Review: The Endgame (Ogawa / Davies)

[RobertJasiek]

As a player, my endgame has improved a lot from considering fractions whenever necessary. Previously, Hayashi Kozo (the currently most popular professional visiting EGCs) noticed my strong positional judgement during the middle game but now he is more impressed by my endgame, praising it regularly.

I also like efficient time management and use simpler evaluations or comparisons when applicable correctly. My calculation speed is still somewhat slow for iterative follow-ups but what used to be 10 - 20 minutes per difficult local endgame a couple of years ago has become more like 15 seconds to 4 minutes. This acceleration is mostly the effect of understanding the theory well now. Surely, I need much more practice to further accelerate such calculations.

Also the microendgame helps. It makes a great difference having no idea at all versus understanding its basics. Fractions hardly need to be calculated for the microendgame because there are simpler principles. Nevertheless, understanding what the fractions or integers are in principle assists the overall understanding of the microendgame.

Playing under area scoring without knowing any of its endgame theory lets one feel hopelessly lost and spend 10 minutes on counting stones and whatnot. The theory is simple but rediscovering it during one's game is close to impossible.

Ko evaluation has become much easier. Now I profit from my opponent's mistakes if they have neglected study of the theory.

The occasional tesuji helps, especially if the opponent overlooks it. Reading blunders of overlooking simple variations may be my greatest endgame weakness at the moment.

Especially weaker opponents make (even big) mistakes in endgame evaluation when relying too much on guessing relative sizes of move values instead of calculating them at least accurately enough for comparing them numerically to close alternative candidates.

[Bill Spight]

As a practical matter, my attitude towards 16ths is pretty much the same as my attitude towards winrate differences of less than 1%: Don't strain after gnats. However, that attitude does not extend to 8ths, based upon traditional yose literature, where it is usual to talk of values of plays as 4 pts. plus or 6½ pts. minus. OC, these are deiri values. To translate to miai values we divide by 2, so 6½ pts. minus becomes 3¼ pts. minus. 3¼ pts. minus covers the range between 3¼ and 3; IOW, 3⅛ more or less. To get to 8ths only requires reading and calculating to depth 3, after all. That is practical.

That said, if the game is very close, where a difference of 1 pt. matters, an error of 1/16 pt. is on the order of a winrate error of 6.25%, which we regard as serious. (It matters by area scoring, as well. Remember that a 1 pt. error by territory scoring can become a 2 pt. error by area scoring.)

Well, it's my bedtime. More later.

[John Fairbairn]

I think the wrong question is being answered. The real question is implicit in what knotwilg wrote, and even in how Robert answered. If you have limited study time (as all amateurs and even many pros do) is it better to spend it on, say, endgame tesujis or learning to calculate sixteenths at high speed? Robert says: "Reading blunders of overlooking simple variations may be my greatest endgame weakness at the moment." I rest my case, m'lud.

Actually, I don't. I think even more fundamental to all this is personality type. Within sensible limits, no one type is better than another, of course, and I'm sure only the sensible types are represented here.

There is another example of Robert's type I'm familiar with in linguistics. Gaelic pronunciation is notoriously difficult. People write jokey books about it, but most people run away in fright. My father was fond of Gaelic and I was a linguist, but I too was one of those who ran away. As an example, not at all exaggerated, of the difficulties, take the common word piobaireachd. In its Scots/English form of pibroch the word is familiar to more than a few English speakers, even in the US, as "something to do with bagpipes" even if they don't quite know what it means (it's a way of playing variations on a theme, usually a funerary or martial theme, and it's therefore a big component in bagpipe competitions). See, you haven't wasted time reading this - you've learnt something new and important!

Now there's a scholar who has written a very large book of nearly 600 pages that is designed to tell you how to pronounce (Scots) Gaelic. It doesn't teach anything else - no grammar, no vocabulary. Many Gaelic speakers claim that the Gaelic spelling system is a divine and beautiful creation, ignoring the fact that the system has been changed quite regularly and recently, which means that using a dictionary more than a few weeks old can be rather fraught. Our scholar is not quite so impressed by the hand of God but does believe that the system is beautiful because it is logical and consistent, and you can turn the rules into a list. You can see the analogy with our go scene, I'm sure.

The scholar's work is actually very impressive (and the book is rather well written). But if you want to know how to pronounce the letter e, for example, you have to work your way through a list of 29 rules. To take just the first rather simple rule, you have to establish whether it is accented and whether it is followed by m, mh or p. And once you've done that the rule tells you only that it is usually pronounced in a certain way. Some other rules can take almost a whole page to work through. Each letter has many such rules and the total number of rules is of the order of 450, and the list alone takes over 100 pages. Our scholar obviously enjoyed compiling it.

This is the Gaelic equivalent of sixteenths. But guess what. It's easy to find words that aren't covered by the rules, and kids speaking Gaelic on the Isle of Skye manage perfectly well without this book, as in the past have great poets such as Sorley Maclean (or as he would have written it: Somhairle MacGill-Eain).

Again, I think you can see the analogy with go.

So it's not just a question of how you best allocate your time. It's also a question of what you enjoy doing. But my experience is that most people would prefer to improve by 10 points rather than by a sixteenth of a point.

[Pio2001]

I will read Robert's new book because I am interested in a better understanding of the theory, even if my level doesn't improve.

My goal is not to become a champion, or to spend all my free time working hard in order to gain a few kyus. My goal is to enjoy a game that I like. And I would like to learn about endgame theory, just for fun, if not to improve. I won't crush my opponent using this knowledge, but it will turn the endgame part more enjoyable.

I am currently 5 kyu KGS / 9 kyu french rating. Regarding endgame theory, I have read Learn to Play go until volume 5 (Janice Kim), Yose (Dai Junfu), and First Fundamentals (Robert Jasiek).

For the time being, the only counting method that I am aware of is counting the difference between the position after black to play and the position after white to play. But it is awfully confusing in area scoring because the values are affected by the number of black and white stones played. It even seems to completely loose its meaning when there are follow-ups, the area values diverging completely from the territory values. I have more or less admitted that anyway, territory counting does the job all right, since in most situations, the outcome is nearly the same under both rules.

I have always learned to prioritize double sente, then sente, then reverse sente, then gote, but I could never remember which one is worth the double of which one. I just know that something doubles somewhere.

Playing double sente before sente, and reverse sente before double gote seems natural to me : if sente is better than gote, then removing sente moves from my opponent's possibilities is good for me.

I've learned in my club, from a dan player commenting one of my games, that I didn't have to sheepishly follow the sente moves of my opponent : it is always possible to answer a sente move with another sente move elsewhere.
This illuminating moment opened the world of mutual reduction and the relativity of "sente" to me. Obviously, if I answer a sente move with another sente, my opponent has the choice between answering my sente (And I get half of the endgame sequences instead of leaving everything to the opponent), or starting the mutual reduction, and I'd better have chosen a more dangerous sente than him, or the mutual reduction will be at my disadvantage !

Using the little I know about endgame theory, I came to the conclusion that I should play a 2 points gote endgame before pushing into a corridor, because in the latter case the value should be something like 1 + 1/2 + 1/4 etc gote, which is less than 2. But since the values are so close, any other consideration, such as safety of the overall group, or psychological pressure (luring my opponent into believing that the move is sente) etc, takes precedence.

I have always been confused by the values of kos. I came to the conclusion that the last ko (if it has no follow up) has an absolute value of two intersections changing colours in area scoring (french rules), rather than 1/3rd of a point, although I admit (without understanding the demonstration) that 1/3 of a point is the right endgame count to use in order to prioritize it among other possible endgame moves. So I always fight the last ko after everything else and before filling the dame.
However, I am completely unable to know the value of a pair of two kos one opening the other, and with no other follow up after the second ko is connected. I don't know if I have to try to win this before a 2 points gote endgame.
Although this is not something important in my games, I feel very frustrated by my complete inability to understand such a basic position. That's why I am interested in microendgame. Not to win tournaments, but to understand what I am doing.

[RobertJasiek]

As I have always said, avoiding blunders is the first priority. This does not mean one should not study anything else just because one makes blunders. We also know that improvement fails if one neglects a study field too much. Neglecting endgame evaluation entirely is no option at all.

Learning tesujis is a fast way for improving a rank or two as 12 - 8 kyu. As is learning to stop the monkey jump at all.

Most endgame decisions can be guesswork because it is fairly easily to distinguish moves of significantly different sizes. This still leaves, say, 40% of the endgame value decisions to be done by calculation. Almost all endgame moves depend on size rather than tesuji or reading. That is, avoiding calculation entirely is plainly wrong for SDK / dan players.

When learning, it is possible to calculate +-3, then +-2, +-1, +-1/2, +-1/4, +-1/8, and eventually accurate whenever possible. 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. That is why I do not recommend sticking to rounding for too long. (More) accurate calculations have just a too great impact because there are too many endgame moves and moves with endgame aspect earlier during the game.

[Knotwilg]

As I have always said, avoiding blunders is the first priority. This does not mean one should not study anything else just because one makes blunders. We also know that improvement fails if one neglects a study field too much. Neglecting endgame evaluation entirely is no option at all.

Learning tesujis is a fast way for improving a rank or two as 12 - 8 kyu. As is learning to stop the monkey jump at all.

Most endgame decisions can be guesswork because it is fairly easily to distinguish moves of significantly different sizes. This still leaves, say, 40% of the endgame value decisions to be done by calculation. Almost all endgame moves depend on size rather than tesuji or reading. That is, avoiding calculation entirely is plainly wrong for SDK / dan players.

When learning, it is possible to calculate +-3, then +-2, +-1, +-1/2, +-1/4, +-1/8, and eventually accurate whenever possible. 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. That is why I do not recommend sticking to rounding for too long. (More) accurate calculations have just a too great impact because there are too many endgame moves and moves with endgame aspect earlier during the game.

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. There is another way, the way chosen by native speakers and professional go players. As amateurs moving into the matter in adult life, it is almost impossible to catch up with native speakers or go professionals who learnt go at an early age. So it may be that the book of Gaelic pronunciation or fractions are the better way for amateur latecomers. My bet is on emulating the native/professional way, even if we keep falling short. Probably I find that more enjoyable too, but clearly others enjoy different ways.

[RobertJasiek]

As interesting as Gaelic may be in itself, how can a dynamic pronunciation be a good metaphor for a static endgame (regardless whether we consider the game tree of go or of a particular go game position)?

You mention the way chosen by professional go players, uhm, but aren't they different? What are their ways aka degrees of accuracy during the endgame? For decades, I have heard praise of professionals attempting to fight for the last point, by myth perfect endgame during the Edo period and admiration of exceptional skill such as Ishida Yoshio, the "computer". I have mentioned more evidence.

Just to repeat the obvious: there is nothing wrong with approximations IF WE KNOW THAT THEY STILL PRODUCE CORRECT RESULTS. Are there any professionals that play flawed endgame deliberately? I do not think so. When approximations are not good enough to determine correct play, we do need accurate (or almost accurate approximative) calculations.

[Uberdude]

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.

[RobertJasiek]

His follow-up report is here http://mateuszsurma.pl/en/2016/05/

[Knotwilg]

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?

[Uberdude]

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.

[John Fairbairn]

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 o-yose 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.

[Gomoto]

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.

[RobertJasiek]

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.

[Bill Spight]

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.