@5598
"only 10^17 positions will need to be examined" ++ Yes, that is right.
"the last TCEC superfinal games"
++ TCEC has 50 imposed openings chosen to be slightly unbalanced:
not too balanced to avoid all draws, not too unbalanced to avoid win / loss.
"The average length of these games is 74 moves" ++ They play on too long.
In ICCF the humans would agree on a draw sooner when there is no hope for either side to win.
"If all analysis games were the same length, a branching factor (adjusted for transposition) of 3 would give 2x10^35 positions." ++ That is neglecting transpositions, essential in Chess.
As said before: with width w and depth d
Upper bound without transpositions 1 + w + w² + w³ + ... w^d = (w^(d+1) - 1) / (w - 1)
Lower bound with full transpositions 1 + w/1! + w²/2! + w³/3! + ... = e^w, regardless of d
For an estimate take the geometric mean of the upper bound and the lower bound.
"Even a branching factor of 2 would give more than 10^22 positions."
++ Neglecting transpositions.
"the game lengths go up to 135 moves" ++ Because they play on too long.
"To illustrate, the average from 1 to 135 of 2^n is 6.45e38" ++ neglecting transpositions.
This also proves the upper bound is way too high: there are less than 10^32 positions that can result from optimal play by both players.
https://arxiv.org/abs/2112.09386
@5596
"how can us humans say a move is a blunder"
++ We have ample evidence that chess is a draw. Thus each decisive game must contain an odd number of mistakes, at least 1. By inspection it is possible to identify at least 1 mistake.
"How can we humans say a move is the best move"
++ We cannot, except for positions with 7 men or less, which have been strongly solved.
We also have statistical evidence. We can say that all the moves of a drawn game in the ICCF world championship finals are > 99% certain to be optimal moves.
For example all moves in this game https://www.iccf.com/game?id=1164259 are > 99% sure to be optimal moves. There is < 1% probability that there are 2 mistakes that undo each other.
Funniest one yet?
Here @tygxc is justifying one of the steps in his faulty reasoning to show chess is a forced draw by starting by assuming the conclusion that chess is a forced draw! Of course, this is a well-known fallacy.
Classic Fallacy 1: Assuming the Conclusion
It's worth drawing attention to another fallacy implicit in almost all of @tygxc's posts, including the above - arguing that something is probable and then assuming it has become certain. He does this twice in above single post! First he thinks "ample evidence" suffices to prove the conclusion that chess is a draw by induction. No. Not a proof. Then he uses "statistical evidence" to justify a claim he then relies on as certain.
This can never be done in a legitimate proof.
Classic Fallacy 2: Appeal to Probability