Go theory and CGT discussion

Discussion moved here from Go theory.

I am making a CGT path (Combinatorial Game Theory) distinct from the endgame path. In this case I think it probably is helpful to maintain the contrast between the traditional theory, and the CGT theory as imported into Go. -- Charles Matthews

Bill Spight: Except that CGT justifies traditional endgame evaluation. It also provides a rationale for understanding sente, gote, double sente, miai, and tedomari. (See temperature.)

Charles Matthews: But when it talks about reverse sente using miai counting, you can't rely on the answers.

Bill: What do you mean? Because thermography requires pictures, there is little about it on SL. But the size of reverse sente and sente, defined in terms of temperature, gives exactly the same result as traditional evaluation, both miai and deiri.

The basic sente-reverse sente thermograph looks like this:

         |
         |\
         | \
        ------

with temperature as the vertical dimension and count as the horizontal dimension. (This is a Black sente. The oblique line represents the reverse sente line of play.) The temperature at which the mast forms is the miai value of both the sente and reverse sente.

The thermograph also explains why the saying is that sente gains nothing.

Charles Matthews: Yes, but, Bill. I don't want to quarrel about this, but that's exactly the reason I feel CGT arguments ought to be studied separately. What I have called the stacks of coins model, which CGT calls sums of switches, is quite complex enough to show that reverse sente isn't subsumed by miai counting: add a sente play to a sum of switches, that is. I think every time this kind of point turns up, there is a potential confusion between what CGT can prove - which is then mathematics - and how it applies to go; and I have had numerous comments from Go players who approach it from the Go side and hit the buffers.

Bill: Well, I worked with sums of switches long before hearing about CGT. And it is true that the time to play sente and reverse sente in even such a simple environment is not necessarily when they are the largest plays. (If that's what you are driving at.) But that fact is peculiar neither to traditional theory nor to CGT. (Although it is a popular misconception that the largest play is the best play.)

As for studying CGT arguments separately, I agree as regards theory. Just speaking personally, I am not altogether happy that so much mathematical material has crept into SL. Not that it is not interesting, but it's moving away from Go. There are certainly people here who are interested in it, but I am afraid that it turns other people off.

On the other hand, there is much of practical value that CGT and thermography can offer Go players. Over a year ago I posted several pages with the aim of making that available here. I also got drawn into some theoretical discussion with people who had questions. Now, maybe I could have done a better job of presentation, but my aim was to provide practical value, not mathematical theory. I certainly do not want that work considered merely "mathematical detail". That's precisely the slant I want to avoid.

Charles: Well, I created the CGT path precisely to do two things: gather up the material that was in many places in SL, and flag it for what it is, namely a special discussion relevant to understanding go more deeply. Bill, given what you have just posted, would you agree with me that some of the links you've just added to the Endgame page (Chilling, etc.) would have been better left to the CGT area?

Bill: Actually, I felt they belong in both. As I mentioned earlier, I think that segregating them makes them less psychologically accessible. I understand the intellectual purity of the classification, but I do not want the extra hurdle for access.

Charles: There is certainly room for more than one view on this topic.

My own opinion is that CGT isn't very accessible to Go players in general, even now. That is, even after Berlekamp's work which has undoubtedly cleaned up the CGT act. I say this, considering myself to have an adequate background both in Go (three decades), and in mathematics, where I actually once took an exam on a course of Conway's, and was for some time a departmental colleague of his.

The existing material on CGT on SL is by no means perfect, but is also well ahead of what could be gleaned from On Numbers and Games and Winning Ways. I'd like to see the process that saw it develop continue, gradually and interactively - it's a much better way to Go than simply copying across any existing treatment.

An example of what is at stake: the point above about not always playing the 'largest' move. That's OK - I think players can swallow that much. But then if temperature is defined via miai counting, and is also called a model of urgency (as at hot), there seems to be a problem of claiming too much. The devil is here in the detail of 'modelling'. The CGT theory tends to work well in environments that are not too 'lacunary', to use a mathematicians' term: the background of available plays doesn't have yawning gaps in it.

Bill: Thanks for your comments, Charles. I'll respond more fully later, but I would like to make a couple of quick points.

First, my aim was not to make CGT accessible to Go players, in general, rather to make some insights that it affords into Go accessible.

Second, I agree about urgency. The term, as used in CGT, clashes with the Go term. Better not use it in the CGT sense at all.

Later comment: I wonder about attractiveness instead of urgency. That seemed OK, but then I thought about saying that a stable follower was less attractive than its parent, and that didn't seem quite right.

Upon further reflection, I am leaning towards importance. Both urgent points and big points are important, stable followers are less important than their ultimate ancestors, and it becomes more important to play sente when the temperature approaches its miai value. (For that last, urgent still seems better, but it clashes with the urgent in urgent point.) Comments?

Third, as for temperature. I was pleasantly surprised to see how it has become a popular term on rec.games.go, as applied to the board as a whole, or ambient temperature. Since the temperature of a game is the same as the miai value of normally correct play, I would prefer not to use it in that sense. However, I have found myself talking about local temperature, as in a drop in local temperature. I have also found people talking about hot positions here on SL.

Fourth, as for the CGT theory's (thermography) requiring a rich environment without significant drops in the ambient temperature, the exact same goes for traditional go evaluation. In fact, CGT does better than traditional Go theory when there are temperature drops, because it has a better handle on tedomari, through the use of infinitesimals. Also, thermography takes better account of the times when the ambient temperature is less than the temperature of the game.

Tom: In mathematics, it is convenient to give concepts names, often mathematicians choose words from outside of mathematics that have some relevant connotation. Unfortunately this gives them the opportunity to exaggerate the scope and power of their theories while overtly they are merely naming. Perhaps the main reason that this is a bad thing is that non-mathematicians are persuaded to learn about these theories and then are disillusioned. They may become predjudiced against maths. For example, I suspect that chaos theory has little to say about the state of my desk.

I think Bill, that by using terms like importance or urgent or even attractive, you are running the risk that people will think that the corresponding non-technical terms are meant. Unfortunately, the maths does not have the power to describe the qualities that these terms usually denote. For this reason I like terms like temperature or hot, perhaps there is an adjective along these lines. I may be being sanctimonious here. -- Tom

Bill: Thank you for your comments, Tom. Temperature and hot are the mathematical terms. Miai value and large are the traditional go terms. I think that urgency is used informally in the mathematical context, and I did so here on SL. The question is one of informal, non-technical discourse. In English, urgent has been used to refer to large plays relating to local shape, so there is the potential for confusion. Otherwise, I think that it is a good informal term.

Many amateur go players believe that the largest (hottest) play is the best play. That is incorrect, as good go players have always known. OTOH, cases where the best play is not the hottest are the exception. So the temperature of a play is an indicator of when it should be played. All we are looking for is an English term, aside from urgency, to fill in the blank in, "The miai value of a play is an indicator of its <blank>."

Hmmm. How about priority? Not as juicy as urgency, perhaps too precise, but in the ball park. :-)

Tom: Ah! Sorry. I thought you were talking about a term for a mathematical concept. The word urgency would seem ideal to mean, well, urgency except for your comment about the local shape plays. You seem to be saying that urgency is already a technical term in go. Could it be argued that these local shape plays are called urgent because they have have a suprising amount of the X-quality that urgency might naively be thought to describe and that you are trying to give a name? The page (urgency) does not mention a local shape meaning.

Bill: Although go players talk about urgent plays in the sense of shape, I do not believe that I have heard a single one talk about the urgency of a shape. That is why I at first thought I could talk about the urgency of a move without confusion. (Alas, that was not the case. <sigh>) But I think that that is why the discussion on the urgency page is not that clear. What sense of urgency are we talking about? Do go players really use the word in two different senses? Unclear.

Charles: I thought I'd go through a traditional analysis of small endgame to give this discussion some content - and clarify the interpretation of 'traditional' I'm using.

I'm not in any doubt that CGT does improve on TGT (traditional Go theory) - not least because the latter isn't really self-consistent while CGT can't help being that. The point about the environment does seem to be key, and it doesn't actually get formulated in TGT, as Bill says.

Bill: For comparison, see CGT analysis of same small endgame.

Jan: While I like CGT and surreal numbers as much as the next mathematician, thinking about them for practical endgame purposes just makes my head hurt: I only know that things are not as easy as the standard material would have me believe, but since I've not (yet) mastered the standard material, this only confuses me further - I look for hidden traps, worry about tedomari and so on while I should just (learn to) find the largest move by traditional theory and play that. I think CGT material is inherently difficult to Go without making a lot of assumptions.

Just my two sente's worth :-)

Bill: Jan, that's worth at least a quarter. ;-) Actually, for me what you have to say is quite valuable. :-)

I have worked with CGT and thermography for only 8 years. For much longer I used traditional Go theory, along with my own corrections and extensions. I had to unlearn some things in traditional theory that I never would have learned if I had started with CGT.

The part of CGT that addresses the size of plays is thermography, and, as Berlekamp says, that is where to start the analysis of go positions. Unfortunately, there is little about that here on SL, because of the problem with displaying graphics. Of course, during a game you won't be drawing thermographs on paper, but it does make finding the size of plays easier and less prone to error.

I would appreciate your further comments, because they will help me in terms of presenting this material.

Thanks,

-- Bill

Sioux Denim: I'm not sure it's the lack of graphics that makes CGT on SL tricky, more the lack of labels. This thermograph has all the information, but is pretty hard to interpret without more labels.

Atomic weight {4¦3}  

G={6^¦^,+-^^}

Example Atomic Thermograph taken from On Numbers and Games. (The original diagram has a labelling error in the 2nd Edn.)

I've also wondered whether there should be a CGT page explaining Nim heaps, or whether it's just too esoteric for SL ( especially as only *, *2 and *3 have been found so far in Go. )

-- Sioux Denim

Jan: I'm no thermographologist, but as far as I'm concerned you just plug in the ambient temperature and find an approximation of the local game as a switch - for example, in Bill's thermograph above, as the temperature drops below the freezing point, the play starts to become increasingly more interesting to White (hmm, that proverb about sente gains nothing starts to makes sense now - but the term 'freezing point' seems weird in context).

On the whole, though, I tend to agree with Charles' view - CGT is no easy matter in its own right. let alone when applied to Go (or even worse, ko). It's alright to discuss CGT here, but I think we should have more emphasis on the interaction between CGT and normal play. To be more concrete, a page on the relation between thermostrat, orthodox play and optimal play would be welcome. The kami no itte is not slowly turning down the heat in the Go room, so maybe something about continuous environments; Assumptions of CGT? perhaps?

One thing that has been bothering me lately is how CGT deals with the type of plays found in the page on mutual damage. Sure, you can make the situation there more symmetrical, add in a layer of insulating eyes (like in the first diagram on BQM372) and hey presto! you're just playing G + (-G)! But that doesn't apply in a real game: most of the time G is not the 'double sente hane along the first line' game, and your play will deteriorate when you just simplify it to { 2 | -2 }. Just as you can't approximate the details of a game by its mast value and temperature, you can't approximate it by its thermograph - only reading will suffice.

OK, enough rambling for now, back to you two :-)