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 Post subject: X marks the spot
Post #1 Posted: Mon Jul 20, 2020 12:33 pm 
Oza

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I present here some of my Equilibrium Theory. It is marked off in several parts - coffee break points, I suggest, as it is rather long.


PART 1 - WHEN MY FLABBER WAS WELL AND TRULY GASTED

The other day I had a half hour to fill in before I had to leave for a lunch appointment. I thought I would try me new equilibrium hypothesis by challenging Lizzie to a game. The short time, and the fact I was checking moves produced by an algorithm, meant I played almost instantly with no reading beyond what floated into my field of vision. It also meant I picked the first blue move Lizzie came up with. Also, because of the time factor, I planned to go only up to about move 50.

I had to tear myself away after move 110, at which point Lizzie was in the lead with a win rate of 60%, having started off at 58%.

Apart from the pulsating awareness I really had to get my skates on, I had two main thoughts I can recall. One was along the lines of "how do I pick my jaw up off the floor". The other - very oddly because I didn't have any strong feelings about the incident at the time - was that the alleged cheating in a European online event that created much froth on L19 may have had a perfectly simple explanation. The one offered, in fact, as I recall, by the person who reported the incident here and who defending the alleged "cheater". His argument was that this player had been studying with nothing but Lizzie and so has developed an AI style of play. With the exception that I have not been studying, this is what had happened with me.

I am in no way arguing that I have become stronger. I expect I would eventually have lost the game heavily. For one thing the board contained a ko/seki that had developed entirely without my knowledge, and even with time to think I would have had no idea how to handle it. Furthermore, there was a strong element of flukiness in that I had Black, had set out single-mindedly to follow my algorithm (actually an over-posh word for what I was doing, but still...) and Lizzie cooperated by going along with the flow of the game (a running battle).

At this point, I'd expect you to have two sensible questions.

One would be to see the game record. My head was in such a spin - surprise and being late for appointment - that the thought never occurred to me. In any case I have never normally recorded my games before.

The other question follows on from that: did I not play another such game later?

Beyond a simple "no", the answer to that's quite complex. The biggest reason for not doing it is that there are other go things I prefer to do - my books. When you are over 70, your priorities are not the same as when you in your 20s. Another reason is that I didn't expect to do so well again. Mind you, I would expect to do better than if I was playing in my normal human way - quite a lot better in fact, but I'm sure I wouldn't really be understanding what is going on, except in the very nebulous terms of my theory (Ill call it that now because hypothesis is longer and harder to say).

Why can I be so confident? Well, I have been following along with Bill's series on Elf evaluations. I haven't been posting my suggestions, but it only takes me a few seconds to choose a move so I have been checking how well I can do. I have been doing much better in matching Elf than matching with the human, and much, much better than I would do if I were playing as my real self. And, of course, there have been other checks.

I don't plan to reveal my method in full here, but I will reveal some highlights and, more importantly, some of the thought processes that got me there, so that - if you feel inclined - you can try to develop something for yourself along similar lines. I could say a lot more but it's too much like hard work, and I want to reserve any energy I've got left for my books.


PART 2 - CHEWING THE CUD

I don't really understand how AI programs work. That may be an advantage. It allows me to let my thoughts wander where they will.

One of my favourite images is Go Seigen studying go in his sanatorium room. His doctor notices he is always doing this but there are always just a few stones on the board, scattered round the centre. I assumed he was obviously concentrating on the early part of the game, but perhaps not on the fuseki as we know it - I thought that banishing that concept may in fact be a way forward. I was influenced in that thinking by the major reappraisal by Chen Zuyuan and Li Zhe of old Chinese go theory. Remember that I am trying only to explain my thought processes, not my actual thoughts, but to avoid too much frustration I will say that an eye-opening moment for me was their revelation that the alleged oldest games of go recorded are probably just fuseki diagrams (and not as old as often thought, but still over a millennium). I was also influenced by a new document attributed to Huang Longshi in which he says the "War [as in Sun Zi's Art of War] has nine grounds; go has five." This is a devastatingly new and stimulating way of looking at go that goes beyond fuseki, and since Go Seigen was a great fan of Huang - he put him on at least a par with Dosaku - I wondered whether Go's sanatorium thoughts and Shin Fuseki may have had something to do with how he viewed Huang's games. (If you want to know what is meant by grounds, look at Chapter 11 in Art of War.)

So I set about ruminating by starting with the empty board and wondering how bots distilled their knowledge - turning grass into milk. It occurred to me that almost certainly have to be using numbers as the basis of their evaluation. In other words they had to be measuring something. But what could they be measuring? There's nothing on the board to measure at the start of the game, and then for a large part of the game there are just a few stones, often seemingly unconnected. Not much to get to grips with?

But I am now well used to the Chinese notion that that emptiness is not nothing. The contrast between solid and empty comes up a lot in old Chinese commentaries. There is in fact a lot to get to grips with - a whole empty board. That emptiness actually has substance. It hides patterns. AI has discerned those patterns. Can we do the same?

The short answer is obviously yes, because we have already done that with our mantra 'corners, side, centre'.

But my gut feeling was that that mantra is misleading, and possibly even wrong. Go Seigen had similar feelings, I suspect. I also believe Huang Longshi was seeing something different with his "5 Grounds".

One good reason for believing it was wrong was that the topography of the game actually changes substantially every time a stone is added. But the addition of stones also changes what can be measured on the board. Quite simply we can now measure stones.

I had previously been rather taken by a book Mizokami Tomochika in which he argued that by splitting the board in half and counting the stones in each half you could (indeed should) choose your move on the basis of which side had a preponderance of stones in that area. There were various problems with MIzokami's approach. The most obvious was that he didn't give a method for choosing which half of the board to look at. Another problem was that if you looked at his examples via bots, the results were very disappointing.

But for the reasons just adumbrated, I still felt he was on the right lines. I wondered whether the problems could be resolved by choosing a different topography. Not just different areas but some overlapping. It was far too tedious to count position after position manually. I therefore wrote a C# program that allows me to step through a game and shows the counts (Black versus White stones) for each of the areas I had defined (14 in all, but in practice 8 seem to suffice).

Completion of this program coincided with Bill's series getting into full swing. As soon as Bill posted a position I called up my program and within a few seconds had a good idea where to play - every time.

Now it's important to stress here that I was NOT looking for the best move. I (following Mizokami) was looking for the right area(s) to play in. Once I had that, I was using my human knowledge to choose a specific move in the relevant area. Needless to say, I was not quite as spot on as my program, although most of the time I did OK.

Most of the time, I then called up Lizzie and looked not so much at the blue move but at all the moves that merited a circle of some colour. I was astonished at how closely the areas in which these moves clustered married with the areas my own program highlighted. I stress again that my program gave areas rather than specific points, but if you allow my human intervention to pick moves within those areas, the clusters showed a great overlap. My program was even suggesting moves like Direct 3-3 and shoulder hits.

But what was most pleasing was that I discovered two things, one of which I would have dismissed (then but not now) as too naive and the which I wouldn't have dreamt of looking for. I believe that when theories do this sort of thing it's usually a good thing. At any rate it was exciting - exciting enough to get me, the ultimate anti-numbers man, to do some counting.

These are the two things I am revealing here.


PART 3 - THE MILK GOES TO THE CHURN

Before revealing my thoughts, let me get the numbers out of the way - the Clean Air Act applies here!

I did a count of the 60 games in which AlphaGo (as Master or Magister) whitewashed human opponents. This seemed to be the purest form of AI versus human. In each game, I counted which side had the most stones on each major diagonal at the end of the first 50 moves. If there was a tie at that point (which was rare) I did a further count at move 100. I did not keep a full record - I have no pretensions of being a scientist - but the upshot was that in almost very case AlphaGo had more stones on the diagonals, and usually a lot more. In those latter cases, the game generally ended quickly.

But there were a very few cases where the computer vs human count was very close, and arguably equal. And guess what, in two of those few cases the human was Ke Jie. In two of those cases the human was Pak Cheong-hwan. In one case the human was Mi Yuting, and in another Jiang Weijie. Furthermore, these games were all very close - defeats by just half a point in a couple of cases.

In other words, the world's best humans were (perhaps unknowingly) following AlphaGo in stressing occupation of the diagonals.

And this was with the most simplistic count - mere occupation of the diagonals. If you looked instead at control of the diagonals (relying simply on my human and amateur judgment admittedly), some of the closes cases just mentioned could easily be resolved into clear differences. There was just one apparent exception. But even that was easy to explain (I thought). It was a case where White occupied some diagonal points (at move 50) but his stones later ended up captured. So apparent control was not real control, at least for White. In fact it was strong control for Black.

I did some further checking but looking at some Go Seigen games. I didn't trust this quite as much as AI vs human, just because it was human vs human. But my (desultory) checks did appear to confirm that, like Ke Jie, Pak Cheong-hwan etc, Go Seigen did manage to occupy/control more diagonal points than his opponents.

Now, although my method of working is very unscientific, and no doubt unsatisfactory in other ways, this finding seems more than plausible in at least one sense. In terms of dividing up the board in equal portions - which seems a reasonable way to start a topographical investigation - stones on the diagonals overlap with at least two areas. In fact, one of the problems with Mizokami's method may be precisely that he excludes the centre lines (orthogonal in his case, but orthogonal overlap does seem les important).

But both experience and common sense tell us that mere occupation of the diagonals is unlikely to be a good strategy - it's like fighting with one hand tied behind more back. Lizzie also confirms that move 1 at the ultimate overlap - tengen - is not a good idea.

When I came to think about more solid explanations of criteria for controlling the diagonals, several ideas came pouring out. Among them were these: (1) a shimari really is a reinforcement, not an enclosure; (2) shoulder hits make perfect sense; (3) it now makes perfect sense to pay less attention than we normally do to the sides and pincers; (4) the vital areas are the barmkins; (5) a Go Seigen area II can be postulated.

I will now explain these ideas after the next coffee. And don't forget we still have my other fundamental discovery for dessert.


PART 4 - THE REIVERS

It may seem that I intend to go on till the cows come home. Maybe. At least Daisy and her ilk still need to be put to bed. But in this case not in the byre. Go is a battleground. There are reivers about. In the border areas where I come from, at about the time learned Chinese gentlemen were creating ingenious under-the-stones problems for the Xuanxuan Qijing while tending their chrysanthemums and sipping plum wine from elegant porcelain bowls, my ancestors were already following the modern fashion for fast food. Cattle rustling. It's no surprise burgers are sold by a company with Mac in its name.

The depredations of these reivers - the rustlers - were so constant that communities built peel towers for protection. You can still see many of these dotted round the countryside. They look like enormous fat chimneys sticking up out of nowhere, usually on top of a small hill, spooky and incongruous. But think of the empty go board as the empty countryside. If you had to build the equivalent of a peel tower on the go board, where would you start - remembering that you want it to be not just strong but accessible to your farmers. A 4-4 point with a knight's move shimari seems like a good design. But note: this is not your farm you are protecting. It is not land. It is not territory. The peel tower is a protected strong point, for emergencies. Real farming goes on elsewhere, whenever you get the chance. In simplistic go terms we can think of moyos protected by shimaris. In more subtle terms we can think of Huang Longshi's 5 grounds.

But in real life peel towers were not enough. They protected the people, but not the cattle. Just like lockdown now, physical safety did not guarantee economic security. If anything, it could exacerbate it.

A wise king of Scotland therefore issued a proclamation. Every peel tower had to have a barmkin. This was an enclosed area attached to the peel tower. The kye and yowes were to be driven in here at times of danger. The stone walls were low but sufficient as the reivers didn't want to kill their potential booty. Most of these barmkins have now disappeared because the small walls were low enough to be accessible to later generations, who filched the material to build the dry-stone walls that now litter the countryside.

But it turns out barmkins are alive and well on the go board! These are the areas around the 5-5 point and other diagonal points into from of the peel tower shimaris. And it is in these barmkins that you accumulate the source of your economic wealth - not in the peel towers.

Keeping this image in mind, think now of the effect of a typical shoulder hit. You are at a stroke messing with your opponent's barmkin area. You can make a good reiver. Think now of the effect of a typical press around the 4-4 point. Again, you are knocking down the barmkin walls before it can be finished.

Similarly, imagine the effect of a typical pincer: you are inviting the opponent to jump out in to your barmkin area! You are welcoming the Trojan horse.

So, you want to protect your barmkin. But reivers like them, too. As they roam around the countryside picking up cows, they can't just stick them on a train and send them North. They can't take the beasts along - the poor things really do want to come home. So, ensconcing them in a spare barmkin can be a very useful temporising measure.

Imagine that, too, in go terms: a joseki where one side cowers (pun intended) inside the peel tower's corner territory while the enemy takes control of the barmkin outside - outside thickness. Par for both sides - they both live to fight another day? Well, the bots have shown what's wrong with that with the Direct 3-3. Don't let everyone cower in the tower double locking the door with a hanetsugi. Instead, let a couple of brave souls rush outside and distract the opponent. Don't let him occupy the barmkin. You may not have your cows there, but he hasn't got them there either.

In my conception of these barmkin areas they centre fairly tightly around the 5-5. 6-6. 7-7 points. It's not a matter of occupying them, necessarily. It's rather a matter of control - you don't want to put your cows there unless you have to, but it's nice to know you've got somewhere to rely. However, once you have that control, the positive effects radiate out to a wider area. That area seems to me to be so important that I now think of it as a Go Seigen areas, somewhat like the way I think of group on the side adjacent to the corner as a Go Seigen group. In fact I believe the two are related in some close way, but I haven't got my head round that properly yet. (But as a priming thought, I think the GSG group negates the power of control in a GSG area. Also, pincering a stone in the GSG group area may stop the full group being formed, but does it create a GSG group-lite?)


PART 5 - THE DISPUTED LANDS

The areas roamed by the reivers were known as the disputed lands - the areas claimed by both England and Scotland. But this very rarely involved pitched battles with both sides in continuous fighting, striving for the initiative. Instead, it was rather like go. They took turns to attack weak points, and if there were no obvious weaknesses they built up their defences (such as building barmkins!).

And the truth of this was revealed to me by my program. What I discovered - simply by noticing it, not by rational thought - was that in a situation where one side had a preponderance of stones, most particularly two or more, and the other side had a similar preponderance in another area, the recommended moves (as confirmed by Lizzie) were always such as to reduce the opponent's preponderance rather than increase one's own preponderance. The only time the recommendation was to increase one's own preponderance was when the position was otherwise stable. In itself, that did not surprise me, because I think it reflects the typical difference between pro pay and amateur play. But I was surprised the difference was so stark and consistent.

So is there an explanation for this? My inclination is to see it as form of unstable equilibrium. There is no deep thought behind that. It's just that the chap who teaches the dances at our Scottish country dancing club used to be a statistics don, and one of our dances is called Equilibrium. Whenever it comes up on the programme, he likes to mention that there is stable equilibrium and unstable equilibrium. In the latter case, a very small change of state can lead very rapidly to wild fluctuations in the overall state. This is his polite way of saying we've really messed up practice of the dance, which happens to be one of those where small errors do lead to chaos. It occurred to me that because go is a game of alternation, it is really a game of disruption rather than a game of creation. If you don't disrupt your opponent's moyo it can quickly grow like weeds. Conversely, if you don't respond to your opponent's disruption, your weak position an collapse like a house of cards. So very move has to combine creation and disruption in such a way as to at least maintain equilibrium, even if in an unstable sense. Of course, you want to edge into the lead, with either a bit ore creation or a bit more disruption than the opponent manages. And guess what - the points on the major diagonals overlap more than one area and so are prime places to achieve that wee extra, decisive edge.

So there you have it - or some of it. I have revealed some of my thinking and some of my results in a way that I hope both entertains you in this boring lockdown era and stimulates you to think about go in a new way suitable for the AI age.

I am unlikely to pursue these lines of thought for myself, for the reasons indicated. But if I do, the areas I would look at are defining "preponderance" in a more rigorous way so as to include control as well as occupation. I am certain we need to redefine the topography of the board, not just away from the outdated corner sides, centre but in a way that extends beyond the fuseki stage. I think the barmkin idea is a step in the right direction but I'd want to see how big a barmkin needs to be (or how small it can be), and in particular I'd want to learn more about moves such as shoulder hits that affect the barmkin area at a distance. I suspect the advice of Huang Longshi to "calculate how near and how far" will turn put to be especially insightful in tis regard.

I also think it is going to increasingly important to move away from the Japanese way of thinking about go, and to go back to the oneness of everything stressed by the old Chinese model. I now believe that to describe go as a game decided by who has the most territory as fundamentally flawed. It is who has control of the most points. But people who present go with Chinese rules and say that the winner demonstrates his victory by being able to fill in stones on all his empty points are also mistaken. You can demonstrate your victory by emptying all the points you occupy. Emptiness is not nothing. As Lao Zi, says it is empty holes for doors and windows that make house useful. AI programs realise that. They work with 1s and 0s. Even we realise it in go, with corners, sides, centres, but we are supplying the 0s and not the 1s. We need to add stones for the 1s. My submission is that the combination of stones forming a peel tower/ shimari (the 1s; but a reinforcement not an enclosure) and barmkin (0s; an enclosure but not a territory) is a useful model that can easily be tested and refined on the way to a more embracing model.

Note: if you want to see what I mean about equilibrium in Scottish country dancing, and also to see what I get up to when lockdown is not operating, take a look at this BBC video: https://www.bing.com/videos/search?q=bb ... &FORM=VIRE (or search 'BBC Schiehallion Scottish country dance' and choose the one that looks brown). It's not the dance Equilibrium but the overhead shots and the professional BBC camerawork will give you a sense of how one small mistake can create havoc, especially if you can watch to the end. You will also see how SCD is about patterns, rather like go.


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Post #2 Posted: Mon Jul 20, 2020 1:32 pm 
Honinbo

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Bravo! :clap: :salute: :clap:

Definitely food for thought. :)

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Post #3 Posted: Mon Jul 20, 2020 6:05 pm 
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I had to read this more than once, and I'm sure I still didn't get everything. That said, I'm wondering:

Can we get an intern to do this same thing with he 50 public games AlphaGo played against itself? (to see if this simple formula continues to be as good of a predictor?)

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Post #4 Posted: Tue Jul 21, 2020 3:27 am 
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I'd also point to this game from 2011 as food for thought.



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Post #5 Posted: Tue Jul 21, 2020 4:10 am 
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I couldn't make heads or tails of this. Is there an "Equilibrium Theory for Dummies" post in another thread somewhere or do I just have to be patient and hope that all become clear as time goes by?
:scratch:

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Post #6 Posted: Tue Jul 21, 2020 5:03 am 
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ez4u wrote:
I couldn't make heads or tails of this. Is there an "Equilibrium Theory for Dummies" post in another thread somewhere or do I just have to be patient and hope that all become clear as time goes by?
:scratch:


I can relate what John says to some things I have learned. OC, he develops the ideas further.

Back in the '90s I did some statistics on pro play and discovered that the majority of plays are adjacent to another stone, diagonal to another stone, or one space away from another stone. OC, you expect that to happen as the board fills up, but, to my surprise, that was true even in the opening. :o In organizing my data I started out with a table of Black stones vs. White stones, but it became clear that it was better to make the table Black stones plus White stones vs. Black stones minus White stones. Within a certain area or window, OC. The most frequent category was a difference of 0, an equal number of White stones and Black stones. And seldom did a pro play so as to make for a difference greater than 2 either way. IOW, with good play there tends to be an equilibrium in the number of stones in any area of the board. And, OC, there tends to be an equilibrium over the whole board because of alternating play. Mizukami apparently developed the idea of equilibrium further, and John has, as well. :)

I can relate the idea of the barmkins to the fact that it seems to me that the bots tend to start off making relatively small strongholds. Even before the AI era I noted that with leaning attacks. Nowadays we see it with shoulder hits and attachments in the opening.

The other stuff about the five battlegrounds and diagonals is new to me, but John has talked about Go Seigen groups before. :)

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Post #7 Posted: Tue Jul 21, 2020 1:56 pm 
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This is epic work!

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Post #8 Posted: Tue Jul 21, 2020 3:11 pm 
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I only vaguely understand the go theory in this post, but I have been absolutely convinced that the author is an amazing writer.

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Post #9 Posted: Tue Jul 21, 2020 8:16 pm 
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I'm trying to dissect this. I probably misunderstand some of it, but here's what I gather so far:
* John did well against an AI program, maintaining a roughly equal position until move 110.
* He made a C# program that splits the board into 8 to 14 areas, counting the black and white stones in each area.
* This computer program was helpful in determining areas to play. I suppose the idea is that you should play in the area where the count is lowest? This part is not really clear to me.
* PART 3 transitions to discussion about counting black and white stones on the diagonals. I'm not sure if these constitute the same areas as in the C# program. But I guess the idea is that having lots of stones on these diagonals is good. I'm not sure *which* diagonals these are.
* Talk about barmkins. I suppose this is just a locally diagonal area?
* When there's somewhat of an equilibrium in two parts of the board, AI favors reducing the opponent's area rather than strengthening its own.
* Go is about control, not territory. "Nothingness" is something.
* Some stuff about cows, but I have to admit, I didn't really get this part.

---

Now thinking about how to practically apply this. I don't know the specifics of what the C# program is doing or which diagonals are being counted. But I guess the general idea is that it's good to maintain balance on the board?

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Post #10 Posted: Tue Jul 21, 2020 8:26 pm 
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Bill Spight wrote:
Back in the '90s I did some statistics on pro play and discovered that the majority of plays are adjacent to another stone, diagonal to another stone, or one space away from another stone. OC, you expect that to happen as the board fills up, but, to my surprise, that was true even in the opening. :o In organizing my data I started out with a table of Black stones vs. White stones, but it became clear that it was better to make the table Black stones plus White stones vs. Black stones minus White stones. Within a certain area or window, OC. The most frequent category was a difference of 0, an equal number of White stones and Black stones. And seldom did a pro play so as to make for a difference greater than 2 either way. IOW, with good play there tends to be an equilibrium in the number of stones in any area of the board. And, OC, there tends to be an equilibrium over the whole board because of alternating play.


Do you simply mean that a given area of the board typically has a roughly equal number of black and white stones when players are playing well? How are areas defined? Just divide the board up into 10 equal pieces?

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Post #11 Posted: Tue Jul 21, 2020 8:50 pm 
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Kirby wrote:
Bill Spight wrote:
Back in the '90s I did some statistics on pro play and discovered that the majority of plays are adjacent to another stone, diagonal to another stone, or one space away from another stone. OC, you expect that to happen as the board fills up, but, to my surprise, that was true even in the opening. :o In organizing my data I started out with a table of Black stones vs. White stones, but it became clear that it was better to make the table Black stones plus White stones vs. Black stones minus White stones. Within a certain area or window, OC. The most frequent category was a difference of 0, an equal number of White stones and Black stones. And seldom did a pro play so as to make for a difference greater than 2 either way. IOW, with good play there tends to be an equilibrium in the number of stones in any area of the board. And, OC, there tends to be an equilibrium over the whole board because of alternating play.


Do you simply mean that a given area of the board typically has a roughly equal number of black and white stones when players are playing well? How are areas defined? Just divide the board up into 10 equal pieces?


My original idea had been to define plays based upon the two nearest features, using Manhattan distance. So there was no defined area per se. For instance, an initial 3-4 point opening, with no other stones on the board, would have as its two closest features the nearest edges of the board. The area to search would be a Manhattan circle with the play at its center. After I developed the sum of stones and difference of stones metric, Bill Fraser wrote a program that used a 3x3 square window to gather statistics of a game. Extending the window to a 5x5 square made classification and analysis more difficult.

But for practical purposes humans are rather good at delineating regions of interest on the go board. IMO a half board is too big to be of much practical value, but Mizukami seems to find it useful, from what John says.

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Post #12 Posted: Wed Jul 22, 2020 7:27 am 
Oza

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I don't want to give too much away, and neither do I want to get drawn into spending too much time on this thread, but I'll address a few points and give an example.

The example is the one below, which was the first example in knotwilg's new series on Attack & Defence. I choose this simply because, when I saw it, I was surprised that he said it was hard to evaluate. It looked simple to me - there was a classic barmkin!



The diagonals I am talking about - which I (?surely correctly) called "major diagonals" - run A1 to T19 and A19 to T1.

My program tells me that the area of interest for the next play is main the left side (the whole half), but with some secondary interest in the top left triangle (north of the A! to T19 line). It also tells me that the likely move will be on the third line or below (but does not have to be).

At this stage I, the human, take over. I choose promising points in the designated areas and then run the new position through the program. I can then choose the move that gives the biggest desirable change. Essentially this is the figure that shows the highest preponderance of control of the entire board, but when I make my choice I impose two things on the available moves: (1) my human knowledge as an amateur go player, and (2) a preference for a move that closes gaps in areas where the opponent had a lead over moves in areas where I already have a lead - lead as defined by the program's preponderance count, of course. This preference is the result of my observation that best results seem to come from avoiding unstable equilibrium.

Note carefully that I am not choosing an area and then trying to get help with the precise spot therein to play. I want the program, which surveys the entire board, to show me the area or areas to play in. This is fundamentally different from what Mizokami advocated.

I ought to have added also that when there is an obvious hotspot, that takes precedence over the program, and I define the hotspots on the fly. I see no hotspot here, so I look for a move on the third line on the left side. Strictly, I should input lots of moves as per what I described just above, but I'm a great fan of common sense (aka laziness) so I would play A.

Beyond saying that it's obviously not a daft play, I'd find it hard to justify it in human terms. I could easily say that I am keeping away from thickness (Black's, above), but I could then say, well, if that's such a good idea, I can go one point further and bang up against the White 3-3 stone. It's already strong, so I don't mind strengthening it further, and I might even overconcentrate it.

I could waffle along further in similar vein, but when it comes down to it, I'm just choosing the moves that I'm familiar with. Strangely (or otherwise?) I seem to do quite well that way, and nearly every time end up on one of Lizzie's blue spots or a second or third best spot.

One thing I do not do is a tactical search beyond a mere glance. Also, I do not factor in sente and gote. This is another thing that I perhaps ought to have mentioned before. I have come to the conclusion (on the basis both of rational thought and observations with my program) that sente and gote don't matter to a bot and probably shouldn't matter to us. That's a big and provocative statement, I know, but I'm fairly sure of it. However, I'm not going to elaborate on it here. I just toss it out as a thought.

So that explains my thought processes in choosing a move. You will note, therefore, that I don't personally do any counting on diagonals, nor do I define barmkins and peel towers. There were just my way of trying to illustrate why I think "preponderance of control" works. Or, more accurately, in which areas does P of C manifest itself.

That said, what I noticed straightaway in the diagram above was the nicely laid out barmkin (the rough and ready enclosure around the 5-5-, 6-6, 7-7 etc points) in the northwest. Even without counting, I could see at once that Black has a strong preponderance of control over the A19/T1 diagonal, and the other diagonal is instantly visible as split 50/50. So, making the usual assumptions about pro games (e.g. that there have been no horrendous mistakes already), Black is comfortably in the lead. I have no idea by how much, but I would certainly prefer to be Black.

I think I already made it plain enough that I am not offering you an algorithm you can start using to make better moves. I wouldn't go so far as to say that counting stones on the major diagonals is a waste of time, but it's not what I do. I just happen to believe that it's implicit in bow bots measure what I call P of C. It seems potentially useful as a ready reckoner to evaluate which side is in the lead, but I think I'd want to work on defining the control part of P of C with a bit more than barmkins before I'd trust it completely. Actually, I did stretch the idea myself a little by assuming extra control of a diagonal if there were likely forcing moves by the opponent that let you occupy or surround a major diagonal, or if you had moves such as presses that guarantee you future control. This seemed a very promising approach.

So, if I am not offering an algorithm, what am I offering? Just exotic food for thought. I think the new nouvelle cuisine can be "fusion" food - a blend of AI and human ingredients. But you have to be your own chef.


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Post #13 Posted: Wed Jul 22, 2020 8:05 pm 
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If there's no algorithm, then to me, I guess it's kind of interesting to read about, but not very useful. Things are useful to me if I understand them. Without an algorithm or a way to describe what's being talked about here in concrete terms, I don't have that understanding.

You have a computer program, apparently. That has an algorithm. It's defined by the code that you wrote.

I guess I can think about barmkins and cows and stuff the next time I play a game, and I'll tell you how it goes.

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Post #14 Posted: Thu Jul 23, 2020 2:41 am 
Oza

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If there's no algorithm, then to me, I guess it's kind of interesting to read about, but not very useful. Things are useful to me if I understand them. Without an algorithm or a way to describe what's being talked about here in concrete terms, I don't have that understanding.


Let me recommend to you the other way of getting understanding: thinking. Cook for yourself instead of devouring fast food.

Quote:
You have a computer program, apparently. That has an algorithm. It's defined by the code that you wrote.


Yes, but it doesn't cover the whole process. As I've explained (twice), it's basically just a calculator for area prediction. I supply missing bits - the precise move selection within the indicated areas - and I also apply the thinking about defining areas and overlaps.

Quote:
I guess I can think about barmkins and cows and stuff the next time I play a game, and I'll tell you how it goes.


Cooking for yourself? Good. But don't end up just telling us how good the beef tastes, or simply what the recipe is. Give us the ambience and the patter. Think tv chef! In any case, when it comes to a recipe, but I am minded to quote (though possibly inaccurately) a famous lecture by Feynman in which (as I recall) he put up on the blackboard two totally different equations which described the same phenomenon. Both were correct, but tweaking each one led to very different results. If you end up with elephants or alligators instead of cows, that would be "zool"! Feynman's idea (if I've remembered it correctly) was demonstrated in a way some years ago when the Big Bang financial revolution brought in lots of new imagery to a very traditional field. Big swinging dicks was one image, not as refined or as useful or as interesting as peel towers and barmkins in my estimation, but some people apparently found it useful as a way of driving forward aggressive risk-taking strategies. They had only partial algorithms in those days, too. It was the days of Alpha Males instead of Alpha Go. But what I found interesting (as an economics correspondent at the time) was the re-discovery by a colleague of Japanese candlestick theory from the time of Dosaku, which (illuminatingly enough) shed light on stockmarket behaviour. Two totally different approaches, and both worked. For me, at any rate, the whimsical (human) version was easier to understand.

The mention of Dosaku allows me to bring in another example. By coincidence, I am reading a Chinese book at the moment which talks about a Chinese master, Wang Hannian, who flourished around 1650 ~ 1670. The book made the point that the manual Ji Qingxia-guan Yipu [Selected games from the Qingxia Pavilion] contains 580 games, only four of which begin with first move at tengen (the Chinese used to call these Taiji Tu - Great Ultimate Games).

Three of these four tengen games were by Wang Hannian. The other was by Zhou Xingyuan, who (the book says) "was a guoshou [a 9-dan] during the Qing Daoguang period [1821~1851] when the Opium War took place." I'm going off at a tangent, but that struck me as odd. What has opium got to do with go? But if you are just adding a bit of colour by mentioning defining events of the period, surely you be writing "when the [First] Opium War and the Taiping Rebellion took place." But you can't easily do that in China. While they may not have to quote Mao's little red book any more, it is still safer to focus on external China-bashing rather than internal rebellion. I notice these things, having been taught by cynical locals how to read between the lines of Communist newspapers when I was a student in Czechoslovakia. We were therefore primed to realise something was afoot one morning when we noticed the picture of President Dubcek in the lecture hall had suddenly disappeared. Sure enough, later that day the Russians tanks rolled in...

But at least the Chinese say very nice things about Dosaku, even though he was a foreigner. Our writer noted that Wang was experimenting with the Great Ultimate at exactly the same time as Dosaku was facing tengen, and in both cases the experiments ended quickly and irrevocably. Dosaku had first had to face tengen in the 1670 Castle Games, in which the term tengen was apparently concocted by his opponent, Yasui Santetsu (aka Shibukawa Harumi, the Court Astronomer). But two years later, "Minamisato Yohee challenged Dosaku again with first move at tengen, but he chose the wrong opponent. The great genius Dosaku completely blocked out the power of tengen, and first move on tengen was thereafter never popular." This is not totally accurate in that, on the one hand, the old Chinese manual Shishi Xianji (Devices from the Hermit's Cave) begins with 20 examples of White 1 on tengen and, on the other hand, Minamisato played another tengen game against "genius" Dosaku and managed to win.

Nevertheless, this comment led me to look again at that victory by Dosaku, to see how he had demolished the mythical power of tengen. I found the final position interesting:



What struck me, starting with the notion of looking for preponderance of control, was, despite the dominating presence of the tengen stone at the beginning, Dosaku had negated Black's control in two barmkin areas and had demolished his third barmkin by killing all the cows with the last, triangled moooooove. Furthermore, if you look at the two major diagonals, White totally dominates the A19/T1 one (control of 15 of the available points, which far outweighs Black's control of the other diagonal. But, as a tip, if you are willing to look into this idea, you can often get a good/better impression by scanning not just the actual major diagonals but also the lines to either side. In other words, visualise a thick X rather than a skinny, minimalist X (and keep those barmkins to the forefront!)

This game also illustrates another idea I've been thinking about. Again no algorithms - just ideas. You will notice that the sides seem to have hardly mattered in this game, at least in the way it has panned out. I have already mentioned that I think the old mantra of corners - sides - centre is flawed. I think this game is useful evidence. My current thinking is that a more correct mantra will be along the lines of "corners 1, corners 2, centre, sides" but with the caveat that you don't so much play in the centre but rather think about controlling (or, worst case scenario: influencing) it. But it's just uncooked porridge at the moment. It will take a few more turns of the spurtle before it's ready to serve up.


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Post #15 Posted: Thu Jul 23, 2020 4:22 am 
Honinbo

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John Fairbairn wrote:
I have already mentioned that I think the old mantra of corners - sides - centre is flawed. I think this game is useful evidence. My current thinking is that a more correct mantra will be along the lines of "corners 1, corners 2, centre, sides" but with the caveat that you don't so much play in the centre but rather think about controlling (or, worst case scenario: influencing) it. But it's just uncooked porridge at the moment. It will take a few more turns of the spurtle before it's ready to serve up.


I also think that corners, sides, center, is flawed. My thinking is more like corners 1, corners 2, sides, and center any time. For instance, sanrensei is doubtful, but suppose that the opponent invades one of the corners and you block on the side facing your other 4-4 stone. The opponent pushes and you extend to the 5-4. If the opponent now slides, the side 4-10 point now becomes good, even before another play in the adjacent corner, because of the power of the center facing 5-4 extension.

I suppose that the three stone wall fits with your idea of exerting control of a major diagonal.

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Post #16 Posted: Thu Jul 23, 2020 7:05 am 
Oza

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I also think that corners, sides, center, is flawed. My thinking is more like corners 1, corners 2, sides, and center any time. For instance, sanrensei is doubtful, but suppose that the opponent invades one of the corners and you block on the side facing your other 4-4 stone. The opponent pushes and you extend to the 5-4. If the opponent now slides, the side 4-10 point now becomes good, even before another play in the adjacent corner, because of the power of the center facing 5-4 extension.


Bill: I agree about 4-10, but in my algorithm the fourth line forms part of the centre. I think even amateurs are always aware that a debate is always possible about extending on the third or fourth line. But that debate is still presented in terms of this side move or that side move. But my AI-influenced thinking is now that you should be thinking centre (4-10) or side (3-10), and that if 3-10 is better for some reason, you have probably made a mistake higher up the tree. Similarly with pincers (a leviori or a fortiori?). As someone who plays a lot of attention to words, I think there is also a strong case to distinguish between playing in the centre and playing to influence the centre.

Not entirely apropos, but I invite you to look at this early 17th century 3-stone game by Guo Bailing (White):



Moves 5 and 7 think about the centre, but so does the very AI-ish 9. It is this move, not my theories, which led Tom Koranda to bring it to my attention. But I couldn't resist looking at the final position. Look at who has control of the major diagonals (and barmkins) despite the 3-stone lightning bolt Black started with.

Incidentally, much of my recent thinking has been heavily swayed by looking at old Chinese games again. Because of the need to stress group connections in view of group tax, they had to pay more attention to centre-influencing moves, and both Tom and I have been astonished at how any AI-type moves they made. I think this is rather similar to what you are noticing about Edo no-komi games in Japan. Because White had to try that bit harder, I suspect he was putting more emphasis on influencing the centre. Again I want to stress the terminology. My choice of 'influencing' may not be the best, but I think it's important to get away from the crude idea of just 'playing' there or 'occupying' it. I am enjoying looking for ways White (or the old Chinese players) do this, and it's been quite illuminating. Here's an example (the triangle was the last move):



The game is GoGoD 1680JQXG208. The great Shi Dingan commented on it. He criticised White 91, which was at A. He basically said it was ajikeshi and White was making his own future play uninteresting, and indeed the result was that White sealed off his side of the corner, and Black got a safe enough group. Shi recommended the cap at B.

I was intrigued by that because A looked fine to me, so I put the position in Lizzie, and was not surprised to see it favoured A. I continued through the game, feeling very smug until it dawned on me what Shi was pointing out. Suddenly B made a lot of sense. I'm not good enough to know whether it really is a better move, but I could see factors that I had overlooked before. First of all, Lizzie's opinion was entirely irrelevant. With group tax this is a different game.

Second, what I noticed as the game progressed was that Black easily joined up his weak top group to a group below, and for a time was even looking at joining up three groups. At 2 points per join, that's a huge difference. B would interfere with possible connections for as many as five Black groups (or six if you consider the cut at P8). This B is a move I regard as 'influencing' the centre big time, in this case.

The third thing that dawned on me was that, having seen the Sino-Japanese character for 'aji', I was still in Japanese mode, and so was thinking in terms of tactical shenanigans to do with the Black group at the top (and that sense of aji was also why I had fancied White A - good idea to get rid of Black's aji in the corner. But this was Sino 'wei' - subtly different connotations in old Chinese: strategic 'taste' as well as 'tactical 'taste'. Shi was talking strategy and I was thinking tactics! I was playing in the centre. He was playing to influence the centre.


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Post #17 Posted: Thu Jul 23, 2020 8:51 am 
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John Fairbairn wrote:
I don't want to give too much away


I for one am more interested in your discovery than the tale of it - while I'm sure the tale is for many's enjoyment.

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neither do I want to get drawn into spending too much time on this thread


A tough challenge!

Quote:

The example is the one below, which was the first example in knotwilg's new series on Attack & Defence. I choose this simply because, when I saw it, I was surprised that he said it was hard to evaluate. It looked simple to me - there was a classic barmkin!


Have you discussed the barmkin theory before? Or is it a recent discovery?



Quote:

The diagonals I am talking about - which I (?surely correctly) called "major diagonals" - run A1 to T19 and A19 to T1.


OK, we can work with that!

Quote:
My program tells me that the area of interest for the next play is main the left side (the whole half), but with some secondary interest in the top left triangle (north of the A! to T19 line).


I'm left to assume that this is due to Black having played 2 stones extra in the remaining area.

Quote:
It also tells me that the likely move will be on the third line or below (but does not have to be).


This I can't reengineer.

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At this stage I, the human, take over. I choose promising points in the designated areas and then run the new position through the program. I can then choose the move that gives the biggest desirable change.


Change in what?

Quote:
Essentially this is the figure that shows the highest preponderance of control of the entire board


How does your program measure "control of the entire board"?

Quote:
but when I make my choice I impose two things on the available moves: (1) my human knowledge as an amateur go player, and (2) a preference for a move that closes gaps in areas where the opponent had a lead over moves in areas where I already have a lead - lead as defined by the program's preponderance count, of course. This preference is the result of my observation that best results seem to come from avoiding unstable equilibrium.


I would think "available moves" are either inspired by your go knowledge, or by the algorithm. Is there a first source for available moves (other than mere legal moves)?

Quote:
Note carefully that I am not choosing an area and then trying to get help with the precise spot therein to play. I want the program, which surveys the entire board, to show me the area or areas to play in. This is fundamentally different from what Mizokami advocated.


So all in all, the program tells you which area to play in, then you apply go knowledge to choose the move. That I can fathom. I still don't see how the diagonals fit in though.

Quote:
I ought to have added also that when there is an obvious hotspot, that takes precedence over the program, and I define the hotspots on the fly. I see no hotspot here, so I look for a move on the third line on the left side. Strictly, I should input lots of moves as per what I described just above, but I'm a great fan of common sense (aka laziness) so I would play A.


So there are exceptions to your procedure where you bypass the area algorithm and just make an obvious best move. Fair enough.
I can see how the left side comes out of your program but not how it will designate the 3rd line (and not the 4th for example). But we're repeating ourselves.

Quote:
Beyond saying that it's obviously not a daft play, I'd find it hard to justify it in human terms. I could easily say that I am keeping away from thickness (Black's, above), but I could then say, well, if that's such a good idea, I can go one point further and bang up against the White 3-3 stone. It's already strong, so I don't mind strengthening it further, and I might even overconcentrate it.


Yes, this is one of the things we still haven't figured out, why in general AI prefers approaching 3-3 and not "shoulder hitting" it. Again I don't understand how your allegedly simple C# program gets to similar conclusions as AI. Why has no programmer figured that out before? Can you really not give us the simple logic behind it?

Quote:
I could waffle along further in similar vein, but when it comes down to it, I'm just choosing the moves that I'm familiar with. Strangely (or otherwise?) I seem to do quite well that way, and nearly every time end up on one of Lizzie's blue spots or a second or third best spot.


Jaw dropping indeed.

Quote:
One thing I do not do is a tactical search beyond a mere glance. Also, I do not factor in sente and gote. This is another thing that I perhaps ought to have mentioned before. I have come to the conclusion (on the basis both of rational thought and observations with my program) that sente and gote don't matter to a bot and probably shouldn't matter to us. That's a big and provocative statement, I know, but I'm fairly sure of it. However, I'm not going to elaborate on it here. I just toss it out as a thought.


It's a big thought. I agree a bot doesn't think of sente or gote. It does in probabilities and game results. But when interpreting those, we must stick with such concepts until we've either become bot-like or the game has been solved, leaving no room for heuristics. Neither is likely to happen. Replacing all concepts with counting arguments is not inconceivable but it's indeed baffling to read this from the biggest enthusiast I've known of Japanese Go terminology amassed through the ages. You are sure you're not impersonating a bot aficionado to make a fool out of all of us?

(...)

Quote:
That said, what I noticed straightaway in the diagram above was the nicely laid out barmkin (the rough and ready enclosure around the 5-5-, 6-6, 7-7 etc points) in the northwest. Even without counting, I could see at once that Black has a strong preponderance of control over the A19/T1 diagonal, and the other diagonal is instantly visible as split 50/50. So, making the usual assumptions about pro games (e.g. that there have been no horrendous mistakes already), Black is comfortably in the lead. I have no idea by how much, but I would certainly prefer to be Black.


I have the feeling we can engineer similar positions where the same reasoning applies but the disposition of the stones is such that White is in the lead. I can't accept that all the heuristics we have developed (shape ...) have become worthless.

(...)

Quote:
So, if I am not offering an algorithm, what am I offering? Just exotic food for thought. I think the new nouvelle cuisine can be "fusion" food - a blend of AI and human ingredients. But you have to be your own chef.


I take this post and the additional comments as an account of an epiphany but it strikes me as too much too soon and too easy. I'm the first to learn from what AI seems to tell us but I'm skeptical of the seemingly casual reduction to a "preponderance of control" algorithm in certain areas which comes close to AI performance.

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Post #18 Posted: Thu Jul 23, 2020 10:00 am 
Oza

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Quote:
I take this post and the additional comments as an account of an epiphany but it strikes me as too much too soon and too easy. I'm the first to learn from what AI seems to tell us but I'm skeptical of the seemingly casual reduction to a "preponderance of control" algorithm in certain areas which comes close to AI performance.


I won't answer your other points, because I think I have addressed them already - except your question whether it was a recent discovery. Not recent, but originally embryonic and developed over a period of some months. The C# program is the only recent bit. The references to barmkins and so on are like icing sugar, and reflect whatever is going on in my mind at the moment. Barmkins came because I had been listening to a beautiful pipe tune that was turned into a song recently by a prominent tv personality. It was about an area I used to go rock climbing in and which is full of peel towers - and cows. (Search on Rothbury Hills and Alexander Armstrong if you want to hear it, but best of all prefer the pure pipe version by Kathryn Tickell.)

It's the ideas that matter not the imagery. That's just for entertainment, which I feel is still sorely needed during lockdown.

I have made plain that I'm as surprised as anybody at the results, and also that I don't understand it (though the diagonals and barmkins were, I think, a successful attempt to get a firm footing on the crags). I have also no idea how to distil and bottle what I have learnt, but am not going to make much effort in that regard either. (But just in case, I'm keeping my topography (the 14 areas and overlaps) under wraps :) )

What I hope to get out of it is what I hope to get out of most of my posts: to stimulate shared ideas from other people. In the case of abstract ideas about AI, the sort of posts I have enjoyed thus far have been from Bill, and to a lesser extent from uberdude, and, er, that's about it - though I think your recent post about 'reinforcement' for shimari deserves an honourable mention. In fact, with that and your post on Attack & Defence, you can take much of the blame for me posting now!

Far from being a spoof, my present posts are more yet another desperate but vain attempt to generate lively discussion here.

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Post #19 Posted: Thu Jul 23, 2020 10:29 am 
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Knotwilg wrote:
I agree a bot doesn't think of sente or gote. It does in probabilities and game results.


I beg to differ. True, as far as we can tell, the bots do not have concepts as we normally understand the term, or at least they cannot communicate them if they do. But they must have some understanding of sente and gote, or they could not play ko fights. Furthermore, as in the recent Attack and Defense problem, they often prefer to play kikashi (sente) before making a big play. OC, they don't say that's what they are doing, but that's what they do.

As for thinking in terms of probabilities and game results, well, that's how the programmers of the bots were thinking, and that is based, I suppose, on Monte Carlo Tree Search and reinforcement learning. We can't really conclude that that's how the bots are thinking, any more that we can conclude that humans are thinking in terms of neurotransmitters and spiking axons. :) Gödel, Escher, Bach delves into such questions.

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Post #20 Posted: Thu Jul 23, 2020 2:35 pm 
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John Fairbairn wrote:



The game is GoGoD 1680JQXG208. The great Shi Dingan commented on it. He criticised White 91, which was at A. He basically said it was ajikeshi and White was making his own future play uninteresting, and indeed the result was that White sealed off his side of the corner, and Black got a safe enough group. Shi recommended the cap at B.

I was intrigued by that because A looked fine to me, so I put the position in Lizzie, and was not surprised to see it favoured A. I continued through the game, feeling very smug until it dawned on me what Shi was pointing out. Suddenly B made a lot of sense. I'm not good enough to know whether it really is a better move, but I could see factors that I had overlooked before. First of all, Lizzie's opinion was entirely irrelevant. With group tax this is a different game.

Second, what I noticed as the game progressed was that Black easily joined up his weak top group to a group below, and for a time was even looking at joining up three groups. At 2 points per join, that's a huge difference. B would interfere with possible connections for as many as five Black groups (or six if you consider the cut at P8). This B is a move I regard as 'influencing' the centre big time, in this case.


For what it's worth, KataGo *does* handle group tax, but even with group tax enabled, it prefers A by a large margin (20% winrate, many points). If I look at the followup variations suggested, it seems like the issue is that the looser B, while strategically interesting, simply loses too much locally by making it too easy for black to settle using white's corner thinness. Well, easier by bot standards at least.

Some playing around with things reveals that although it doesn't change the judgment of this move much, group tax *does* affect KataGo's strategic choices quite significantly in some positions. I started another thread here with some examples: https://lifein19x19.com/viewtopic.php?f=15&t=17674

Bill Spight wrote:
Knotwilg wrote:
I agree a bot doesn't think of sente or gote. It does in probabilities and game results.


I beg to differ. True, as far as we can tell, the bots do not have concepts as we normally understand the term, or at least they cannot communicate them if they do. But they must have some understanding of sente and gote, or they could not play ko fights. Furthermore, as in the recent Attack and Defense problem, they often prefer to play kikashi (sente) before making a big play. OC, they don't say that's what they are doing, but that's what they do.

As for thinking in terms of probabilities and game results, well, that's how the programmers of the bots were thinking, and that is based, I suppsose, on Monte Carlo Tree Search and reinforcement learning. We can't really conclude that that's how the bots are thinking, any more that we can conclude that humans are thinking in terms of neurotransmitters and spiking axons. :) Gödel, Escher, Bach delves into such questions.


As a bot programmer, I mostly agree with Bill here. :)

Way back when I was initially playing with neural net move prediction (no self-play, just trying to predict pro moves), I found through some visualizations that the neural net had developed internal features that clearly corresponded to things like "ko" and "territorial control" and "incomplete borders", see here:
https://github.com/lightvector/GoNN#glo ... s-dec-2017

For "territorial control", the fascinating part was that the neural net was *not* trained to predict the outcome of the game, it was only ever shown pairs of (board position, location where the pro would move next). So in some sense, the net was not explicitly given any notion that this was a game with an actual goal, that areas could be owned or not, or that stones could live or die. Nonetheless, presumably it discovered on its own that summing up "control" of areas of the board, including correctly identifying when stones should not negate that control (due to being dead), correlated reliably with stylistic shifts in how pro players would play.

Buried somewhere in current nets, it's extremely likely there are channels or combinations of channels that activate according to or otherwise encode concepts that correspond loosely to what humans would call "sente vs gote", as well as finer judgments their relative urgency or threat potential, whether they are losing or gaining, and so on. Very likely sliced up and parameterized and blended with other concepts in ways that aren't the ways humans would, but still there nonetheless.


This post by lightvector was liked by: Bill Spight
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