Don Dailey wrote:
You are still missing the point.
I can say the same of you.

I merely am raising a question about the assertion that doubling of _human_ thinking time results in _linear_ improvements. I am not claiming that there is no improvement - never have. I am not claiming that every turn must produce better results to improve overall play - never have. However I am trying to explain a rationale for the possibility that improvements may not be linear based on the nature of Go.

What you are describing looks great on paper,  but that's now how
the extra time works.   Even if you are given 10X more time,  the
benefit will come from not from suddenly being able to grasp master
level concepts, but from repairing the little mundane problems that are just within your reach.
How do you know this? Improvements could come from many other different sources.


And it will only effect a small number of moves.   Most of the
moves will be exactly as you say, confusing, and you will not be
able to improve them (and I think this is the partly the source of what I consider the misconception some of us are having.)
I don't have this "misconception". I basically agree with this and don't think I said anything explicitly contradictory to this.


The other source of the misconception you also touched on.  You
mentioned "enormous extra time", which is correct.  It DOES INDEED
require enormous extra time,  even in computer chess to make
anything more than a modest improvement.    The reason you just
can't imagine that "a lot" of extra time will help you play a
better move is because most of the time it won't! Your intuition is correct but your conclusion is incorrect.
You are putting words into my posts. As I said several times already I am not claiming extra time won't help improve play. Of course it will. You are not listening to my conclusion. Step back and re-read my posts. I don't claim my writing to be of super clarity and I might not be explaining myself well enough, but why not try to keep an open mind and not make assumptions about things I didn't write.


The improvement will come only from little mundane improvements
of a very small number of moves - but that is enough to make
your level of play go up a  bit.
Yes and improvement may also come from other insights as well.


Please note that for weak players,  a LOT of moves need to be
improved, and for strong players only a few need to be improved.
But the way this works is that the stronger you get, the more impact improving just a few moves makes because your
opponent is more likely to take advantage of your mistakes.
Sounds reasonable.

Someone once did a computer chess experiment with really long
and deep searches and they studied how often computers "changed
their minds" when making moves.   As it turns out,  the rate
of change (per ply or per doubling) tapers off as you go deeper
and deeper.    And yet the strength improvement is almost
the same for each doubling.
But I' not talking about computers or chess. I think there is already a consensus that the doubling rule holds well in chess. You don't have to continue to convince me of that.

The computers follow your cognitive intuition that you posted
about,  they can think for an enormous amount of time and still
not improve on the move.    Improvement isn't about making ALL the
moves better, only a few.   It's almost always possible, given
more time, to find some improvements in a few of your moves
and this is what makes you play better.
Yes. You are repeating yourself.

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