Is this an empty triangle?

Uberdude · #1

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Over on Facebook I claimed that calling every occurrence of the 2×2 pattern of 3 stones of 1 colour and the other intersection empty an empty triangle was over simplistic, and a false positive on above example at edge of board where it would be illegal to fill in the empty intersection with a stone of the other colour. To me shapes are about function as well as form, or at least the pattern match needs to consider the intersections adjacent to the empty one. Curious what other people think, particularly John with his knowledge of Japanese terminology.

John Fairbairn · #2

At first I was surprised you were even having a discussion about this - or were you being trolled? Then realisation sank in. Far too many western go players are obsessed with definitions. and with such people common sense often goes out the window. (And I refuse to define the window, say where it is, what size it is and whether it was open or closed.) One particular hives-inducing remark for me is that proverb X is contradicted by proverb Y, therefore both proverbs are rubbish. There are many times when I believe there are more than one species of mankind on Earth. Some species have not yet evolved to master flexibility.

As to empty triangle, the usual Japanese term is akisankaku (literally empty triangle), but it comes up in other forms, such as akisan, or just sankaku (no emptiness there). There is also a synonym: shuusan (clump three). But strictly it is an abbreviation of dameakisankaku, and that is the important form. That one tells us that the triangle in question has an empty dame. The dame is a worthless point. A bad empty triangle is one surrounding a worthless point, and is bad for similar reasons that we try not to connect on a dame. The dotted stone in the diagram above surrounds a very worthy point - an eye.

Furthermore, the Japanese proverb referring to ETs is "An empty triangle is a SPECIMEN (mihon) of good shape." Which even to a rationalist must surely be very different from saying ALL ETs are bad.

It is true that as a first-pass heuristic we often start from the premise that an ET is bad, but then FLEXIBLE brains switch in, in some species.

The commonest example in Japanese sources of a case where an ET is good (i.e. a guzumi move) is the triangled move in the top of diagram below. Those of certain generation will recognise this as the sort of stuff we used to get spoon-fed to us in Go Review and the like, in the days when the Japanese thought we were only capable of playing 9-stone games.

But pros often provide exceptions that prove the rule, and on that I like is in the White triangled move lower right, which is a joseki variation suggested by Komatsu Hideki. There are TWO White ETS here, by the second, triangled one is especially good because it makes miai of A and B.

A more obtuse example is the one in the lower left, which became a joseki after Miyasaka Shinji played it against Go Seigen in 1932. This particular line was not the version he played, but the point was that Go was so impressed with it that he started playing it regularly (in this version). The Ishida joseki dictionary, I think, also calls it a "stylish result." The key feature is the five-stone clump called an umebachi, i.e. the cinquefoil crest of a plum blossom (which will soon be appearing outside my house!). A further significant point is that from this time the proverb "Umebachi wa angai sharete iru (The plum blossom looks unexpectedly beautiful) began to be used in the go press (along with a similar one, "Iwa yori katai umebachigata" (A plum blossom can be more solid than a rock). So a plum blossom proverb with two ETs contradicts one with one ET? Heaven forfend!

schrody · #3

I don't know what an official definition of the empty triangle is but I wouldn't call this an empty triangle. While this shape doesn't wrap around an opponent's stone it does wrap around and, consequently, make an eye so it's not empty (though I suppose this also depends on your definition of 'empty').

This also got me thinking about the interaction between shapes and the edges of the board. I usually describe the edges of the go board to beginners as walls that are already pre-built into the board. If we use this way of thinking, then your shape actually looks like this:

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So it's a square rather than a triangle. In the same way a one-point jump at the edge of the board acts similar to a tiger mouth in the middle of the board:

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I suppose this is another form vs. function debate and I'm more on the side of function here.

Edit: I wrote this before reading the Facebook discussion. Seems you've reached the same conclusion there.

dust · #4

Agree with Eduardo in the Facebook link.

The obsession with definitions is mostly harmless, though the risk is always that we'll end up with:

"Continued research into the theory of empty triangles at low temperature in the larger local endgame environment with one follow up, based on an early pioneering conjectural taxonomy" [Part 6]

Uberdude · #5

Thanks for the reply John.

John Fairbairn wrote:

At first I was surprised you were even having a discussion about this - or were you being trolled?

In case you didn't check the facebook thread, some player I don't know, presumably not that strong, posted this problem with the comment "Why you can't always avoid an empty triangle...." to which I replied "I wouldn't even think of this as an empty triangle, it's making an eye. The edge of the board means a simplistic empty triangle shape detector gives a false positive here.". So at this point I think I'm right it's not an empty triangle (according to my own fuzzy mental definition rather than any Robert Jasiek style attempt to create a precise formulation) because I know more about Go and terminology than the poster. But then Eduardo Lopez Herero (you probably know him), an Argentine 6d who is fluent in Japanese (I remember thinking it was cool he translated the Final Fantasy computer games to English when first meeting him in IGS chat many years ago) said it was an empty triangle I doubt myself as he is presumably familiar with Japanese terminology. Hence seeking your input.

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John Fairbairn wrote:

Far too many western go players are obsessed with definitions. and with such people common sense often goes out the window.

I was quite happy with my imprecise definition of "an empty triangle is whatever my brain with its deep and mysterious neural networks thinks is an empty triangle having played go and read books and seen/used the term for many years". So I think I'm more on the anti-definition side.

Quote:

Which even to a rationalist must surely be very different from saying ALL ETs are bad. It is true that as a first-pass heuristic we often start from the premise that an ET is bad, but then FLEXIBLE brains switch in, in some species.

Preaching to the choir! I am a big fan of the much maligned empty triangle, which I think many Western players take the proverb about them being bad far too broadly and it stunts their development to then not consider the many cases it is good. Why else would I play this empty triangle in a British championship title match?! ;-)

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kvasir · #6

Surely the joseki mentioned is like this, with no bad exchange at the "X" but sometimes black or white following up with a move at the "O" right away.

Click Here To Show Diagram Code: [go]$$Wc $$ | . . . , . . . . . , $$ | . . . . . . . . . . $$ | . . . 3 . . . . . . $$ | . . . . . . . . . . $$ | . . . . . . . . . . $$ | . . 2 . . . . . . . $$ | . . 9 6 . . . . . , $$ | . 7 4 1 8 . . . . . $$ | . . 5 0 . . . . . . $$ | . . . . . . . . . . $$ ---------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm11 $$ | . . . , . . . . . , $$ | . . . . . . . . . . $$ | . . . O . . . . . . $$ | . 5 . . . . . . . . $$ | . . 4 M . . . . . . $$ | . 3 X . 2 . . . . . $$ | . . O X . C . . . , $$ | . O 1 O X . . . . . $$ | . . O X . . . . . . $$ | . . . . . . . . . . $$ ---------------------[/go]

The Miyasaka Shinji vs. Go Seigen game is very instructive and I remember watching a lecture about it. Especially white's play is high quality according to the computer but he still loses because it is a no komi game.

Click Here To Show Diagram Code: [go]$$cm17 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 4 9 . . . . . . . . . . . . . . . | $$ | . 6 3 O 7 . . . . . . . . . O . . . . | $$ | . . 8 5 . . . . . , . . . . . , X . . | $$ | . . 1 . . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 2 . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . X X O O . . . O . . . . X , . . . | $$ | . . . . X O . . . . . . . . . X . . . | $$ | . . . . X . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm27 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O X 9 0 . . . . . . . . . . . . . | $$ | . O 1 O X . . . . . 3 . . . O . . . . | $$ | . . O X 6 5 . . . , . . . . . , X . . | $$ | . . X 8 2 . . . . . . . . . . X . . . | $$ | . . . 7 . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 4 . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . X X O O . . . O . . . . X , . . . | $$ | . . . . X O . . . . . . . . . X . . . | $$ | . . . . X . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm37 $$ --------------------------------------- $$ | . . . 1 . . . . . . . . . . . . . . . | $$ | . . O X O X . . . . . . . . . . . . . | $$ | . O O O X 2 . 3 . . O . . . O . . . . | $$ | . . O X X O . . . , . . . . . , X . . | $$ | . 4 X X X . . . . . . . . . . X . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . X X O O . . . O . . . . X , . . . | $$ | . . . . X O . . . . . . . . . X . . . | $$ | . . . . X . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

These days there is a real empty triangle in this joseki because the computer move is to connect. I find this especially interesting because my KataGo considers playing the triangle spot to remove the half-eye. With a half eye is this triangle half-empty or half-full?

Click Here To Show Diagram Code: [go]$$cm23 $$ --------------------------------------- $$ | . 4 . . . . . . . . . . . . . . . . . | $$ | 5 3 O . 6 . . . . . . . . . . . . . . | $$ | . O X O 2 . . 8 . . . . . . O . . . . | $$ | . 7 1 X . . . . . , . . . . . , X . . | $$ | . . X . . . . . . . . . . . . X . . . | $$ | . T . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . 9 . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . X X O O . . . O . . . . X , . . . | $$ | . . . . X O . . . . . . . . . X . . . | $$ | . . . . X . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

John Fairbairn · #7

Quote:

I find this especially interesting because my KataGo considers playing the triangle spot to remove the half-eye. With a half eye is this triangle half-empty or half-full?

Although strong players like Andrew do this automatically and so usually don't think to mention it, we should remember to factor in tewari. An ET may not be objectively good in its own right, but can be excusable if the opponent has made an offsetting inefficient move, e.g. connection on a dame point. So we get into bragging rights: my empty inefficiency is more efficient than your full inefficiency.

But since I have made the admonition not to be too dogmatic about terms, I would suggest Burns has already given us the right retort:

We are na fou, we're nae that fou, But just a drappie in our e'e! The cock may craw, the day may daw, And ay we'll taste the barley-bree!

Slàinte mhath!

(For the non-English speakers or those south of Watford, na(e) = not, fou = full = drunk, drappie = a wee drop, e'e = eye, daw = dawn, craw = crow, and bree = brew = whisky (nb whisky, not whiskey, which is Irish))

PS It's from a rousing song Willie Brewed a Peck o' Maut, which I imagine you can easily hear on Youtube. I had to learn measures such as peck, gill, and bushel, hundredweights and proper tons (not tonnes) when I was at school. But at least we still drive on the right side of the road, i.e. the left.

Uberdude · #8

John Fairbairn wrote:

Although strong players like Andrew do this automatically and so usually don't think to mention it, we should remember to factor in tewari. An ET may not be objectively good in its own right, but can be excusable if the opponent has made an offsetting inefficient move, e.g. connection on a dame point. So we get into bragging rights: my empty inefficiency is more efficient than your full inefficiency.

I have come to appreciate that plum blossom shape, having originally found it ugly. White's inside empty triangle is a darn sight more efficient than the black stone that used to be in the centre of the blossom now sitting in White's lid! It makes the corner 100% alive (so black connecting the 1 stone isn't sente) and also covers the 2nd line cutting point enabling white to safely jump out into the side. And the full triangles poking into Black's shape give some useful peeps/cuts which can turn black outside into quite the dango itself, but one without eyes.

John Fairbairn · #9

While preparing the new edition of Kamakura, I just came across an interesting related example of the error of being rigidly bound by definitions. It's the triangled move played by Kitami against Go Seigen. Let's make it a simple hide-and-seek problem. It's nothing to do with ETs but it is everything to do with shape. How would you comment on the move 54 shown?

Uberdude · **#10**

I presume it was played in response to the L7 peep. I would say that, if you do want to respond directly, then there are 3 choices, this L6, direct capture at k6, or A=k7. Each has pros and cons. Pro of l6 is it ensures k5 is a true eye and takes a liberty of L7, con is A is sente (how useful is that? somewhat, but not hugely as it is short of libs and doesn't allow black to seal white in so ends up a bit of a squeezing toothpaste if you tryl but it is at least a big ko threat). Pro of k6 is no more forcing moves for black, con is it's only half an eye as later black can l6 to falsify. k7 is not even half en eye as l6 is sente, so inferior in that regard, but pro is you get a stone at k7 which you might think is useful facing that way e.g. next k9 1 point jump is unconditionally connected rather than being a cuttable knight's move.

I would also say white could consider not obeying black's peep and considering a counter-attack with something like n8, inviting black to save the cutting stone and fight. Given the weakness of the resulting 2 separate groups I think that's a risky idea, but I don't much like answering it either. If the counter is a good idea, then probably black's peep was a mistake of bad timing: it's not like white was going to play around L7 anytime soon was it? Separating m6 from r8 looks like the most important strategic idea from a topological perspective here, and n8 is trying to connect them and treat the j7 stones lightly for now.

bernds · **#11**

Uberdude wrote:

I would also say white could consider not obeying black's peep and considering a counter-attack with something like n8, inviting black to save the cutting stone and fight.

Something you realize when you look at a number of games with KataGo is that it is often uninterested in making bad-shape connections, and this case is no different. It does not even consider the game move and wants to play something along the lines of

Click Here To Show Diagram Code: [go]$$Wc19 $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . O X . . . . X . . . . O . O . . | $$ | . . O . X . . . . . . . . X . X . O . | $$ | . . . O . . . . . . . . . . . . X O . | $$ | . . . . . . . . . . . . . . . X O X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . X . . . . . . . . 0 . . . . . . | $$ | . . . . . . . . . . . 8 7 . . . . . . | $$ | . . . . . . . . . . . X 3 . 6 . O . . | $$ | . . . . . . . . O . X 4 . 1 2 . . . . | $$ | . . . . . . . X O . . O 5 . 9 X . . . | $$ | . . O . O . . X O X O O X . . . . . . | $$ | . . . . O X . X O O X O . . . X . . . | $$ | . . . O X X . O X X X . . . . . . . . | $$ | . . . O . . . X . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

Threaten to connect to the stone on the right, threaten a ladder or a net in case Black does try to cut, and so on. I think this is something we could try to learn from the AI - at a minimum the attitude to look for something better. The game move does occur in some variations it gives, but usually fairly late into the sequence.

Knotwilg · **#12**

Somewhat unrelated, there's definitely a fixation with shape, substituting evaluation of a particular sequence or move with the recognition of a "good" shape (the table shape for example) or a "bad" shape (such as the empty triangle). It's one of my own bad habits acquired over the years, probably keeping me from getting stronger. Not easy to get rid off either after all these years.

The problem is that this bad habit is a perversion of an essential strength: visual pattern recognition. I'm rather happy to substitute 20 moves of reading with my knowledge of the L-group, door group, bent four, ... But indeed, recently I killed an L+1-group because I knew I could, while KataGo showed that doing so, allowing the opponent forcing moves on the outside, was worse than going out and letting live.

On the topic: any solid turn around a point that represents a captured stone or that delivers an eye regardless, is not an empty triangle. And even real empty triangles can be good. That goes almost without saying.

Uberdude · **#13**

bernds wrote:

Something you realize when you look at a number of games with KataGo is that it is often uninterested in making bad-shape connections, and this case is no different. It does not even consider the game move and wants to play something along the lines of

So Go Seigen was overplaying and got away with it!

kvasir · **#14**

I didn't understand why KataGo didn't cut but eventually it did when I checked. A plethora of empty triangles follows!

Click Here To Show Diagram Code: [go]$$Wc19 $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . O X . . . . X . . . . O . O . . | $$ | . . O . X . . . . . . . . X . X . O . | $$ | . . . O . . . . . . . . . . . . X O . | $$ | . . . . . . . . . . . . . . . X O X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . X . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . X . . . . O . . | $$ | . . . . . . . . O . X 4 3 1 . . . . . | $$ | . . . . . . . X O . . O 2 . . X . . . | $$ | . . O . O . . X O X O O X 6 . . . . . | $$ | . . . . O X . X O O X O 5 . . X . . . | $$ | . . . O X X . O X X X . . . . 7 . . . | $$ | . . . O . . . X . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

jlt · **#15**

An easier example of a good empty triangle that I missed in one of my kyu games. The experience was so traumatic that I still remember it from Feb 2021.

Click Here To Show Diagram Code: [go]$$Bc Black to play $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X O . . . . . X O O . . | $$ | . X X X . X X O O . . . . O X X O . . | $$ | . . O O O O O X . , . . . X . X O O . | $$ | . . . . . . . . . . . . . . . . X O . | $$ | . . . . . . . . . . . . . . . . X X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O O . . . . . . . . . . . . . . . | $$ | . . O X . . X . . , . . . . . , . . . | $$ | . . X X . X . . . . O . . . . . O . . | $$ | . . . . O O X X X O . . . . . X . . . | $$ | . . . . . . . O O X O . . . . X O . . | $$ | . . . . . . O . . X O . . . . X O . . | $$ | . . . O . . . . X . O . . . . . O . . | $$ | . . O , . O O X . , . . . . X , . . . | $$ | . X . W X X O X . . O . X . . X . . . | $$ | . . X . . . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Knotwilg · **#16**

jlt wrote:

Click Here To Show Diagram Code: [go]$$B $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O O . . . . . . . . . . . . . . . | $$ | . . O X . . X . . , . . . . . , . . . | $$ | . . X X . X . . . . O . . . . . O . . | $$ | . . . . O O X X X O . . . . . X . . . | $$ | . . . . . . . O O X O . . . . X O . . | $$ | . . . . . . O . . X O . . . . X O . . | $$ | . . . O . . . . X . O . . . . . O . . | $$ | . . O , . O O X . , . . . . X , . . . | $$ | . X . W B B O X . . O . X . . X . . . | $$ | . . X . 1 . X . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

A very good example of something that really falls on the border of being an empty triangle.

Knotwilg · **#17**

Click Here To Show Diagram Code: [go]$$ Black to play $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . O O X . . . . . . . . . . . | $$ | . . O O . O . O X . . X . X . . . . . | $$ | . . O X . O . O . X X O . X . X . . . | $$ | . . O X . X O . O O X . O O . . X X . | $$ | . . X X . . O . X O X . . . . O O . . | $$ | . . . . . . . . . X . . . . . . . . . | $$ | . . . . . . O . . . . . . O X . X O . | $$ | . . . . . . . . . . . . . . . X O 2 . | $$ | . . . X . . . . . , . . . . O X O O 1 | $$ | . . . . . . . . . . . . . . . O X X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . X X . . . . X . . . . . . . . . . | $$ | . . O X . . X . . . . . . . . X . . . | $$ | . . O , . . . O . , . . O X . , X . . | $$ | . . . O . O . . . . . . O . O . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

jlt · **#18**

Click Here To Show Diagram Code: [go]$$ $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . O O X . . . . . . . . . . . | $$ | . . O O . O . O X . . X . X . . . . . | $$ | . . O X . O . O . X X O . X . X . . . | $$ | . . O X . X O . O O X . O O . . X X . | $$ | . . X X . . O . X O X . . . . O O . . | $$ | . . . . . . . . . X . . . . . . . . . | $$ | . . . . . . O . . . . . . O X 3 X O . | $$ | . . . . . . . . . . . . . . . X O 2 . | $$ | . . . X . . . . . , . . . . O X O O 1 | $$ | . . . . . . . . . . . . . . . O X X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . X X . . . . X . . . . . . . . . . | $$ | . . O X . . X . . . . . . . . X . . . | $$ | . . O , . . . O . , . . O X . , X . . | $$ | . . . O . O . . . . . . O . O . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Still, the fight doesn't look easy after that.

dhu163 · **#19**

Back to Uberdude's original example, my graph theory-ish explanation for why an empty triangle is good shape here is:

1) The eyespace is already "empty triangle like", being enclosed on all sides. Playing in the middle only makes a few more empty triangles, but the shape was already a bit overconcentrated.
2) The group is almost dead, and that is when one move can have a very large value.

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From the perspective of nakade vital points, one move is worth so much when it is adjacent to all the eyespace. Then when either side plays there, it will shift control on all the eyespace. When white has no back-up eye, turning one eye into two is important.

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(Edit:20220213, building on hyperpape)
A healthy group with space around doesn't have to worry about making two eyes just yet and instead needs to ensure connection (to save dangling dragons) and successfully blocking off large territories.

Empty triangles are a valid criticism for both of these points :
1) empty triangles are over connected
2) empty triangles are slow to surround territory.

However here we have a life and death problem where a group is on the boundary of life and death. A different sort of rulebook (NP style) comes into play here, when a large group is surrounded and urgently needs to make eyes locally.

These situations are harder to recognise than others, can require seemingly unlimited reading, and yet can also be of critical importance. Hence why tsumego is valuable for building strength, even if it can feel like squeezing your brain into a fractured glass pane.

hyperpape · **#20**

One conciliatory option is to say "it is an empty triangle, but it would be unhelpful to mention it." In such cases, competent speakers may disagree, as there's very little practical difference between "it's true but not worth mentioning" and "it's false." For more background on why one might say that, here's a great introduction to a bit of philosophy: https://aeon.co/ideas/what-we-say-vs-wh ... mplicature.

Is this an empty triangle?

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