Single Comment

Hans Aberg:
| You do not get a theory that predicts winning chances, as chess 
| isn't random. If the assumption is that opponents will have a 
| random style similar in nature to the analyzed data, then it might 
| be used for predictions.
This is where we fundamentally differ, and it makes it completely
pointless to discuss anything in detail as long as we argue based on such
mutually excusive axioms. Chess as we play it is a game of chance, as
players don't have perfect knowledge, and thus randomly choose between
positions they cannot distinguish based on the knowledge they have. And
there is no logical necessity for the condition of similar randomness that
you impose. It is well known that the eventual distribution of  random
walker does not depend on the details of the steps he can make. Only on
the variance. (The central limit theorem of probability theory!) In
particular, it is an empirical fact that statistical analysis of
computer-computer games, as I did, produces the same winning probabilities
as analyzing GM games (as Kaufman did). So even if you were in principle
right (which I doubt) that sufficiently different nature of the randomness
would produce different overall statistics, observations then apparently
show that computers and Human GMs are not 'sufficiently different'.

| It is clear that Larry Kaufman does not think of his theory in 
| terms of 'x pawns ahead leads to a winning chance p'. You can 
| analyze your data and make such statements, but it is an incorrect 
| conclusion it will be a valid chess theory predicting future games 
| - it only refers to the data of past games you have analyzed.
For one, this is not clear at all, and very unlikely to be true. Anyway,
you cannot know what Kaufman thinks or doesn't. Fact is that he
translates the statistics into piece values in exactly the same way I do.
The rest of you statement is totally at odds with standard statistical
theory, which maintains that probabilities of stochastic events can be
measured to any desired accuracy / confidence by sampling. This is really
to ridiculous for words.