Hello,

When I studied in Korea I solved an endgame book and at that time my teacher told me this move in A is less than 4 but more than 3. I am reading robert jasiek's books and when I use this methode I found 1⅔ pt for this move in A. Am I right?

I think you cut off too much on the right to surely say.

Note that this would be consistent with your korean teachers using »deiri« counting (swing) but Robert using »miai« counting (difference from average expectation).

_________________
A good system naturally covers all corner cases without further effort.

Why was it again that a seemingly handful of Western amateurs promote the miai method while the great majority of Go players everywhere use the delta method?

There are both Western and Eastern, amateur and professional players that use traditional ("delta") and / or modern ("miai") endgame theory.

Both methods have their uses but traditional endgame theory is almost only useful for some of the most basic decisions while modern endgame theory can be used for all decisions.

If easily available teaching (verbal, books, videos) and talk is a correct indication, traditional endgame theory is still more popular. Neglecting almost all endgame theory beyond some of the most basic decisions is also still more popular.

People understanding more of endgame theory than only some of the most basic decisions promote modern endgame theory to enable all decisions and avoid almost all mistakes. - Players neglecting endgame theory beyond some of the most basic decisions prefer traditional endgame theory because they are too lazy to improve knowledge of endgame theory significantly beyond the means they already know. People only teaching traditional endgame theory tend to make frequent mistakes in evaluation, characterisation of types, move order and duration of correct local play.

This presumably a rhetorical question, but I'd very much like to know the answer myself. O Meien seems to kick against deiri and claims pros in China (by which he may mean Taiwan) all do likewise. But he shies away from calling his own (Chinese) method miai counting. He says 'absolute counting'. Is that really different?

If anyone is prepared to give an answer, I'd prefer it in English and not numberese.

Oh, while we are (supposedly) on the topic of the endgame. I came across a piece of text in a book about Hikaru no Go a couple of days ago which I will use as part of my long-running campaign to get people to say boundary play instead of endgame. It said:

陣地の境界線をはっきりさせるために石を置いていく。これをヨセとおうぞ。

DeepL gives this as : "Stones are placed on the ground to demarcate the boundaries of the camp. This is called yose."

I would give it as: "When we put down stones to clarify the boundary lines of territories, we call this yose." (For the ambiguity hunters, we know its stoneS because of the repetition implied in いく.)

But, either way, "endgame" is conspicuous by its absence.

AFAIK, miai counting, absolute counting and modern endgame theory are all just different names for the same study field.

"Endgame" includes boundary plays during the opening, middle game and endgame. "Boundary play" occurs during the opening, middle game and endgame.

So is 1 2/3 is correct ?

Thanks. I have always wanted to assume that, but Bill Spight always gave me the impression he demurred. And as for O Meien's new term, well I suppose he had a book to sell.



Not to me. If I order a steak I don't expect to get a hamburger.

If you want to argue that the endgame (proper) includes more than the yose, i.e. the boundary plays, I'm fine with that, but it's not a new idea. The Japanese atsui covers many of the other aspects, and timing is also an old big topic. Then we can add kimari to the mix, etc etc.

However, the answer I'm looking for is to the question of why deiri has been the favoured medium in Japan when they were well aware of miai counting. The best explanation I've come up with is that they are both accountancy terms but deiri accounting is more usual (easier?) in real life, and the same attitude just carried over into go. But that's just my own speculation.

Within modern endgame theory, there are different approaches, such as without or with combinatorial game theory, which is like mechanics without or with considering each elementary particle separately:) Bill might have referred to such advanced study. From the practical point of view, the infinitesemal differences can often be ignored.

Maybe a rhetorical question in the sense of creating dramatic effect but not in the sense of making a point. I am also interested in the "why" because we seem to have people adopting the method and the notation, especially in this forum and on sensei's.

I think many pros might just count the end positions in their head, count the difference between positions and basically do dead reckoning (I mean not use any recognizable method). They also seem to be able to switch gear easily and apply different methods. As far as I can tell, pros that do count endgame moves (or teach how to do it) use what one might call the "2x miai counting" because the values are doubled (for gote moves) and they certainly take into account how many moves are played, what is sente and so on. It is possible that Chinese pros, who use half counting (or how to call it), may use same values as miai counting -- I don't really know but I assume they have the half count in mind when the game is about finished.

I wasn't going to write so much, I was just trying to start some discussion. There are so many things that could be said about endgame theory really. I am not taking a firm side, but it seems to cause enough confusion to say -1.25 instead of 2.5 gote for white that you rarely see people do the former. At least that is my experience.

I think so (assuming no further relevant stones to the right), but I'm not an expert in such exact values.

However »more than 3 but less than 4« is also correct (using a different, also popular, counting method, which generally gives about double the numeric value).

Sorry for the derailing discussion.

_________________
A good system naturally covers all corner cases without further effort.

Thank you very much. Actually is it also interesting^^
I wasn't sure about the value so thank you.

Click Here To Show Diagram Code

[go]$$B initial position
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | . X X X X O O O O
$$ | . X O O O . . . .
$$ | . . . . . . . . .
$$ ------------------[/go]

Click Here To Show Diagram Code

[go]$$B locale
$$ | X X X . . . . . .
$$ | C C X . . . . . .
$$ | C X X X X O O O O
$$ | C X O O O . . . .
$$ | C C C C C C . . .
$$ ------------------[/go]

Click Here To Show Diagram Code

[go]$$B assuming Black 3, count 5
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | . X X X X O O O O
$$ | . X O O O . . . .
$$ | . . 1 3 . 4 . . .
$$ ------------------[/go]

To save time, I make some assumptions, which should be verified or refuted.

Click Here To Show Diagram Code

[go]$$W Variation I, assuming gote
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | . X X X X O O O O
$$ | . X O O O . . . .
$$ | . . 1 C C C . . .
$$ ------------------[/go]

Looking up the count of Black's region, it is 3 2/3. White's region has -3 in the locale. The count is 2/3.

If variation I dominates, the initial gote count is (5 + 2/3) / 2 = 2 5/6 and gote move value is (5 - 2/3) / 2 = 2 1/6.

Click Here To Show Diagram Code

[go]$$W Variation II, assuming Black 2 - White 3
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | . X X X X O O O O
$$ | . X O O O . . . .
$$ | . 1 2 3 C . . . .
$$ ------------------[/go]

White's region has the count -2 in the locale including the 1 black prisoner stone.

The count of Black's region in this position still needs to be calculated taking into account any later ko-atari on the stone 1.

If the intermediate white string were connected, the count of Black's region would be 2 2/3. Assuming the later ko-atari on the stone 1 is worth 1/6, I expect the count of Black's region to be 2 5/6.

Therefore, the count is 5/6.

If so and variation II dominates, the initial gote count is (5 + 5/6) / 2 = 2 11/12 and gote move value is (5 - 5/6) / 2 = 2 1/12.

White chooses the smaller count of variation I, which thus dominates. The move value is 2 1/6.

I have not proofread the calculations so there may still be mistakes.


EDIT: White has 1 point less in variation II. Correcting calculations accordingly.

Thank you so much. Actually the picture wasn't clear. So I am porting this again but with the right situation.
And your explaination is wonderful. Thabk you so much.

I need to lie down after reading the above. And it still ends up as gibberish for me. If I do the calculations my own deiri based way, I very quickly establish that the basic gote-gote deiri value is 3, but White has the potential of an extra small gain with a follow-up move after his gote. So the !true" value is, in my terms, a little under 4.

If we convert that to a miai count we get "a little under 2".

So, I then have two questions:

(1) In practical terms what is the difference between 1.67 and "a little under 2". Or, more specifically, What is it about this difference that makes a too-difficult-for-me and error-prone (error even by a yose maven - see above) calculation worth attempting? The miniscule number of games in which it can make a genuine difference is probably more than outweighed by the number of times the calculations are miscalculated anyway.

(2) The REAL question, which everyone (pros and amateurs) seems to avoid answering, is still: why use one technique over another, especially when we keep getting told you can convert from to the other by dividing or multiplying by 2? Even if there is some obscure reason for saying one is superior to the other that can be demonstrated, it's not enough to say vague things like it helps with strategic choices. It may - but just saying just that is just like saying this margarine tastes like butter (and then wondering why most people and top chefs still prefer butter).

Endgame considerations affect, say, 100 moves of a player. Losing on average 1/3 per endgame-related move amounts to losing more than two ranks.

If time spent during the game must be managed, not spending it on exact values of difficult shapes may be a good idea. That is why one should study such in between games and learn these shapes and their values by heart, quite like one practises tsumego. You have praised some professional players for knowing thousands of such values by heart. We all know that rote memorization is hard without understanding. Therefore we must invest effort in understanding the calculations.

Just claiming to do an approximation quickly is as "cute" as claiming a life status without shape knowledge and reading.

If you want a detailed explanation why the modern endgame theory's division by 2 is much more powerful, study all the theory and notice that for by far the most applications the easiest use of a traditional gote move value in otherwise modern endgame theory is to first convert it to the modern move value by dividing by 2.

In practise, the major reasons for the modern gote move value are:
- It equals the gain of either player's move, that is, the difference of the values of the positions before and after the move. Therefore, we can say that the move has its value because it transforms the value of the preceding position to the value of the created position. You cannot say so for the traditional move values.
- The modern move value is always a value per move. Therefore, we can compare move values directly regardless whether the move occurs in a gote, sente, ko or ko threat, or is a follow-up of possibly a different type.
- By comparing a move value to the gains of alternating sequences' moves, we can verify whether our assumed type (gote, sente,...) is correct and therefore we have calculated the right move value. Traditional go theory lacked verification so made frequent mistakes.

Now that we have the whole problem, adding white's tiger mouth(at 7-2) simplifies the calculations by a lot.
White gains 1 point (A=1) from being able to block if black plays first, and white gains slightly more than zero points (B=0+) from being able to hane and not worry about the connection. Hence, overall calculating from black's perspective, the move gain should have changed by (-A - (-B))/2 = (B-A)/2 or a bit more than -0.5.

Hence, assuming Robert's calculations are correct, I will guess that the answer to the problem is a gain of

2 1/12 - 0.5 + (0+) ~ 1 2/3

where (0+) means something a bit more than zero.

A little under 2 should be correct, agreeing with lichigo's teacher and JF's estimate.
____
I will give my own answers to JF's questions.



It is a theorem of miai counting (see RJ's Endgame 5 I think) (ignoring kos) that if you don't play the right move when the largest endgame move has gain T, then you lose (under optimal play) at most 2T.(edit: I wrongly wrote T here before)

A simple gote is a position settled by one move (or one gote forcing sequence) by either side.
If only simple gotes remain and you play a move of gain t instead of T (t<T), then you lose at most 2(T-t).
For example not playing the final 0.5 gain but passing (0 gain) instead will lose you 2(0.5-0)= 1 point.

(This result can be found from a discussion between Robert and I previously).

I do not know how this generalises to more complicated endgames, but simple gotes are often a good rule of thumb.

As for whether it is worth it, I think such calculations are often not worth it unless it is a very close game and you have some time to work it out. To do a full miai calculation, you need to calculate every single possible optimal variation (including tenuki) locally which is very tiresome. It can be used to double check and pre-calculate the values of moves, allowing memorisation before a match (I think you mentioned how Rob van Zeijst memorised the values of hundreds of yose positions). Although the theory works perfectly and is simplest for small and simple problems in the late endgame, the principles still work for the early endgame, where the sizes of moves are bigger and hence it is more important to play accurately. You can use rules of thumb or estimates based on principles you learn from doing the simpler problem.

From a mathematical point of view, I find the theory impressive in how it solves what seems like a very complicated problem (the endgame of Go) in a fairly clean way, almost to perfection. Only almost because it can't easily handle ko and independence tends to require "immortal stones" which isn't always realistic.



For simple gotes, deiri counting = miai counting * 2.
For anything more complicated, miai counting handles it perfectly, whereas deiri is a simplification (I don't know how you define deiri counting for more complicated problems, but probably by the swing - the difference between optimal play if black plays first and optimal play if white plays first.) Frankly, most of the time the half the swing is a very good estimate for a move gain. (NB: I may have slightly misused the term "swing" here).

It is a go player's intuition that it is a good rule of thumb, while it is a mathematicians job to prove that, and the only way is to use the more general theory in miai counting. Miai counting will handle all the weird and wonderful cases, as well as create "magic tricks", manufacture problems which are counter to intuition or any one rule of thumb.

Why multiply/halve by 2? Well, deiri simply counts the points difference between two real board positions, so it is natural to complain and ask what the point of dividing by 2 is. Miai counting requires a bit more abstraction/imagination and tries to look at all possible variations at once, but it makes it very natural to think in terms of each move making a contribution to the score. The final score is initial count plus the sum of the gains of all your moves minus the sum of the gains of your opponent's moves. S=C+Σm-Σm

In this case, the gain is like half the deiri move value, since it requires two moves (one by you or one by your opponent) to get to those two board positions being compared.

___

Just from watching Chinese pro commentaries careful counting beyond rough estimates (+/- 1 point) is rare. But they sometimes talk about 1/6, 1/12 etc. (sometimes in a joking way, or saying how such analysis can be very professional), or about how a cut on the 2nd line is best defended by a tiger mouth than the descend or solid connection (i.e. CGT Tinies/Minies), but I haven't heard much more than that. Some do seem to be able to calculate the sizes of small endgame using miai counting very quickly, but as kvasir says, they use double the gain instead, mimicking deiri numbers. But I don't know how much they know about the theory or invest it understanding it/using it behind the scenes. In my imagination, there are experts at universities. But in any case, I get the impression Bill Spight's understanding of and ability to analyse endgame is much more advanced than most top pros.

As for practical theory, I would like to push a version of miai counting on the board that I am surprised not to have seen anywhere else. Perhaps JF has been hinting at it?

Let's call it

Iterative deiri counting

The idea is to start with deiri and then iteratively improve estimates. Perhaps this will help people who are good at deiri counting make a slight upgrade in accuracy.

Start with deiri
The deiri estimate compares

Click Here To Show Diagram Code

[go]$$B Black plays first
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | . X X X X O O O O
$$ | C X O O O . O . .
$$ | C 3 1 2 . . . . .
$$ ------------------[/go]

This diagram is a gote forcing sequence( , are sente)

to

Click Here To Show Diagram Code

[go]$$W White plays first
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | . X X X X O O O O
$$ | 2 X O O O . O . .
$$ | . 1 . C . . . . .
$$ ------------------[/go]

The difference is 2 black points and 1 white point or 3 points total.

Divide by 2 to get a miai count of 3/2= 1 1/2.
In general, we divide by 2^k where k is the number of moves it takes to get a different move in the 2 diagrams we are comparing. In the above 2 diagrams, move 1 is already difference, so k=1 and 2^k=2 as expected.

First iteration
The second diagram was not a gote forcing sequence, so we need to insert : tenuki

Click Here To Show Diagram Code

[go]$$W White plays first, Black tenukis, White continues
$$ | X X X . . . . . .
$$ | . . X . . . . . .
$$ | 6 X X X X O O O O
$$ | 3 X O O O . O . .
$$ | . 1 5 . . . . . .
$$ ------------------[/go]

Here, is gote, but and are miai.
In this diagram, black has lost a point at , but as is in atari, black has an extra 1/3.

Hence, this diagram gains white 2/3 over the second diagram (a deiri value).

We need to check if this position can arise. i.e. If is sente, this variation is impossible. To check, at the divergence point, white has played two more moves than in the 2nd diagram. (i.e. , is 2 more W moves vs is even). At the divergence point, the 2nd diagram has one more white move than the 1st diagram. We divide the move value by the number of moves difference. So compare
(2/3)/2 to (1 1/2)/1
The former is much less so is gote for sure. So we include this variation.

But as this position arises from a follow-up, and divergence is on the 2nd move, k=2.
We must divide by 2^k to get (2/3 )/4 = 1/6.

There are no other variations. Therefore, the gain of the first move is 1 1/2 + 1/6 = 1 2/3.

Woohoo! My guess at the top of this post was correct.

The general process is to add more variations at depth 1, then depth 2 and so on as required. You do not need to do the full miai calculation starting from the bottom of the tree. Instead, deiri from the top with iterative deepening is a better practical method.

You can perhaps understand how this idea is helpful for estimating the size of very complicated large endgames. I have little doubt that pros and amateurs have been using this sort of technique once they realise deiri counting isn't perfect. But it takes a little miai counting theory to prove that it works and to make sure you are doing the steps correctly - checking gote/sente as well as choosing the correct k to divide by 2^k.

To me this method also reminds me of a lecture by Bill on influence functions. Those familiar with the halving influence down CGT corridors may know what I mean. I have plans to develop this theory further.

BTW: I tried to develop this method on the spot in this video: https://www.youtube.com/watch?v=rcz9b6k ... e&index=15 but made a mess of it. Hopefully my explanation above is more clear.

You seem to be misstating a game theory theorem (but then you refer to a book by RJ so I am not sure what you actually mean). I think this would apply only if there are not moves that make a negative gain (i.e. negative moves for black and positive moves for white). To see why this does not apply to Go, consider a game with a seki position and make bad move in the seki. There are obviously other ways to squander away points so this could only hold under some unstated assumptions.

My passing knowledge of game theory is that there are games that have nice properties, like the one that you refer to, and then there are most games that don't. That is not to say that analyzing games under strong assumptions is not useful.

I kind of lost you at this point but then I gathered that you tried to explain how one really doesn't need heavy mathematical formalism and can achieve accurate results using a more traditional approach. Sorry if I am paraphrasing incorrectly, but I think I have seen many teachers give similar accounts of how to compute values but using the traditional values. Including how to handle ko's and ko threats. It seems unclear to me where "traditional" meets "miai" in this. It can't be that it is a slippery slope that you either do it completely wrong or you end up doing it in surreal numbers? What I mean is that some powerful tools are surely part of the "traditional" method too.

OK, true. I need to add the assumption that you only play locally optimal moves. If you make a mistake and play in the wrong local area, you can lose at most 2T. Note that the right local area is not necessarily the one with maximal gain (T).

I do not know if it appears in Endgame 5 so I shouldn't have mentioned it, but the proof is just 2 inequalities.

I remember a time (probably around 1d) when I tried to explain deiri counting and realised I didn't even understand that well enough. So I think it takes some time to absorb the concepts.


Yes, basically. I'm also trying to explain the method I try to use when playing a real game.

The iterative method I describe gives a sequence of counts that starts with deiri and converges to the full miai counting method. I'm glad if this is well known, but if so, it seems that miai counting is basically well-known, but just seen from a different perspective. If deiri was good enough for pros in the past, it can't be that bad.

Frankly, AFAIK miai counting shows how to calculate gain with some general results/principles about how to choose between different moves (highest gain normally first, except when etc.). Even this doesn't perfectly solve an endgame puzzle without lots of reading, so I exaggerated when I said/implied miai counting was perfect. I don't know if there are better tricks in surreal numbers, but I imagine there isn't that much better.


I'm curious as to what you mean because I am partway through writing a paper on how to play a simple ko optimally(with some assumptions) that is more realistic than Tavernier's BGJ article. I am quite pleased to have solved and proved the problem when I thought it might not be solvable, so I hope it isn't well known.

Thanks to RJ and dhu. RJ made one statement that helped me: "Therefore, we can compare move values directly regardless whether the move occurs in a gote, sente, ko or ko threat, or is a follow-up of possibly a different type." I'm pretty certain that people have said this sort of thing before, and it's more than likely that I have read such stuff, but it has never registered before.

Starting an explanation, as dhu did, and most rules mavens do, with:



is a guaranteed way of losing my attention. And it's not just me. There are good reasons why publishers usually employ journalists rather than tecchies to explain technical subjects to the masses. The main reason is precisely that we are the masses.

However, dhu switched tack and empathetically pretended to be one of the masses and thereafter wrote accordingly. I found that very helpful, thank you. The iterative method you use is indeed roughly the one I use, though only on the rare occasions when the planets are in the right alignment. However, I would never have got as far as the refinement of 2^k. I just pile approximation on approximation. It seems to work well enough. I don't actually use the method in play, as I very rarely do play. My interest is almost entirely to do with understanding comments on move values given in commentaries. I try to check them, so that I can make use of them in my own commentaries, and almost always manage to some out with the same value. This makes me believe that approximations are sufficient in practice.

I'm not quite as boundary-play dumb as I sound, I should add. I may even be the only one here who has read O Meien's book. I even put some effort in. What I mean by that is that, in the first place, I translated it. That wasn't too much effort because I use shorthand, so it was almost as quick as just reading it. But I enjoyed the book, and it was being discussed a lot here, so I put in more effort and actually typed it up (you can do word searches on typed text; you can't do that with shorthand). I even understood it, in a way. What was lacking (for me), though, was a clear statement of the type RJ provided above. Armed with that, perhaps I should now re-read it.

However, I'm still not getting the answer from anyone, including O Meien, to the question I keep posing. I suppose the reason is that the question is being posed in an ambiguous way - real ambiguity, not the imagined type elsewhere on L19. That's entirely my fault, so I'll try again with baby steps and a sound basis, if I may.

First, my base is that miai (as an accountancy term, not the alternative points meaning) goes back to Meiji times in go. It is not "modern". It may be argued that modern treatment of it (theorems and all that) is what makes it modern. I'd take issue with that, on the grounds that Shimada Takuji and others were giving it the full mathematical treatment in the 1920s and 1930s, and Shimada himself published a book called 囲碁の数理. The clue's in the title: "Mathematical Principles of Go". This appeared in 1943, and a revised version followed in 1958. During this period, Kido and other magazines were replete with articles full of subscripts, superscripts, sigma signs and more arrows than a darts match.

This defines the context, which is that there was a known alternative to the deiri method of boundary-play calculation. It was being widely publicised in go journals. It was being pursued by eminent mathematicians. Even if this new method took longer than ordinary deiri, pro players then had plenty of time. They could have up to 16 hours each, and a fast game was defined as 5 hours each. I think we may also safely supposed that at least most of the players were open to using any legal means that would enable them to win more games. Even if we assume (as I do) that RJ's suggestion of 200 boundary-plays per game each potentially losing a third of a point is total bollocks, he is right in a way. My new book on Go Seigen (now being proof-read by someone else) is full of boundary-play mistakes, by both Go and his opponents. And these mistakes were picked up by other pros in their commentaries. That is, pros do care about the percentages.

So, as I see it, the situation has been as if all the pros were using old-fashioned phones (deiri technology) and someone comes along and says, hey try out the ne iPhone (miai technology). And all the pros ignore him. Not just for a few months, or even years, as habits die hard and oldies enjoy grumbling about new-fangled things. This ignoring has gone for a century. My real question is not in which ways is miai better than deiri - I can take that on trust even when I don't understand the reasons. My real question is why have pros, people for whom it matters, not made the switch to miai. Silly answers such as they are "just Japanese 9-dans" don't cut the mustard.

In the absence of sensible answers, we therefore have to allow for the possibility that the pros have seen something we haven't. Mathematicians have spent decades trying to prove miai is better, but have they been seduced by the fact that miai is (they say) better suited to the theorems, lemmata and propositions they all adore? Have they perhaps just kept sailing on into the empty void, forgetting where they came from? It has happened often in other sciences. It often pays off to revisit old, abandoned theories. Is it perhaps time to revisit deiri and really look at it in detail, with the same level of effort they gave miai?

Such effort may not (or even may) allow the proofs they cherish, but may reveal unsuspected practical reasons why deiri has been so favoured. I do know that Rob van Zeijst's revelation that he memorised something like 1,000 standard counts created a lot of surprise here (he was just following the pros but they had never let on to the rest of us). I now know other pros do this, though I have no idea what the memorisation record might be. I do know that at least some Chinese pros use deiri and for that reason they also, in their heads, may use 7.5 komi instead of 3.75.

O Meien himself revealed another previously unpublished trick (margin of error). He used it in the context of absolute counting (i.e. miai) but I imagine it could be adapted for deiri. What other methods and tricks remain to be revealed - if only the mavens actively go looking for them? As I said in a previous post, these (if they exist) may be subsumed under headings like atsui and timing, and the ability of miai to handle move types other than gote, or to make strategic choices, may be provided in other ways by deiri players.

I don't know. That's why I'm asking. Why have pros not switched over? Or, to repeat my earlier analogy, why do experts in organolepsis and top chefs prefer butter over margarine when self-appointed experts hired by marketing men tell us margarine tastes better, tastes just as good, or you can't tell the difference?