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Review: The Endgame (Ogawa / Davies) http://www.lifein19x19.com/viewtopic.php?f=57&t=16012 
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Author:  Uberdude [ Wed Aug 29, 2018 8:47 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Knotwilg wrote: OK. So pros know about fractions and use them to calculate positions in problems. The question is: do they use them nowadays in their decision making? Do they effectively, in the late endgame, rank moves according to these calculated values? Given five or more moves to evaluate, I would think they need to know these values by heart. Nothing is impossible, in a mankind where already three centuries ago professional composers could make a composition for an orchestra without ever hearing it elsewhere than in their head. But do they? Or will they calculate these >5 moves on the fly? Or will they intuitively prune it down and choose the one with the highest winning probability, including the effect on neighboring positions and potential ko? I recall reading that Rob van Zeijst 7d (so not a pro, but studied as insei) had memorised the fractional miai values of loads (100s, 1000s?) of commonly seen endgame positions and this helped him to play a strong endgame quickly. FWIW when I was 3d EGF and active on correspondence OGS I would calculate endgame of my close games with fractional swing values to help me decide the course of play with tedomari considerations (and write them down in private board notes; I found this simpler / more useful than miai values, this wasn't crazy corridor with huge fractions, but things like this move is 3 points gote with a 2 point followup if sente or the followup is 11 1/3 points (simple endgame ko is easy fraction) for 2 gotes). I won quite a few close games in endgame due to putting in that effort (and didn't lose too much in endgame vs breakfast, perhaps my biggest mistake was playing a timesuji which ruined a clever tesuji that Toru Imamura 5d spotted), though I can't say now if I didn't bother with the fractions (which were mostly just halves and thirds) would some wins have turned into losses; though there were half pointers so I guess maybe. 
Author:  John Fairbairn [ Wed Aug 29, 2018 9:19 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Quote: If you calculate +1/2 during your, say, 75 endgame moves and round wrongly half of the time, your mistakes amount to 75 * 1/2 * 1/2 ~= 19 points, or 1.5 ranks. Utter poppycock and balderdash. This is giving mathematics a bad name. If you have 75 boundary plays, a large proportion of them must be in the oyose stage where strategic or psychological considerations such playing thickly, eliminating aji or playing safe carry much, much more weight than half points (or even whole points), let alone 16th points. Nor are many of the plays discrete plays. A goodly proportion of even the small yose plays left will involve sequences such as hanetsugi or the monkey jump. Another goodly proportion will be simple sente moves, and many others will clearly not need rounding. Of the very few moves then left, the chances of any two or more involving the same integer and an obscure fraction are very small, perhaps vanishingly small. Even if there are some, the ignorant player will still get half right randomly. On top of all that, even if you found a game where familiarity with obscure fractions made a difference, does it to make enough difference to win the game? And if you keep disappearing down the hole until you find one of those, you still can't say you've improved any number of ranks unless you improve enough to win a lot games you lost before  not just one in a thousand. Even where you do improve after a period of endgame study, how much is due to new arithmetic and how much is due to the simple fact that you now strongly concentrating on the endgame and so avoid errors that you made when you weren't concentrating so hard? On the basis of the common observation that even dan players can easily play 2 or 3 grades below their true rank when they mess about with fast games, simple concentration is likely to improve endgame play significantly using even the simplified model of counting. The fact that some people learn to make counts down to a 48th of a point (I've seen even smaller in Japanese magazines) just shows there are go players as daft as those people who learn to pronounce words backwards. It's just a party trick, and not a very entertaining one. 
Author:  Gomoto [ Wed Aug 29, 2018 9:22 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Even if I can not count correctly during a game and did not memorize a shape yet. I always wanted a way to compare two "similar" end game moves exactly. I always strived for this knowledge, which move is better in this position. I cant stand it if I have no means to estimate the category of a move. In the fuseki and middlegame there is now AI. For the endgame I can use modern endgame theory to scratch my itch. 
Author:  RobertJasiek [ Wed Aug 29, 2018 10:02 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
John, I know that the estimated sum of average mistakes is rough. Improvements on such estimates are welcome. Note that players also make larger endgame mistakes. If you think that middle game / early endgame moves resembling endgame moves (or their territory components) cannot be approximated well by endgame calculations, learn it. Such is sometimes useful even during the opening. Calculating 32th of points of corridors is superfluous during one's games because there are very much simpler principles and formulas for corridors. For move order, use the principles. For positional judgement during the endgame, use a formula for the count. Calculating 48th of points for other local endgames occurs, e.g., when adding 8th and 6th of points without calculation tricks. 6th occur when a follower has a ko. After forming a sum, one can immediately try to simplify the resulting fraction. While you will tell everybody it is only "for the show", serious players just do necessary calculations and finish while you will still be lamenting. Needless to say, it would not be about adding 1/8 to 1/6 but about (much) larger numerators. 
Author:  Bill Spight [ Wed Aug 29, 2018 10:24 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Knotwilg wrote: While I believe it is not impossible to reach expert level in the endgame by taking the route of fractions, I believe John's comparison to the book of 600 pages on Gaelic pronunciation is spot on. I strongly beg to differ. Calculating to 16ths, which is more than most people need, is equivalent to calculating 4 moves deep, which, while perhaps daunting, is nowhere close to reading 600 pages of technical text. 
Author:  Bill Spight [ Wed Aug 29, 2018 10:39 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Knotwilg wrote: Uberdude wrote: BTW, when Mateusz Surma (now 1p EGF) was studying in a Go school in China he did problems with yose calculations down to 1/48 of a point: http://mateuszsurma.pl/en/2016/04/15/sc ... 5042016/ I think it quite likely Japanese pros of the 1970s study in a different way to kids aspiring to be pros in a go school in China in the 2010s. OK. So pros know about fractions and use them to calculate positions in problems. The question is: do they use them nowadays in their decision making? Do they effectively, in the late endgame, rank moves according to these calculated values? Given five or more moves to evaluate, I would think they need to know these values by heart. Nothing is impossible, in a mankind where already three centuries ago professional composers could make a composition for an orchestra without ever hearing it elsewhere than in their head. But do they? Or will they calculate these >5 moves on the fly? Or will they intuitively prune it down and choose the one with the highest winning probability, including the effect on neighboring positions and potential ko? 1/48 = (1/16)/3. That indicates a depth of 5, including one ko. As a practical matter the sequence must almost be a one lane road. Remember, you have to consider the opponent's possibilities as well. To reach a depth of 5 in every branch requires evaluating something like a minimum of 32 positions, assuming only one choice for each player at each turn! If you assume only two choices for each player at each turn, we are up to 4^5 positions, or 1024 positions! No puedo, señor! (OC, several positions will be duplicates, but still!) Remember, the deeper you go, the more the uncertainty. Unless the positions are special, a precision of 1/48 pt. is swamped by the noise. 
Author:  Bill Spight [ Wed Aug 29, 2018 10:47 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Uberdude wrote: I recall reading that Rob van Zeijst 7d (so not a pro, but studied as insei) had memorised the fractional miai values of loads (100s, 1000s?) of commonly seen endgame positions and this helped him to play a strong endgame quickly. Over 1,000 is what I heard. Impressive! Nothing against Van Zeijst, but unfortunately much of what he learned was wrong. In fact, his columns afforded me a number of endgame problems. I could just look at a sequence and say, Nope! 
Author:  Bill Spight [ Wed Aug 29, 2018 10:59 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
BTW, while I am thinking of this: Several years ago I thought about writing an endgame book aimed at 10 kyus. So I looked at a large number of 911 kyu games online. My conclusion was the main endgame lesson for players at that level is damezumari. They were throwing away dozens of points at the very end of play by missing invasions and protective plays, etc. Gaining 2 pts. pales in comparison with losing 20. As far as calculations go, they are not practical unless you can prune the game tree without missing the best plays. But there are strategic lessons in the endgame that generalize to other parts of the game. 
Author:  John Fairbairn [ Wed Aug 29, 2018 11:31 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
I invite you all to consider the following position, from O Meien's book. It might be better in a separate thread of its own but I think it belongs here for two reasons. One is that (eventually, once I've provided the followup) it will illustrate (I believe, just like Robert) that the Ogawa/Davies book  the main theme of this thread  is wanting in many respects. Second, it touches on several of the subthemes. I happen to believe it supports what I have said and contradicts at least some of what Robert has said. Since he concedes O's book is a good one but "nonessential" I think he has to stand up and explain why he says that. The first step would be if he tells us, using the Harry Potterish method of divination he says enables him to discern exactly what O says in Japanese, what O says on page 146 (which is all text). This diagram is on page 147 and O's discussion of it goes up to page 155 (with quite a lot of text). I invite Robert here, too, to explain what O is saying. It's a chance to plug his book and I won't actually be surprised if he explains the position well. My main contention is not that his own method is wrong, just that it's overkill. Of course other opinions on the position would be valuable (preferably using Hide?). In due course, I'll give O's version. This, I hope, will also be seen as a kind of review for his book. The portion here does not explain his basic thinking or his methodology. It's in the section that deals with how these work out in practice. but I think it's an illuminating case, somewhat like the mutual damage diagram in Kageyama's book that caused so much jawdropping when it first appeared in the west  but at a much higher level in this case. White has just played the triangled move. You have to decide whether or not to answer at A, and if not, play where? Obviously you also have to show your working. This year's exams aren't over yet! 5.5 komi. Black ha captured 2, White has captured 1. 
Author:  RobertJasiek [ Wed Aug 29, 2018 12:07 pm ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
This is a whole board position during the early endgame. I will study related theory for that in Volume 5. To start with, we also need to consider the temperature T and maybe secondlargest move value in the environment besides a considered ensemble. Maybe O also uses an error margin, of which I am not so much a fan. Do not ssk me where I have buried O's book in the current chaos here. I recall reading the lower left local endgame is sophisticated. In modern endgame theory, starting in the environment is worth T/2, as Bill and I have studied here earlier incl. proof for an ideal environment. Apparently O wants to compensate uncertainty of nonideal environments by a defensive error margin to predict whether a player has a guaranteed win. 
Author:  Bill Spight [ Wed Aug 29, 2018 1:08 pm ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
John Fairbairn wrote: White has just played the triangled move. You have to decide whether or not to answer at A, and if not, play where? Obviously you also have to show your working. This year's exams aren't over yet! 5.5 komi. Black ha captured 2, White has captured 1. To be fair to Robert's new book, it is about evaluation. As I have pointed out, to be able to use evaluation effectively, you have to be able to prune the search tree without eliminating best plays. This position is too open for accurate evaluation, IMO. Not that approximation can't help. Edit: White has just play a double sente, so of course Black should answer. 
Author:  Uberdude [ Wed Aug 29, 2018 1:24 pm ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Author:  Knotwilg [ Wed Aug 29, 2018 3:08 pm ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Edit: 
Author:  John Fairbairn [ Wed Aug 29, 2018 11:43 pm ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
It's a shame that Robert chose not to share his magical method of knowing exactly what O Meien said without reading Japanese. The rest of you will have to make do with my translation. As I said before, I hope this extract will be taken as a review, showing the quality of O's work and also how much further he goes than the Ogawa/Davies book. This is from the more advanced portion of the book, but O does cover the basics and does explain his method. The latter involves a fascinating formula, referred to in this section, which I have explained elsewhere in L19. You will have to hunt for that yourselves, but the keywords may be "Meien" (of course) and "certainty of election" (or just "certainty"). This refers to what Americans call "calling an election," which means something very different in British English, and it is to do with being able to predict the final result without waiting for all the votes to come in. A reminder of the book's ISBN: 4839915083 ("Absolute Counting in the Endgame"). It is from 2004, so maybe getting hard to find, but I think it should be on your shelf even if you don't read Japanese. First, page 146. Quote: CHAPTER 5: ANALYSIS OF ENDGAMES IN ACTUAL GAMES
The aim of this chapter I will now explain the endgame in several games: six of my own and one classical game from Edo times, plus a game by the Korean player Yi Ch’angho. I am hoping that I will be able to summarise what we have been talking about in this book by touching on things like what sort of things to think about while playing the endgame, and when to play for “certainty.” I have striven, as far as I am able, to reproduce faithfully what I was thinking about at the time in my games, and so I will go into a fair amount of detail, the content of which may become a little difficult. However, I do think that it will be enough if you can simply appreciate things like “this territory can be counted as soandso” or “for a pro this seems like a win or a loss at this point in time” without worrying too much about precise figures. 
Author:  John Fairbairn [ Wed Aug 29, 2018 11:54 pm ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
TRANSLATION (unedited) Example 1: Black to play Attachment: O Meien p147.png [ 8.46 KiB  Viewed 3476 times ] White: Kobayashi Koichi Meijin, Black: O Meien 6dan; 41st Honinbo League, 9 January 1986 I am taking Black against Kobayashi Koichi, then the Meijin. White has just played the diagonal move 1 in the lower left. The first thing to think about is whether or not Black needs to answer at A on the lower side. And then, if he does not, where should he turn to? This position is to find out something about your ability to evaluate. (Komi 5½ points) Attachment: O Meien p148a.png [ 16.5 KiB  Viewed 3476 times ] Actual game (1~ 120) This was a game in the 41st Honinbo League, having secured my first entry in a league. I was then 6dan. It was my third game in the league, having scored 11. There had been no fighting of any note and we were on the threshold of the endgame. The balance of territories was fairly even. White’s diagonal move at 120 was the biggest move on the board and could not be missed out. If he does omit it … Attachment: O Meien p148b.png [ 9.08 KiB  Viewed 3476 times ] Diagram 1 Diagram 1: Black’s attachandpullback 1 and 3 will end up being an especially large boundary play. Even just in deiri terms of pure territory it is almost 20 points, and following this there remains Black A, White B and so on up to the pushthrough of Black G, White H, Black I. Therefore, White 120 in the actual game diagram was a natural move. The block on the lower side is small. Now, as to whether or not Black should answer on the low side, to give the conclusion first, he “absolutely must not defend.” The reason for saying that is … [I am limited to 3 attachments so must keep going to new posts to continue. JF] 
Author:  John Fairbairn [ Thu Aug 30, 2018 12:00 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
TRANSLATION CONTINUED Attachment: O Meien p149.png [ 9.41 KiB  Viewed 3475 times ] Diagram 2 Diagram 2: White’s jump into 1 is not actually very big. If now Black 2 to 12, answering each time as White wants, this boundary play is only 7 points in sente. Also, it makes Black thick at his back, which gives him a bigger say in the centre (in other words, it will become difficult for White to consolidate his centre moyo), and so it is actually more like 5point sente. At this stage there are moves all over the place that can gain 5 points per move. Attachment: O Meien p150a.png [ 3.91 KiB  Viewed 3475 times ] Diagram 3 Diagram 3: It is good enough for Black if he defends against White’s further incursion at 1 with 2. Attachment: O Meien p150b.png [ 4.31 KiB  Viewed 3475 times ] Diagram 4 Diagram 4: Also, if White slides in at 1, Black can omit yet another move and defend free of concern against White 3 with 4 and 6. At any rate a Black move to defend the lower side is small. Playing elsewhere is the right answer here. 
Author:  John Fairbairn [ Thu Aug 30, 2018 12:06 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
TRANSLATION CONTINUED The capture of four stones may be big but … If White looks elsewhere … Attachment: O Meien p150c.png [ 9.66 KiB  Viewed 3474 times ] Diagram 5 (Black 2 omitted) Diagram 5: White’s diagonal play at 1 also commands attention. This move is not just coming back to connect up his four stones; it is also promising the sente boundary plays next from White 3 to Black 8, and so in that respect it is extremely big. Attachment: O Meien p151.png [ 9.7 KiB  Viewed 3474 times ] Diagram 6 Diagram 6: Therefore, for Black, the move 1 to enfold the four White stones is a really big move. The block at A on the lower side is at best something like a 5point reverse sente, and it should be apparent that in size it bears no comparison with Black 1. I therefore wanted to play Black 1, but there was one concern. Yes, White 4, swelling his moyo in the centre, is what I feared most. In this game, the only unresolved area is the centre, and if White can puff himself up in this area it would cast a great shadow over Black’ s prospects. Because Black can erase with something like 5 (I didn’t feel confident about intruding any further for fear of being counterattacked), the moves up to White 12 can be expected. Let us try an evaluation of this position (see next diagram). Attachment: O Meien p152.png [ 10.9 KiB  Viewed 3474 times ] Diagram 7 Diagram 7: Black’s territory is marked and White’s is marked X. As regards how to count the swathe in the lower right, we first assume that if White starts and forces with White A, Black B. If Black starts, with C, then White D, Black E, White F is forced and the cut at Black G remains, so that the territory at the triangled White stone is counted as a Black territory of 1 point. Therefore: * Black’s territory: 69 points * White’s territory: 67 points. Even if we consider that next it is Black’s turn to play, we can hardly say that Black can feel confident about this position. The consequence is that capturing the four White stones with Black 1 in Diagram 6 is dubious. 
Author:  John Fairbairn [ Thu Aug 30, 2018 12:10 am ]  
Post subject:  Re: Review: The Endgame (Ogawa / Davies)  
TRANSLATION CONTINUED First preventing expansion of the moyo Attachment: O Meien p153a.png [ 8.51 KiB  Viewed 3474 times ] Diagram 8 Diagram 8: I therefore turned to Black 1 to whittle down White’s moyo. It would have been dangerous to go any further than this, and so this was as far as I could intrude. In addition, it looks at Black A next and so it is a doublepurpose move. After suffering this Black A, White will see his territory on the left side reduce by about 10 points. Attachment: O Meien p153b.png [ 11.8 KiB  Viewed 3474 times ] Diagram 9 Diagram 9: Therefore, Koichi defended at White 1. Then I captured the four White stones with Black 2. The assessment must be that the exchange of Black 1 in Diagram 8 and the White 1 here has played a major role in blocking the development of the White moyo before it got started. Play then proceeded up to Black 33, at which point we can again do an evaluation of the position. It will be clear to what extent the exchange of Black 1 in Diagram 8 and White 1 in Diagram 9 has been a plus.

Author:  John Fairbairn [ Thu Aug 30, 2018 12:14 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
TRANSLATION ENDS Attachment: O Meien p154.png [ 10.66 KiB  Viewed 3474 times ] Diagram 10 Diagram 10: The situation as regards the growth of the White moyo compared with Diagram 7 is very different, isn’t it? Nevertheless, White is still thick and so he can expect a point around A. * Black territory: 74 points * White territory: 64 points It is White to play next. The biggest move on the board is an 8point gote at White B. Therefore the “value of the move” is half that, or 4 points, and so the “advantage of first move” is half again of that, or 2 points. Adding the “margin of error” of 1 point (half the advantage of first move) to these 2 points, 3 points are added to White’s territory of 64 points to give 67 points, but that still leaves him 7 points behind on the board (and at the time of this game komi was still 5½ points). We can say that as long as the figure produced by adding the advantage of first move and the margin of error gives a lead, even by as little as half a point, you can be 99% certain. Therefore the light showing certainty of election can be switched for Black at this point in the game. Attachment: O Meien p155.png [ 17.44 KiB  Viewed 3474 times ] Rest of moves (154 ~238) This is the endgame played after Diagram 9. Eventually Black won by 2½ points. I was very happy to have my second win in a league. Key point of this game The main focus was on Diagrams 5 ~ 8. If I could have won by simply capturing the four White stones with Black 1 in Diagram 5, that would have been best. But I could not feel confident about that after the evaluation done in Diagram 7, and so I had to look for a move that would reduce White’s moyo. I hope you can all appreciate the dynamics around here. 
Author:  Tami [ Thu Aug 30, 2018 12:57 am ] 
Post subject:  Re: Review: The Endgame (Ogawa / Davies) 
Thanks John for providing this lengthy excerpt from O Meien. It was very interesting indeed! I am going to put his book onto my "to acquire" list. Judging from your translation, it sounds like an O Meien book that I might be actually be able to understand in Japanese (I've tried Zone Press Park in both the original and in English, and neither makes much sense to me). 
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