Review: The Endgame (Ogawa / Davies)

[Bill Spight]

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 ... 5-04-2016/ 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.

[Bill Spight]

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!

[Bill Spight]

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 9-11 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.

[John Fairbairn]

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 follow-up) 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 sub-themes.

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 "non-essential" 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 Potter-ish 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 jaw-dropping 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.

[RobertJasiek]

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 second-largest 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 non-ideal environments by a defensive error margin to predict whether a player has a guaranteed win.

[Bill Spight]

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.

[Uberdude]

Without any counting or calculation of endgame values, my inclination is not to block because I don't like being a wimp and white jumping in there isn't sente for any life and death and j2 being sente for a cut isn't too sad to answer. That h7 area is an awfully large open space where it's very hard for me to know what is even a a good first move for either side (white h6 probably easiest) let alone a long sequence of skilled reduction by black. Other important areas to my eye are B k13 (points and safety) vs W k14 and any life and death or gote endgame becoming sente on top group effects. And what's going on at q13, does black pull back or cut and could be a semedori.

[Knotwilg]

Edit:

When reading Uberdude's hidden post after publishing mine, I can see he found all the issues LZ found too

[John Fairbairn]

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: 4-8399-1508-3 ("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.

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’ang-ho.

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 so-and-so” or “for a pro this seems like a win or a loss at this point in time” without worrying too much about precise figures.

[John Fairbairn]

TRANSLATION (unedited)

Example 1: Black to play

O Meien p147.png (8.46 KiB) Viewed 16619 times

White: Kobayashi Koichi Meijin, Black: O Meien 6-dan; 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)

O Meien p148a.png (16.5 KiB) Viewed 16619 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 6-dan. It was my third game in the league, having scored 1-1.

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 …

O Meien p148b.png (9.08 KiB) Viewed 16619 times

Diagram 1

Diagram 1: Black’s attach-and-pullback 1 and 3 will end up being an especially large boundary play. Even just in de-iri terms of pure territory it is almost 20 points, and following this there remains Black A, White B and so on up to the push-through 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]

[John Fairbairn]

TRANSLATION CONTINUED

O Meien p149.png (9.41 KiB) Viewed 16618 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 5-point sente.

At this stage there are moves all over the place that can gain 5 points per move.

O Meien p150a.png (3.91 KiB) Viewed 16618 times

Diagram 3

Diagram 3: It is good enough for Black if he defends against White’s further incursion at 1 with 2.

O Meien p150b.png (4.31 KiB) Viewed 16618 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.

[John Fairbairn]

TRANSLATION CONTINUED

The capture of four stones may be big but …

If White looks elsewhere …

O Meien p150c.png (9.66 KiB) Viewed 16617 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.

O Meien p151.png (9.7 KiB) Viewed 16617 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 5-point 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 counter-attacked), the moves up to White 12 can be expected. Let us try an evaluation of this position (see next diagram).

O Meien p152.png (10.9 KiB) Viewed 16617 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.

[John Fairbairn]

TRANSLATION CONTINUED

First preventing expansion of the moyo

O Meien p153a.png (8.51 KiB) Viewed 16617 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 double-purpose move.

After suffering this Black A, White will see his territory on the left side reduce by about 10 points.

O Meien p153b.png (11.8 KiB) Viewed 16617 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.

[John Fairbairn]

TRANSLATION ENDS

O Meien p154.png (10.66 KiB) Viewed 16617 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 8-point 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.

O Meien p155.png (17.44 KiB) Viewed 16617 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.

[Tami]

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).