Yes. We pretty much have to rely upon experience there. In a way it is a statistical question, but questions such as the universe of players arise. If your opponents do not punish your errors, making them isn't so bad.John Fairbairn wrote:If they do try to play an endgame properly, I suspect most people this way most of the time - perhaps even pros, too. Calculating the numbers is indeed easy enough. What is not easy is to form a view on how much it matters (on average) when using these values turns out to be wrong.deiri values are fine, and perhaps easier for most people to handle....As we know, playing the averages by choosing the theoretically largest play is typically correct, and not often wrong
Not having good numbers does not mean that words are better. Since experience matters, feelings and hunches may be best.John Fairbairn wrote:Such a view by an endgame expert is one of the things I have in mind when I argue in favour of words and not purely numbers in the exposition of boundary play.
Based on my experience, starting from the mid-endgame, where plays gain on average around 5 points, low level dans chuck around 15 points. To anticipate the discussion below, if they play solidly they can probably cut that loss in half. If their opponent does not play solidly, the question then becomes how well they can punish their opponent's mistakes.If, for example, it turns out that at low dan level the most you can lose on average in a typical endgame against a player of your level (who makes the same sort of mistakes) is just 5 points, it would be very useful to know that. MUCH MUCH more useful than being told how to calculate fractions of a move value,
It is painfully obvious that most of them are not.John Fairbairn wrote:I can understand that endgame books are usually written by people of mathematical bent
Although Mathematical Go sold pretty well, especially in Japan, I felt that it suffered from having a dual audience, one of mathematicians and one of go players. It was not easy to satisfy both.John Fairbairn wrote:But I say they have to be less concerned with what other mathematicians might think of them and more concerned with how they can help the typical reader.
Back in 2011 I decided to write an endgame book aimed at middle SDKs, and assembled a group of readers who would give me feedback. To my surprise, it wasn't the math that was the problem, it was the go.
The obvious one is the strategy of playing the largest play, AKA hotstrat. The main exception comes when there is a significant drop in the global temperature. It will often be worth playing to get the last play before that drop. This is something that go players noticed long ago, leading to the advice to get the last big play of the opening, the last play of the large yose, and the last play of the game. For the last play of the game, there are both absolute plays and heuristics. My research with the Elf files suggests that getting the last big play of the opening is almost worthless advice. There is in general no significant temperature drop between the opening and the middle game. I have, however, come up with the following last play advice, which is to occupy the last open corner, as a rule. I know that occupying any open corner is said to be good, but in the pre-AI era pros often left the last open corner unoccupied in order to fight elsewhere. That was usually an error. Getting the last large yose does seem to be good advice. More on that later.John Fairbairn wrote:I'm sure I'm part of a chorus here: what are they?Theory only provides heuristics.
Professor Berlekamp came up with a heuristic he called sentestrat, which is basically to answer your opponent's sente if it raises the global temperature. The idea is to limit your losses. Berlekamp was around 3 kyu, and I privately scoffed at the idea, dubbing it gotestrat. As a dan player I felt that I was duty bound to find a good intervening play, if I could. Sentestrat sounded like trying to make a virtue of followitis. Berlekamp was right about limiting your losses, OC.
But consider your question about how many points a low dan chucks in the endgame. Sentestrat is a way that they could limit their losses. It goes against the grain, but there we are. High dans and pros may interpose a play instead of meekly replying to an opponent's sente. OC, we cannot say that they are wrong to do so, but the result is often a fairly long term increase in the global temperature. When that occurs, it will frequently become important to get the last play before the temperature drops back down. This is why I say that getting the last big yose is often a good idea.
This kind of phenomenon cannot simply be observed by words. It is necessary to have the technical chops to do so.
Today's top bots do not often seem to play thickly, but play lightly and flexibly. That style of play may be difficult for humans to emulate, given our propensity for depth first search. However, especially at the large yose stage, it behooves us to be on the lookout for temperature drops and to consider tenuki when that happens.
The reputation of the Edo players is mostly intact. True, the bots may differ, but the large yose is one place where humans, given enough time, may play better than today's bots. By the 20th century, with 10 hours of time, I noted in the 1970s that top pros rarely made errors when the average gain dropped below 3 points. 3 points is in the middle yose range.John Fairbairn wrote:That doesn't seem to square with Edo players being so good at the endgame.However, by the 1970s players and writers realized that there was a theoretical problem with double sente.
I acknowledged that at the time, didn't I? But O Meien did not include double sente as a classification for calculating the size of plays, which was, and is, my concern. Kano in the 70s and the Nihon Kiin, as late as 2000, tripped up badly in that regard. As I said above, it is not difficult to find examples of double sente in practice. The problem is that it is too easy to find false examples if you believe in double sente.John Fairbairn wrote:But, leaving that aside I'll make a couple of other points. One is that you say in the thread you referenced that O Meien didn't talk about double sente. He did, twice, and on one occasion said he felt smug about playing it.
As you know, I gradually developed a thick style of play. The bots would probably regard it as heavy, what can I say? But one advantage of playing thickly in the large yose, or maybe earlier, is that it frees you play enterprisingly to take advantage of your opponent's misplays. Also, IMX, when the average gain drops to around 7 points is often when plays in the corner, often involving ko, become significant again. Thick play prepares the way for ko fights by reducing the number of possible ko threats by the opponent.John Fairbairn wrote:Switching back to words over numbers, one of the most noticeable features of pro commentaries towards the end of a game is that they VERY rarely mention numbers (for move sizes) but they BVERY often describe a move or a position as thick, and therefore advantageous.
In vol. 6 of Sakata no Go, which is about endgame calculation, Sakata shows a good example of thick play in the endgame. That play allowed Sakata to continue enterprisingly. To show the advantage of the thick play, you cannot just rely upon words, you have to have the technical chops.John Fairbairn wrote:Now it seems to be that if it is worth harping on about gaining a point or a fraction in the micro-endgame (not that I think it is, but there's an 'if' in there), then it must be worth a humungous amount more to study the earlier and bigger stage when thick moves or positions become an issue. It would be immensely valuable, therefore, to have an authoritative endgame writer write a book or a chapter on how and when to play such thick moves, how to recognise andr appreciate them, and so on. There's vast number of examples in the literature. This exposition would have to be done mostly in words, of course, but that underlies my point: words are more useful than numbers for many people. Instead of improving by a point two you can look forward to improving by a grade or two.
This is speculative, but it may well be that thick play tends to produce positions where humans, even strong amateurs, can play better than today's bots. I doubt if I well be able to research that question, but I think it is worth doing.
