Informal global endgame theory

[RobertJasiek]

Probably they aren't relevant enough to be included

Of course, there can also be flawed ad hoc theory. Without such, we might not always be able to find correct, permanent theory.

I note that all your principles are about the structure of endgame trees like in CGT. Shapes on the board such as thickness, tesuji are not mentioned, which is probably what pros talk more about. For example Gopro yeonwoo made an endgame video, and it made me wonder about when it is right to play from inside the territory (i.e. cut) vs from outside. It is probably somewhat related to inside/outside in semeais. And might be worth investigation.

Currently, I study the purely territorial aspects of the endgame. Already they are very much richer than one might expect at first. Bill will tell you to have spent some 5 decades on them and my related study has at least reached a couple of years now.

One can also study non-territorial aspects (such as those you mention) but most of that belongs to the middle game.

Before we can hope to develop a systematic understanding of the combination of territorial and non-territorial aspects, we must first establish it for territorial aspects alone. It was done for the basic microendgames. (Bill started to do it and) I am doing it for the large territorial endgame.

[RobertJasiek]

You suggest mutual reduction if there are more local endgames with the opponent's follow-ups than local endgames with the player's follow-ups. Please explain why you think so and why it should be independent of local move values and follow-up move values!

(I cannot read your SGF in GoWrite.)

[dhu163]

I will be quite busy in the foreseeable future, and I wanted to reply properly, so it took me a while.

Thanks for your reply. I aim to read some of Bill's work and your work.

I'm not sure what you classify as "informal endgame theory".
Personally, my ideas are mostly based around miai counting (which I learnt from Sensei's library) because I think the mean value theorem makes non-trivial progress. But miai counting does seem to have some flaws around distinguishing gote/sente and hence infinitesimals. As far as I can tell, your first post is pretty much a list of the concepts that miai counting is based on (in the sense that "play gote in order of decreasing move values" isn't as good advice if you use deiri counting)

For sure move values come first. Tedomari is subtle enough that it is as easy to lose as gain if you don't read far enough ahead, and even if you succeed in tedomari, you gain at most the largest move value (in the rest of the game) compared to the greedy algorithm of always taking the move of largest miai value.

As for mutual reduction, I guess one would need to define or work out what counts as a defender's endgame tree vs attacker's.

All else being equal, my point was that mutual reduction only works if you have some sort of advantage that breaks the symmetry, generally being "thicker" on the board, or having more follow ups from going further into your opponent's area (the opposite of how you phrased my point). I now see that what I said about more follow ups may be misleading, at the least it is non-linear. It seems not so easy to describe what the conditions are for mutual reduction to work except in the simplest cases.

You could view this in terms of miai values: if your follow ups are larger/sente this increases the miai values of moves you play attacking your opponent's territory rather than defending your own.

You could also view this in terms of the structure of the game tree (my point still can hold if miai values are the same). For example you could say that in the defender's tree, there are more places for them to retreat to and often just one move of theirs will settle the position, whereas for the attacker to enter further, they need several moves in a row. This becomes related to the UPs and DOWNs of CGT. In my sgf there was the most simple scenario of two corridors that end in TINY/MINY and that you have the opportunity to play a mutual reduction if the corridor lengths are equal and you have a larger sente at the end.

If the corridor lengths are not equal or there are multiple, I'm not sure what happens. But in the simple case of two corridors ending in TINY/MINY, it seems your phrasing works (sort of). If the corridor in your opponent's territory is shorter, you have an advantage because you can reach the sente faster before coming back to defend your own. (it is a bit like moves closer to the root of the game tree count with a higher weight than those further down)

I wrote up some somewhat related ideas, nothing to do with mutual reduction, but just some calculations of elementary endgame scenarios over the last few days here: https://dhu163go.files.wordpress.com/20 ... ciples.pdf

I see there has been a lot of discussion on the endgame on L19 over the last few years and I hope to read some of it.

[Bill Spight]

Global endgame theory is definitely not traditional go endgame theory, except for getting the last play, which is not at all developed. Traditional go endgame theory is mainly about estimating local territory and the size of local plays. It makes use of sente and gote, but they are not formally defined. Combinatorial game theory (CGT) is a more formal theory of local positions and plays, in which it is possible to formally define local sente, gote, and ambiguous positions. In both traditional go theory and CGT whose turn it is is not part of the definition of a game.

There is another type of game theory in which whose turn it is is part of the definition of the game. Starting from node A in the game tree with perfect play to leaf node Z, the value of A is equal to the value of Z. It is possible to evaluate a game node as win, loss, or draw, or as a score. There is only one game, so this is indeed a global game theory. With alternating play, sente and gote have no global meaning. Without knowing correct play, today's neural net bots can evaluate a node in terms of the estimated probability of winning, given certain assumptions. These estimates provide an informal global endgame theory.

There are problems with such a theory for human play. First, humans cannot make these evaluations. A theory of how humans might evaluate positions and plays has not yet been developed, nor even how to make relative evaluations. Second, humans play differently from bots, and the assumptions behind these evaluations are typically that bots are playing. Third, humans play better than bots in some ways. A good global theory should take these human plays into account.

Not to be particularly discouraging, because I do think that better endgame theories for humans can be developed with the help of neural networks, but not very quickly. Meanwhile, the proof is in the pudding. How well do certain rules of thumb work, and under what conditions?

[RobertJasiek]

dhu163, I read your paper a bit later. BTW, except for CGT people, the number of people digging into formal endgame theory has recently increased from 2 to 5. The future is bright! :)

Formal endgame theory is established as maths. Informal endgame theory is not. Of course, there is a grey area of principles and methods containing cores that we can hope to be proved by maths later but whose presuppositions might need to be worked out carefully and possibly corrected.

Classification of local endgames as gote / sente etc. is not flawed per se but does not claim to always predict global play in global environments. A local gote / sente need not be a global gote / sente.

Not move values come first but scores do, then counts.

Mutual reduction does not only occur as a consequence of thickness but also occurs in the microendgame. Right, solving mutual reduction in general is hard.

Bill, traditional endgame theory is not only about local sizes but also about tactical reading and the occasionally useful, but heavily over-emphasised tesujis.

Some theories of positional judgement have been developed (see, e.g., my texts) but they float in the air without being based on and derived from low level maths. Such theories are very useful in practice but unproved in maths.