain consensus here, it wouldn't change the existing literature. For the moment, as long there's always a diagram whenever talking about indirect kos, the reader should be able to figure out what is meant. Robert: looking at your classification, you might be interested in cyclic positions taxonomy and [ext] a taxonomy of iterated ko.

Bill: Robert, I also do not believe that Davies changed his terminology until recently, and I have not been able to check the Go Review reference. It's not like it's in the local library. ;-) It is possible that the Japanese Go Review editor switched Davies' terms, while Bozulich did not.

I did not object to your terminology per se. You may be able to show its value, how it helps us to understand and talk about different kos. It is not so much that it is new, but that it is untried. Give it a chance. If it is worthwhile, other people will take it up. It is too early to say that it should supersede existing terminology.

Here is a graph of the ko in LD24, taking the scores only in the corner:

             /   / \   \
            3   /   \   \
               /     \   \
          D---E       F---G
         /     \     /     \
        2       \   /       0
                 \ /

(The current node is C.)

This graph bears a certain resemblance to the usual one point nidan ko and a lesser resemblance to a yose ko. But based on temperature, B-C is a sente ko. Black's play from C to B raises the local temperature from 1/3 to 7/9.

Now, to call it a sente ko leaves out a lot of information. But it does tell us something useful in go terms about the ko. We know something about how it is played. (Hmmm. I see that a better term might be ambiguous ko).

Your terminology tells us something else about the ko. How that might help us understand it and talk about it is something that you may be able to show. Then people will start to adopt it. (I do not know if people will start talking about ambiguous kos or not. ;-))

The different terminologies may not conflict, anyway. Again, it is too early to tell.

John F. I no longer have the Winter 74 Go Review, but in the 1975 first edition of Tesuji by Davies, he talks about nidankou as two-stage kos (page 48) and he also talks about multistep kos (approach move kos) and direct/indirect kos. Both editions of the Almanac use the same terminology. I personally have no preferences as to English term - on the rare occasions a nidankou swims into my ken I think of it as nidankou. I tend to use approach-move ko and yosekou fairly indiscriminately, but behind the split there is the desire to dissuade people that yosekou has anything to do with the endgame. Given the vast readership of Tesuji and the Almanac, and no doubt other books from the same stable that repeat the terms, I'd say that Robert is tilting at windmills in trying to change the terminology. The only way for that to happen would seem, as Charles says, to come up with an all-embracing theory of ko. But if that involves graph theory and the like, I wouldn't give that much hope either.

[1] Actually, because of the dame outside of the kos, there is no territory. This example is simply about life and death. One of the white ko stones is dead (the one in atari), but cannot be removed.

[2] As for editing, I would suggest moving the current discussion, started by Robert Pauli, to Two Step Ko Talk, since it is about the recommendation to avoid the term, two step ko, and deep sixing the rest, which is obsolete and confusing.

Two step ko - Two stage ko - Discussion last edited by RobertPauli on January 4, 2019 - 15:58
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