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.
Endgmame question
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RobertJasiek
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Re: Endgmame question
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.
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 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 This diagram is a gote forcing sequence(
, 
are sente)
to
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
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.
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)John Fairbairn wrote:(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.
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.John Fairbairn wrote:(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).
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 This diagram is a gote forcing sequence(
, are sente)to
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
: tenukiHere,
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.
Last edited by dhu163 on Fri Oct 22, 2021 6:42 am, edited 4 times in total.
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kvasir
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Re: Endgmame question
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.dhu163 wrote: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 T.
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.
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dhu163
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Re: Endgmame question
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).kvasir wrote:You seem to be misstating a game theory theorem
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.kvasir wrote: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.
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.kvasir wrote:Including how to handle ko's and ko threats.
Last edited by dhu163 on Thu Oct 21, 2021 1:58 pm, edited 1 time in total.
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John Fairbairn
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Re: Endgmame question
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:
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?
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.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 T.
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?
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Schachus
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Re: Endgmame question
Isnt the second statement immediately a counterexample to the first one if t<T/2?dhu163 wrote:
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 T.
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.
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dhu163
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Re: Endgmame question
True, I am being careless, just going off memory. Since I'm used to using deiri swings too.
I guess it should be less than 2T. I'll edit accordingly.
Now I think about it, the proof works for all endgames where gote/sente is clearly defined, not just simple gotes. But the bound is 2T-t.
In fact, the proof for the simple gotes bound of 2(T-t) is a more difficult proof.
I guess it should be less than 2T. I'll edit accordingly.
Now I think about it, the proof works for all endgames where gote/sente is clearly defined, not just simple gotes. But the bound is 2T-t.
In fact, the proof for the simple gotes bound of 2(T-t) is a more difficult proof.
Last edited by dhu163 on Fri Oct 22, 2021 5:10 am, edited 1 time in total.
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RobertJasiek
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Re: Endgmame question
First I had to learn traditional endgame theory. It was hard because there was little theory, little explanation and bad explanation verbally or written. Later I heard of modern endgame theory, of which there was more with more explanation but explanation was more often for CGT theorists than players. I had to write my own explanations to understand modern endgame theory well but this was my breakthrough to it so profoundly that I could also expand the theory a lot. Understanding modern endgame theory also enabled me to understand traditional endgame theory were it exists for some subconsciously but is well hidden and not described openly. Including this, there simply is very little traditional theory of endgame evaluation, and part of it is wrong. The amount of traditional endgame evaluation theory is a tiny fraction of the amount of modern endgame theory.
Supposing you are right that most pros do not or hardly use modern endgame theory, you ask why. I think some reasons are:
- They learn go early and spend much time on go study so that their mathematical skills are often under-developed. (I know there are exceptions.)
- Although there are expert explanations for expert theory, presumably there are still too few non-English practically useful explanations of modern endgame theory beyond its bare basics.
- Their tactical reading is so good that they can compensate their suboptimal knowledge of endgame theory to some extent by much use of the method of reading and counting.
- Most research in modern endgame theory is in English and does not reach most of them fast enough, especially if they under-estimate the volume of available knowledge.
If the pros had more insight (beyond O's book) in endgame evaluation theory, they would teach it, but they don't. We do not live in the Edo period with secrets kept.
Pros teach endgame as tactical reading (which is as important as evaluation), tesujis (hardly relevant except for a few moves per game) and, as a footnote only, the hint to calculate values. They know that evaluation is important but relatively neglect it in their teaching. Sure, teaching tesujis is 1000 times easier than teaching calculations, which takes time and easily made mistakes endanger reputation. (Yes, again, there are exceptions. Three?)
Supposing you are right that most pros do not or hardly use modern endgame theory, you ask why. I think some reasons are:
- They learn go early and spend much time on go study so that their mathematical skills are often under-developed. (I know there are exceptions.)
- Although there are expert explanations for expert theory, presumably there are still too few non-English practically useful explanations of modern endgame theory beyond its bare basics.
- Their tactical reading is so good that they can compensate their suboptimal knowledge of endgame theory to some extent by much use of the method of reading and counting.
- Most research in modern endgame theory is in English and does not reach most of them fast enough, especially if they under-estimate the volume of available knowledge.
If the pros had more insight (beyond O's book) in endgame evaluation theory, they would teach it, but they don't. We do not live in the Edo period with secrets kept.
Pros teach endgame as tactical reading (which is as important as evaluation), tesujis (hardly relevant except for a few moves per game) and, as a footnote only, the hint to calculate values. They know that evaluation is important but relatively neglect it in their teaching. Sure, teaching tesujis is 1000 times easier than teaching calculations, which takes time and easily made mistakes endanger reputation. (Yes, again, there are exceptions. Three?)
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jlt
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Re: Endgmame question
Just a dumb question: how practical is it to count precisely the values of moves during a live game? What time controls would be needed for a player with a lot of training?
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dhu163
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Re: Endgmame question
Ke Jie has started live streaming lately and he sometimes counts out loud though most of it seems to be dissing his own moves, saying how badly he is playing and how he will lose, only to turn the game around. There is good Go theory he describes as well, when explaining his moves or his judgement of what is going on.
My guess is positions with depth 3 or more take more than 1 second.
He also seemed to take around 5 seconds to count the size of a 38 point seki and judge it was worth saving despite the lack of liberties.
My guess is positions with depth 3 or more take more than 1 second.
He also seemed to take around 5 seconds to count the size of a 38 point seki and judge it was worth saving despite the lack of liberties.
Last edited by dhu163 on Thu Oct 21, 2021 3:56 pm, edited 2 times in total.
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John Fairbairn
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Re: Endgmame question
I'd accept that all the reasons you list come into the reckoning, but would have reservations about the last: most modern research is in English and doesn't filter through.Supposing you are right that most pros do not or hardly use modern endgame theory, you ask why. I think some reasons are:
First I think the term "modern" is misnomer, as I explained above ("post-modern" could be better!). But that's by the by. More important is that I think you are underestimating what has been going on for decades in Japan. Have you actually read Shimada? Have you actually read O Meien, apart from the bits I've posted here? And Berlekamp's work is certainly known in the Far East (though obviously only to the same sort of small audience that applies over here). It may well be, of course, that research is currently more active in the west. I haven't seen a mathematical discourse in Japanese for a while (or in Korean or Chinese, but I don't keep tabs on them as much).
I don't rate secrecy as a factor worthy of more than a milli-second of consideration. Recall that Genan's deiri classic Igo Shukairoku appeared in Edo times (1844 - see New In Go) and didn't attract any complaints from the other families. Josekis might be kept under wraps for important castle games, but that's just temporary gamesmanship. Deaths may also may kept secret temporarily to preserve stipends. Game records may be kept hidden (or destroyed) to save face - ever wonder why Dosaku won so many of his surviving games? But keeping boundary-plays secret? There's not a tittle of opening-preparation/cash/face advantage in that. If anything, people would laugh at a top pro who gave the impression he could only win with secret boundary-play counting techniques.
What I think may better explain lack of pro explanations is that Japanese amateur tournaments have traditionally been sudden death. Under those conditions there is little call for boundary-play techniques, especially those that are complex, which leads to little demand for pro instruction, which leads to pros not wasting their time giving it. Simple as that, though things might be changing in the era of fancy clocks. In similar fashion you don't get books on kiai. Even on things that matter to amateurs such as sabaki or tewari, books are like hen's teeth. It's all supply and demand in other words. And as in the real world there is always high demand for drugs: josekis and tsumego.
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RobertJasiek
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Re: Endgmame question
I understand that "modern" may not be the best word from a historian's perspective but I use a functional perspective in the context of usage by development of relative popularity.
I have not read Shimada's endgame texts; given your earlier hints and his rules texts (of which I saw some in English), he might have described some basics or maybe a bit maths. I have read O Meien's book (where "read" means diagrams, decrypting a few Japanese text symbols by positional text context, understanding the number calculations and finding that the contents must be very close to what you had described earlier about the book). I have had "read" some other Asian endgame books but as to calculations they were dull, such as stating the guesstimate 15 points, leaving the actual calculation of the move value as an "exercise".
Most research is a) combinatorial game theory by mathematicians (other than Berlekamp / Wolfe), b) my research and c) Bill's research. So far I see no indication of Asian professionals taking much notice of that.
Your reason about sudden death in Asia and related demand is valid.
"how practical is it to count precisely the values of moves during a live game?"
It depends on how complicated the calculation needs to be. how accurate it must be, whether verification of methodical correctness is done, the time limits, each player's general calculation skill and his skill needed for every particular problem. Except very great differences between players and different problems. In particular, expect many professionals to calculate (approximately) very much faster than almost all strong amateurs, like pros are very much faster on average in tactical reading.
Endgame evaluation is a skill that can be trained like other effortful go skill, such as tactics. A life and death beginner's tactical reading is extremely slow. A dan player is much faster. A pro yet much faster. Similarly, calculation speeds differ dramatically depending on training and talent. We should practise thousands of LD problems - we should also practise thousands of endgame evaluation problems (with correct calculations or only tiny approximation mistakes, verified due to solutions with trustworthy correctness or verified by one's own understanding).
In practise, calculations must be precise enough to make the relevant move decisions. "Roughly 7 is larger than roughly 5" can be good enough but it can be necessary to distinguish 4 1/3 from 4 1/4.
I have not read Shimada's endgame texts; given your earlier hints and his rules texts (of which I saw some in English), he might have described some basics or maybe a bit maths. I have read O Meien's book (where "read" means diagrams, decrypting a few Japanese text symbols by positional text context, understanding the number calculations and finding that the contents must be very close to what you had described earlier about the book). I have had "read" some other Asian endgame books but as to calculations they were dull, such as stating the guesstimate 15 points, leaving the actual calculation of the move value as an "exercise".
Most research is a) combinatorial game theory by mathematicians (other than Berlekamp / Wolfe), b) my research and c) Bill's research. So far I see no indication of Asian professionals taking much notice of that.
Your reason about sudden death in Asia and related demand is valid.
"how practical is it to count precisely the values of moves during a live game?"
It depends on how complicated the calculation needs to be. how accurate it must be, whether verification of methodical correctness is done, the time limits, each player's general calculation skill and his skill needed for every particular problem. Except very great differences between players and different problems. In particular, expect many professionals to calculate (approximately) very much faster than almost all strong amateurs, like pros are very much faster on average in tactical reading.
Endgame evaluation is a skill that can be trained like other effortful go skill, such as tactics. A life and death beginner's tactical reading is extremely slow. A dan player is much faster. A pro yet much faster. Similarly, calculation speeds differ dramatically depending on training and talent. We should practise thousands of LD problems - we should also practise thousands of endgame evaluation problems (with correct calculations or only tiny approximation mistakes, verified due to solutions with trustworthy correctness or verified by one's own understanding).
In practise, calculations must be precise enough to make the relevant move decisions. "Roughly 7 is larger than roughly 5" can be good enough but it can be necessary to distinguish 4 1/3 from 4 1/4.
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jlt
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Re: Endgmame question
I understand from this that a trained and talented player is able to calculate the value of moves much faster and in many more situations than the average trained amateur, but often lacks time during a live game to make precise calculations so needs to make estimates?RobertJasiek wrote:In particular, expect many professionals to calculate (approximately) very much faster than almost all strong amateurs,
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RobertJasiek
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Re: Endgmame question
Yes. Where the experienced, trained player's approximations are 1/4 or smaller whenever necessary.