Bill Spight wrote:
the insights about CGT infinitesimals can help us to realize when non-infinitesimals act like infinitesimals.
Uhm, how? With which applications? (I am still learning infinitesimals...)
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games and, hence, sums of games can be simplified by recognizing dominance and reversals, both of which may be analyzed using difference games.
We can take dominance, traversal (reversal is a misnomer by CGT people creating unnecessary confusion with [e.g., joseki] reversal and offering no hint about meaning, whereas traversal offers a hint: just traverse the skipped part of a tree) and equal options for granted.
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I have also done a good bit of work with difference games. :) Some of what I have found is fairly general.
I guess. We all await your publication on (also) this topic.
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I don't know what use there might be for an environment of plays of the form, {a | b || c}, a ≥ b ≥ c,
For the early endgame, an environment of simple gotes is good enough. For the (very) late endgame, we do not need additional complexity by introducing any environment at all.
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but we may order those plays such that, given two such plays, A = {a | b || c} and D = {d | e || f}, if d - e ≥ a - b and e - f ≥ b - c, then each player does at least as well to play in D as in A, with the usual caveat about no kos.
Considering these two plays (possibly in an environment of unknown details), is this useful during the early endgame? It seems useful during the late endgame and related to our recent proofs. I need to study the relation between this and our recent study. If this is genuinely different, do you already have the proof available?
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When asking for general insight about iterative follow-ups, I have had in mind first of all the late endgame and local endgames (also) with iteration deeper than 1 step. Apart from dominance, traversal, equal options and occasional use of infinitesimals, do we still know essentially nothing general other than reading (and playing simple gotes in decreasing order)? I ask because reading quickly explodes even for just a few local endgames with follow-ups.
Everywhere I see endless praise of professionals said to be playing near perfect (late) endgame, but what is the justification for this? Has anybody done systematic studies (not just for one game or two) of whether professional endgames are played correctly? Proving correctness can be hard easily. Can we do it for, say, the late endgame stage with "only" ca. 7 local endgames with (possibly) iterative follow-ups and move values larger than 1 (together with some simple gotes and local endgames with iterative follow-ups and move value 1 or smaller)? Is the praise of professional endgame play not just our excuse for not actually studying the late endgame carefully? Asked from the complementary view, if we know that professionals play perfect late endgame, what theory is it that we should be knowing and applying WRT iterative follow-ups of local endgames with move values larger than 1? Recall the evidence of Mathematical Go Endgames that they (and we) do not even play move values 1 correctly:) Instead of myths, I want real, proven, applicable theory.