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.
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. 