As to how many playouts are enough, people with weak hardware might deceive themselves by misinterpreting early stability as sufficient condidence. If some almost correct move is good enough for a purpose, this can be fine but also result in wild AI play. If one wants correct moves (such as for finding josekis), forget about anything below 100,000 playouts because AI changes its preference too often until then and early ghosts frequently turn out to be real alternatives! So now, for joseki study, I presume 100,000+ per top candidate. At least for the top-most but hetter for each candidate seriously competing for the top.

One can be confident to have enough playouts if stability in top candidate selection has been reached for quite some time of increasing numbers of playouts. The more difficult the position and the closer the next candidates the longer search must proceed! Furthermore, the most difficult josekis have their best move appearing only after ca. 5 million playouts per top move! So for such josekis, use at least as many playouts per move!

There are rare cases in the most difficult josekis. A few such cases within half a year of full time AI study. Cases for which AI changes its mind after 10, 50 (so far once) or 90 (once) million moves for the top candidate. Or, we can imagine, after an eternity. One must be pragmatic but also cautious whenever it is difficult and the candidates are rather close in values. I was motivated to wait for the RAM to fill when previous values contradicted the decision-making. Luckily, my 64GB RAM has always been large enough to dissolve contradictions. 32GB would have been too small.

It's an interesting question.

My answer will be too vague for some, but I consider "joseki" to be a set of variations on a certain starting pattern, where one or more are considered to be "best for both" assuming alternate play, others are probably still acceptable and other variations are considered mistakes. Aspects for evaluation include: territory, influence, "strength" (of that influence), aji and sente. Tenuki variations are a little different: if one player has invested two stones more than the opponent, the result is expected to be lopsided but exactly how lopsided is not easy to judge. Since one player decided to play elsewhere the whole board is probably more relevant to the evaluation.

There is a notion of a significant drop in the local temperature by the end of what is considered joseki, so playing elsewhere at that point is more likely. We usually speak of "follow-ups" from that point onwards. With AI we have seen that tenuki can happen very early (depending ...). Since local play can resume later, often as if the play elsewhere was only incidental, I consider that to be one and the same joseki (variation). It is useful to mark the moves where tenuki is more likely / less harmful.

In some cases tenuki results in the position reverting to another joseki. A trivial example is 3-5, 4-3 tenuki = 3-4, 5-3 continued.

It can be unclear but the word "joseki" at least is more specific than "standard sequence". It is also one less syllable and lot fewer stop sounds (when airflow in the mouth is completely obstructed), it is therefore easier to say. It also allows for "non-standard joseki", "joseki sequence" and "non-standard joseki sequence", were as "non-standard standard sequence sequence" would be unusable.

Maybe joseki only means the kind of diagrams you'd find in a joseki book?

That said, you are right about the tenuki. The tenuki at , and are all common. I believe pros have played away at most of the time since this joseki became common, there are other moves for white here. Tenuki at is now common. I believe tenuki at some of the other moves are rare in pro games, for the reason that they tend to anticipate it and time their play to make it more awkward to tenuki. Pros are also averse to aji-keshi. Then is one place where it is possible to tenuki, white has two continuations here, which are less urgent than the previous moves. I'd expect pros to try to time their move here while considering the possibility that is tenuki.

Click Here To Show Diagram Code

[go]$$Bm6 Simple but lot of tenuki in the way of reaching this diagram.
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . 1 . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . 3 O . 2 . . . . .
$$ | . . 5 4 . . . . . . .
$$ | . . X 6 X . . . . . .
$$ | . . 7 8 . O . . . , .
$$ | . . . O . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]

Variations like the one in the OP would seem farfetched for some players and reasonable to others, dependent on if they are likely to follow the moves up to that point. It is a lot of moves in this case but it is the kind of thing I'd expect to find in multi-volume joseki books.

Interesting.
Assume a joseki begin at temperature T on the board. Does it make sense to say:
1) after the last move of the joseki the local temperature is not higher than T
2) after each other moves of the joseki the local temperature cannot be smaller than T
BTW can we consider that in the first phase of the game the temperature of the all board is always higher than 12?

Not always. Mistakes can raise the temperature.

OC but what is your point? My two points are not expected to be a definition of a joseki but only two caracteristics.
For a definition of a joseki I guess you will add some other points like that all moves should be considered more or less good moves.

I'm not sure this is strictly true, but I'm not well versed enough in these things to be sure. Consider the diagram below for discussion:

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . 6 . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . 2 . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . 4 . 1 . . . . . , .
$$ | . . 5 . . 3 . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]

Here's a fairly standard corner position that would certainly have been called a joseki in the past. I'm not sure any of moves 2, 3 or 4 are strictly speaking sente; there are certainly examples in pro play where tenuki has been played. Doesn't that mean that the local temperature can be lower than the rest of the board? Of all the moves here, I think that 5 is the only one that almost certainly raises the temperature enough locally to demand a response.

For me even after black can also play tenuki.
BTW where is finished the joseki? After to it is quite common to see the folllow-up here after:

Click Here To Show Diagram Code

[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . 6 . . . . . . . .
$$ | . . 8 7 . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . 2 9 . . . . . . .
$$ | . . 0 . . . . . . . .
$$ | . 4 . 1 . . . . . , .
$$ | . . 5 . . 3 . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]

Indeed, I think this is the question. I would have put it at the end of my diagram, with your diagram as one option for a follow up.

What I take from this is that "a joseki" has a number of branch points where tenuki is viable, which lines up with your point #1 about the local temperature cooling below competing points elsewhere on the board. Your point #2 is less clear, however. Within our reference joseki it looks like temperatures can drop below the temperature elsewhere on the board before a line of play starts that heats things back up again and requires a response.

Unless my understanding of temperature is incorrect. In either my reference diagram or yours, do you think they would quality as josekis, and does the local temperature always stay higher than the board's global starting temperature?

Strictly speaking I cannot answer your question about temperature because the notion of temperature has been defined only for endgame positions with various independant areas. Typically in the fuseki a joseki in one corner have an impact on the other three corners => no indepenance of the areas.

Anyway we can try to define what could be a temperature of a fuseki position. Assume you have a magic fonction (katago?) which gives you the result of a game starting from a given position P : result = magic(P)
1) you use your magic function to evaluate position P : magic(P)
2) you use your magic function to evaluate the position P followed by a pass : magic (P + pass)
by definition you say that the temperature of position P is magic(P) - magic(P + pass)
Assume magic(empty board) = 7 then magic(empty board + pass) = -7 and the temperature of the emptby board is 14.

Using this approach you can define the value of a move M in a position P by:
value of move M = magic(P + M) - magic(P + pass)
Finally you can define the temperature of a local area (a corner?) by max(value of move M) where M is in the considered area.

What about my two following points
1) after the last move of the joseki the local temperature is not higher than T
2) after each other moves of the joseki the local temperature cannot be smaller than T

The first point indicate that after a joseki you generaly have a pause before returning in the correcponding corner.
The second point tells you that all the sequence of the joseki is in general playable without any tenuki
Strictly speaking the two points above are not correct because a joseki in a corner has an impact on the temperature of the other corners so you have only to take the general idea.

Pwaldron, I hope these explanations will help you but the temperature notion is not an easy one.

Would it be helpful to define

A = an area on the board that holds position P
T_A = "temperature of P in area A" = "max(value of move M in A)" where magic() is applied to the whole board in the actual game
LT_A = "localized temperature of P in area A" = "max(value of move M in A)" where magic() is applied to a board that is empty outside A

Perhaps we should have a separate thread on 'temperature'? I've never been able to wrap my head round it as a non-mathematician., and the definition of temperature itself seems to depend on the definition of other related concepts such as 'cooling', 'chilling',and 'short games'.

Is there a way to translate it into words that doesn't depend on CGT mathematical theory?

Agree on a separate thread. As for your question, Gerard's explanation is very clear, even though it uses mathematical notation. I would argue because it uses mathematical notation, at the risk of being pedantic. Although we have made great progress since algebraic notation has replaced the verbose explanations prior, it seems math/algebra is putting many people off, so let me try rewording Gerard's approach:

1) suppose you have a way of calculating the score resulting from any position; take KataGo's scoring as a substitute (math: magic(P))
2) the temperature of the board, being how "hot" is it, how bad would it be not to play the best move on the board, is the difference between the result from that position when black plays next or white plays next (math: T = magic(P) - magic(P+pass))

At the end of a game, when only dame remain, with territory scoring, the temperature is 0. There's no difference between a black or a white move next.
At the start of the game, assuming we know that perfect komi is 7, the difference between black and a white move first is twice the komi, so the temperature is 14.

Intuitively you might expect temperature to slowly decrease from 14 to 0. But that is obviously not the case. At the dame stage, when a chain of 10 stones is in atari, the difference between playing and passing is 20 points.

So far, so good.

The reason why "temperature" is more difficult than this is 1) we don't have that magic scoring function, but ok we have KataGo as a substitute 2) the local effect of a move/pass must be weighed against moves elsewhere 3) most importantly, local outcomes influence the whole board.

I'll create the thread.

You and I are in the same boat. As a heuristic, I take the temperature concept to be roughly how many points I would take to pass instead of playing a move.

That's exactly what it is, conceptually. What it is exactly, is the whole discussion here.

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X O . O . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X O X . . . . . . . . . . . . . . |
$$ | . . b X a O . . . , . . . . . X . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

For these swapped adjacent corners, the initial choice is extraordinarily one-sided.

a = 44.3% -0.6, correct, 25.6 million playouts
b = 60.7% 1.4, mistake, 7.2k playouts

Next, I have analysed the consequence of the mistake.

Click Here To Show Diagram Code

[go]$$W initial mistake and reply
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X O . O . . . . . . . . . . . . . |
$$ | . . X O . . . . . . . . . . . . . . . |
$$ | . . X O X . . . . . . . . . . . . . . |
$$ | . . 1 X 2 O . . . , . . . . . X . . . |
$$ | . . b O a . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

After a few million playouts, values were similar to the final values. Then move b became increasingly better and was about to surpass move a at the intermediate values. However, a few million playouts later, again values became and then remained similar to the final values. Therefore, the final values have become stable. With the many playouts of the final values, they have a very high confidence.

Intermediate values

a = 61.6% 1.2, correct, 11.5 million playouts
b = 61.6% 1.3, very good, 3.6 million playouts

Final values

a = 62.2% 1.3, correct, 70.1 million playouts
b = 64.2% 1.6, mistake, 11.3 million playouts

Click Here To Show Diagram Code

[go]$$W correct move continuation
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . a 8 . . . . , . . . . . , . . . |
$$ | . . . X 7 9 . . . . . . . . . . . . . |
$$ | . . 6 5 . . . . d . . . . . . . . . . |
$$ | . . X O . O . . . . . . . . . . . . . |
$$ | . . X O . . c . . . . . . . . . . . . |
$$ | . . X O X 2 . . . . . . . . . . . . . |
$$ | . . O X X O 4 . . , . . . . . X . . . |
$$ | . 3 . O 1 b e . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Close to 15 million playouts for White 1 were needed to also forsee Black 8 as correct follow-up.

Click Here To Show Diagram Code

[go]$$W correct continuation after the mistake
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |
$$ | . . X O . O . . . . . . . . . . . . . |
$$ | . c X O . 3 . . . . . . . . . . . . . |
$$ | . b X O X 5 . . . . . . . . . . . . . |
$$ | . . O X X O . . . , . . . . . X . . . |
$$ | . e 1 O 4 7 . . . . . . . . . . . . . |
$$ | . 8 9 . 6 a d . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

I know you do not like mistakes. (Nor do I;) ) However, Katago's magic does make mistakes so your magic move value or temperatures can become negative:)

CGT itself has provided a means to leave the nasty parts of CGT by ignoring infinitesimals by defining some higher level values, such as temperature, modulo infinitesimals. I have applied this in [22] and thereafter happily used local move values, counts, gains, only global temperature (simply the largest move value on the rest of the board) by good, old, easy school mathematics for practical application and in theorems and their proofs.

I recall (very possibly incorrectly) by Richard Feynman in which he said that if you had two theories, A and B, that produced the same outcomes, then it could be mathematically proven that the two theories were equivalent even if their make-up was radically different. As I recall, for the purpose of the exposition, he described A as a purely mathematical theory full of difficult calculations and hard to work with, but at least it proved theory A. Theory was a verbose one but gave the same outcome and so was equivalent to B, but if theory A had not existed we could not be sure that theory B could be proved.

But, once theory A did exist, that made theory B the more useful one because it was much easier to use in practice. I think Feynman also said that some topics in theoretical physics had up to seven concurrent theories, and each had an appeal ("psychologically" I think he said) for a different type of person.

The context (maybe even the title of the lecture) was the difference between knowing and understanding.

Let us make a not entirely safe but perhaps safe enough assumption that Katago is providing the equivalent of a mathematical scoring function and is thus the equivalent of theory A. If, for our amateur purposes, we can further assume that pros have got close enough to katago's overall strength on a "good enough" basis with their theories B and so on, we can deduce that these human theories are in fact equivalent (near enough) to theory A. We all seem to agree that theory A in go is unusable by humans for the simple reason we don't know what the calculations are (and of course we are making a possibly incorrect assumption in even assuming that katago's calculations are correct, but let's work on a "near enough" basis). So, that leaves only theories B and so on as ones usable by humans in practice.

It therefore seems to me that the real argument is not over whether the "purely mathematical" theory A is better than the others, but rather which of B, C, D, E, F.... is better for individual humans. The choice is a psychological one (to use Feynman's word) and is based on the make-up, training and experience of each individual human. If person X chooses to use temperature or some other form of numbers, it does not mean his theory B is better or can expect better results than a person who, according to theory Q, sacrifices goats on the altar at Stonehenge and prays to the gods - and vice versa, of course - so long as they get outcomes that are near enough the same. Each theory is just more convenient for different individuals.

It then seems to me that, in terms of application, katago is not actually a substitute for anything. It has done its job by acting as theory A, confirming that theories B, C, D, E, F are all near enough equivalent.

I would concede that theories B and so on have recently been corrected and refined in the light of katago's theory A. But that is surely not much different from physicists correcting and refining Newton's laws on the path to relativity and beyond. And we still use Newton's laws usefully in everyday life, do we not?

And that's just for amateurs. I suspect pros would be even more confident that A and B+ are near enough equivalent.

Much of what you, John, write in your message about theories makes sense, except for the following:

- Besides AI theory and professional player theory there are also further theories, such as those of researchers in go theory.

- You underestimate the impact of Katago on go theory. It does not just correct a few bits here and there but its extensive use has the potential to develop go theory very much.