"If humans and A0 (and engines) share a lot of knowledge, how can they be totally different"
++ Because in the vast majority of legal, sensible, reachable, and relevant postions all that acquired knowledge is not sufficient to select a correct move flawlessly.
We agree on that, but that does not prove they their decisions are totally different and uncorrelated.
"if I find that the evaluations of two equally strong engines are correlated, how can their errors (i.e. they play a non-optimal move), which are based on those evaluations, be totally uncorrelated?"
++ I gave the example of equally strong Tal and Petrosian engines. Sometimes the Tal engine wins because the Petrosian engine erroneously allows a correct sacrifice. Sometimes the Petrosian engine wins because the Tal engine sacrifices incorrectly. At the decision neither of them knows if it is correct or not. A bias in allowing or making sacrifices explains the errors.
But you exclude that their ignorance can lead to a chain of errors by the two, because they both ignore one made a mistake, but to you at least one of them knows how to play perfectly, even with a flawed evaluation...
"Should I do the homework for you?" ++ No, I did my homework, you do yours.
How convenient for you.
"Can you post the link to the exact page/s you are talking about?"
++ No, I use a link I cannot post here. Google, TCEC superfinals gets you there. https://tcec-chess.com/ is the official site, but a bit difficult to navigate.
"I am trying to determine if the statistical independence can be proven without assuming it as a premise" ++ Well TCEC provides ample data, just like ICCF
In other words, we cannot know exactly which data you used and how, and that should substatiate your assumptions. Fantastic.
"I am trying to determine if the statistical independence can be proven without assuming it as a premise" ++ Well TCEC provides ample data, just like ICCF
Very precise and unambiguos, as usual.
#3411
"If humans and A0 (and engines) share a lot of knowledge, how can they be totally different"
++ Because in the vast majority of legal, sensible, reachable, and relevant postions all that acquired knowledge is not sufficient to select a correct move flawlessly.
"if I find that the evaluations of two equally strong engines are correlated, how can their errors (i.e. they play a non-optimal move), which are based on those evaluations, be totally uncorrelated?"
++ I gave the example of equally strong Tal and Petrosian engines. Sometimes the Tal engine wins because the Petrosian engine erroneously allows a correct sacrifice. Sometimes the Petrosian engine wins because the Tal engine sacrifices incorrectly. At the decision neither of them knows if it is correct or not. A bias in allowing or making sacrifices explains the errors.
"Should I do the homework for you?" ++ No, I did my homework, you do yours.
"Can you post the link to the exact page/s you are talking about?"
++ No, I use a link I cannot post here. Google, TCEC superfinals gets you there. https://tcec-chess.com/ is the official site, but a bit difficult to navigate.
"I am trying to determine if the statistical independence can be proven without assuming it as a premise" ++ Well TCEC provides ample data, just like ICCF