When is 3-3 alive?

Inspired by @bugcat’s OGS proverb and especially from playing a lot of 9x9, I’ve become interested in whether a lone stone at 3-3 can make territory or be killed, depending on nearby threats. For example, I would expect to kill Black in this position:

image

If Black plays first at the marked point instead, his stones will live. Often the outcome seems obvious (to me at 8 kyu), but sometimes it’s unclear, so I was thinking that a good way to get stronger would be to systematically learn a bunch of the cases.

I haven’t found any catalogs of these situations online, so I thought about trying to analyze them with AI. I downloaded Lizzie and set up this framework where White wins by only 2.5 points if black fails to invade the upper-left corner:

This means if Black can secure even a tiny bit of territory there, he can win. There’s also nothing else interesting to do anywhere else on the board, which should help focus attention on that corner. Note that I don’t know what I’m doing. Is there a more straightforward way to approach corner problems with AI?

Anyway, with this setup, KataGo correctly evaluates the position above as hopeless for Black:

image

But with one of the white stones moved two steps away, the game swings completely in Black’s favor:

one_point_three_point

What surprises me is that with the stone at the intermediate point, KataGo is undecided on the result:

one_point_two_point

Leela Zero gives a similarly inconclusive result, ~70% favorable to black. Even after a million playouts it’s apparently unclear whether that stone is alive or dead. Is this real or just an artifact of my contrived setup? Some of the playouts do seem to involve ladder-like formations:

So maybe the AI is not very good at working with such thick and distant walls? Or is this actually an unsolved position? Again, I don’t know what I’m doing here. Is this interesting at all? Anyone have any pointers or other feedback?

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In many cases it’s impossible to live with such thick walls (even when they are as distant as here). I don’t think it’s a weakness of AI that they see no way to live here.

But situations like these are pretty rare in real games, so why bother to accurately determine in which cases black can or can’t live?

A thick wall on the 10th line is completely different to a 9x9 board edge.

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https://senseis.xmp.net/?BiggestCorner

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I find this type of question quite interesting, but as gennan points out it’s not very applicable to real games, since the global position affects the local one much more than one might think!

But who cares about the usefulness of it, this is an interesting theoretical question: which shapes are possible to live inside, and which are not? Here is some discussion that happened on senseis library many years ago: https://senseis.xmp.net/?BiggestCorner (lol, @teapoweredrobot beat me to this link while I was still writing this :stuck_out_tongue:)

Determining the status can be extremely complicated (after all, we are essentially trying to “solve” go in a special case). So a formal proof for if a big corner can be invaded might be unfeasible for now, but with AI help we could get some strong evidence.

So to start with, can we try to settle the question “what’s the biggest empty corner square that is still secure territory?”. There should be a single well-defined answer to this, and presumably it is the same in all major rule-sets.

After that we could also look at rectangular corner shapes, and see how many of them we can classify somewhat confidently. I think this would be a fun thing to do as a team effort here on the forums!

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Sorry I was lazy (but also not clever enough to explain more)
I might add that the interesting question from my point of view is to understand when a 3-3 works or not as the local position differs and critically as the outside position changes. I’m not explaining very well and can’t do diagrams at the moment but sometimes one thinks of some kind of enclosure are pretty solid territory but then as the outside situation evolves it becomes invadeable or reduceable…

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Setting up a test board for an 8x8-corner actually works out very nicely! With 7.5 komi white is winning by half a point on this board:


With just a few thousand playouts KataGo really can’t tell if a black invasion should live or die. Wouldn’t it be great if it turned out that 2-2 lived and 3-3 died? :smile:

(before I do more playouts, I’ll probably add some more black stones in the upper right, just to ensure that there are no non-local ko threats)

Update: 100k playouts


Leaning towards death, but still unclear.

Almost all the playouts went into these first two moves, after which there’s a lot more branching:

325k playouts after c3-d2


Winrate is not quite approaching 0 yet, but all of the main variations seem to end in death.

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Someone has to train AI which goal is to save or capture marked stone instead of winning a game.
LZ or Kata certainly ignores some important points in so strange situation and wastes a lot of power on useless ones.

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Might be a stupid question, but:
Does AI compute winning? Simply winning? Would it make a difference if it was told to win by X points (as in, that whole corner needs to be dead/ this territory needs to be this big etc)?

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It seems like a good starting point would be to know if the stone lives or dies on a large, otherwise empty board. Then, if you know how that goes, you can try to judge the effect of additional nearby stones. I’d be happy to get rid of the white wall, but without it I don’t know how to discourage black from playing away from the corner.

If there is a position that depends critically on the details of such a distant wall, that would be interesting too!

neural network knows patterns that are usually good to win a game.
neural network doesn’t know that her purpose is to win a game.
neural network learned to kill and save stones “accidentally
other parts of AI choose from what neural network suggests

So ( neural network that will be trained in order to “capture stones” will be much better specialist at capturing stones ) than ( neural network that was trained in order to “win a game”. )

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Indeed, one could consider doing something similar like this experiment (where KataGo was trained specifically to understand Igo Hatsuyoron 120), and that would certainly yield better results than throwing normal KataGo in such an unfamiliar position.

But the positions here are relatively much more normal than Igo Hatsuyoron 120 I would say, so KataGo is playing very strong moves even without any specific training. Of course, it will never be any good at solving a position, that would require some completely different program.

So I think it is an interesting challenge for us humans to get as close as we can to correct answers on which corner sizes are invade-able, with the limited tools we already have available today. Instead of having some oracle which just tells us a yes/no answer for each shape, we have a super-strong player which gives us plausible sequences, and we have to try to interpret those results for ourselves, probably discovering some really cool variations along the way :slight_smile:

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I guess tsumego solver may proof that 3-3 can’t survive in some too small boxes. I don’t know with how big box they can work with.

KataGo seems quite confident about living inside a 9x9 area!

So a first working hypothesis is that 8x8 is secure, 9x9 is invadable.

How about 8x9 then?


Could go either way! Isn’t it cool that 2-3 is the most explored after 15k playouts?

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How do we read these analysis diagrams?

What does KataGo and/or pros say about the shape game?

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The most meaningful numbers here are the winning percentages, so the numbers 61.4 and 52.2 in this image:


If white were completely certain of living with the 3-3 invasion, that 61.4 would be a 100.0. Of course just looking at the numbers doesn’t give very much information, the fun part is looking at the different sequences it is thinking about. I just wanted to share the preliminary results since I got excited, I’ll make a higher-effort post with variations another day :slight_smile:

I’ve heard different strong players have wildly different opinions ^^ It would be very cool to get KataGo’s opinion, but I think that will be a lot more difficult than asking it about these corners. In my experience it doesn’t handle huge komi too well, so it’s not so easy to even set up the shape game for it. And then the game itself is of course much harder since the open area is so much bigger than here, and the strategy involved might be even further removed from what it has seen in training. But if anyone can manage to set it up it would be very interesting.

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I think these are all very distinct questions / research topics:

  1. how strong does a moyo need to be to prevent a successful invasion?
  2. what is the status of different “wall games”?
  3. how can KataGo be tricked into solving tsumego problems?
  4. will results for question 2 be helpful to answer question 1?

Mixing all these questions together is posing an ambiguous question IMO, so expect to get ambiguous results. KataGo is not like a strong human player (or some kind of go oracle) that can give a good answer to all kinds of questions.
So I think you need to clearly determine what you’re looking for first and then try to find a good method to tease meaningful answers from KataGo.

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I’m not very interested in the “wall games” and would just like to develop better intuition about whether a stone at 3-3 is alive or not, when it comes up in real games. I suppose that if Black dies, it’s hard to know whether the wall played a role, but if Black can live, he would probably also survive on an empty board.

Considering this discussion about how it’s only barely possible to live within a 9x9 corner, I guess I need to weaken the wall. And it turns out that moving the wall out by 2 points changes things a lot! Black can now survive in the case that I thought was hopeless:

I guess I should have known better, since this pattern is in the joseki database. Interestingly, placing one additional white stone all the way out at 7-7 is enough to make KataGo think it’s a fair fight:

image

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I think you are asking KataGo the wrong questions.

None of the joseki in the Joseki Dictionary will make sense in a “wall” position. A wall like that is a game changer.

So if you’re not interested in “wall” games and you just want to learn about corner status in normal game situations, I think you’d better forget about experimenting with “wall” positions. It’s a completely different rabbit hole.

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I’d like to give an analogy, in case you know a bit about chess:

Suppose I try to use AI to investigate some chess opening, and I come up with the idea of replacing all black pawns by black rooks, before I start interrogating the AI about the opening under investigation. That may be fun and perhaps even interesting for chess philosophers. But whatever results I get, will most likely not translate well to a normal chess game with that opening.

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I don’t think they’re as unrelated as are being made out though, it’s still the same board, the same corner, the same game at the end of the day.

The thick wall invasions (lets say) just allow the attacker to play more aggressively than normal, which they could still do on a normal board without the wall up to a point.

So one could try out the walled sequences on an empty board to see what goes wrong with them.

In some cases the wall might let stones escape on the first line that couldn’t otherwise, or similarly it might just make the centre too small when escape is usually the option to really aggressive attacks.

In the image is there not still a ko if Black plays the 98% move? I don’t really understand moves 18 or 28 either, but I’m not looking at it with katago.

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