ironically your assumptions of correct gameplay outcomes arent even connected to your core errors, but i feel it is important to point them out regardless.
" If a black move leads to a 7-men endgame table base draw, then it is good enough to achieve the game-theoretic value of a draw."
you need to prove it leads to a draw or not, your explanation doesnt do that. it just puts it off.
@7809
"black is not inherently winning, that hasnt been proven"
++ That is proven. See https://www.iccf.com/tables
Assume Chess is a black or white win and try to fit a Poisson distribution of the number of errors per game such that the probability of an odd number of errors corresponds. It is impossible.
Assume Chess a draw and try to fit a Poisson distribution of the errors per game such that the probability of an odd number of errors per game is. It is possible and leads to >1000 perfect drawn games with optimal play from both sides.
White has the advantage of the initiative, worth 1 tempo, but not enough to win.
@7806
"for chess to be solved, an extremely strong engine needs to analyse an incredible 10^120 different games (estimation), a number higher than the number of atoms in the universe."
++ No. There are only 10^44 legal positions, of which 10^17 are relevant to weakly solving chess. There are between 10^29241 and 10^34082 different Chess games.
"you never know if the present engine's recommendations are truly the absolute 'best' moves"
++ We do know. If a black move leads to a 7-men endgame table base draw, then it is good enough to achieve the game-theoretic value of a draw.
As for white moves we need to explore all reasonable moves that oppose to the draw.
"We really should hope that chess never gets solved."
++ If it is desirable or not is a different question. Ask the Checkers, Nine Men's Morris, Connect Four and Losing Chess players, whose favorite games have been weakly solved.
10^29241?? 💀
It is solved for a 7-piece endgame but not the entire game. You can't determine if a move suggest by Stockfish in a complex middle game truly the 'best' possible.
Chess getting solved would be a disaster as it would end the beauty of this game. The game would turn from a competetive sport to something like Tic-Tac-Toe. The future generations won't be able to learn from the valuable life lessons learnt from the game. And also it won't be fun anymore.
@7811
"you need to prove it leads to a draw or not, your explanation doesnt do that"
++ Maybe an example makes it clear.
Look at this game
https://www.iccf.com/game?id=1164344
From statistics this is >99% certain to be a perfect game with optimal play from both sides.
It starts from the initial position and ends in a 7-men endgame table base draw.
That means all 56 black moves are justified in retrospect as fit to achieve the game-theoretical value of the draw.
To weakly solve Chess, we need to explore alternatives for the 57 white moves. If all of these alternative lead to a 7-men endgame table base draw or a prior 3-fol repetition as well, then Chess is weakly solved.
"https://www.iccf.com/game?id=1164344
From statistics this is >99% certain to be a perfect game with optimal play from both sides"
no it isnt. thats using an imperfect evaluator, and >99% is not 100%. thats how math works.
@7813
"10^29241?" ++ Yes: https://wismuth.com/chess/longest-game.html
"It is solved for a 7-piece endgame but not the entire game." ++ Correct.
"You can't determine if a move suggest by Stockfish in a complex middle game truly the 'best' possible." ++ Yes, we can. For a black move: if it ends up with a 7-men endgame table base draw, then it is justified in retrospect. For white all reasonable alternatives need to be explored.
"The game would turn from a competetive sport to something like Tic-Tac-Toe"
++ Yes, that is the case for Checkers, Nine Men's Morris, Connect Four, Losing Chess...
How do you know that the moves made before the 7-piece endgame were perfect?
by the way, if you do somehow manage to successfully prove that black doesnt win with perfect play by white, you will be the first person in the world to do so.
How do you know that the moves made before the 7-piece endgame were perfect?
he doesnt. thats one of his errors
How do you know that the moves made before the 7-piece endgame were perfect?
i would look at the wikipedia article for solving chess, as well as the proof for solving Chomp.
@7815
"thats using an imperfect evaluator, and >99% is not 100%. thats how math works."
++ That is not an evaluator, the 7-men endgame table base is the perfect evaluator.
The game ends in a 7-men endgame table base draw, so the black moves need not be questioned. The white moves need to be questioned and alternatives explored, as there is a < 1% probability that some better white move is avaible.
How do you know that the moves made before the 7-piece endgame were perfect?
I would recommend reading the wikipedia article on solving chess. tygxc makes a lot of assumptions that would not be accepted in a math proof, so its easier if you just get it from the experts instead of having myself try to repeat the step by step explanation.
@7815
"thats using an imperfect evaluator, and >99% is not 100%. thats how math works."
++ That is not an evaluator, the 7-men endgame table base is the perfect evaluator.
The game ends in a 7-men endgame table base draw, so the black moves need not be questioned. The white moves need to be questioned and alternatives explored, as there is a < 1% probability that some better white move is avaible.
you need to prove that the game ends in a 7 men table base draw
prove it
im still waiting for the proof that black doesnt win with perfect play.
@7803
"Checkers had a simplification algorithm/position"
++ Checkers used Chinook and an endgame table base.
Chess has Stockfish and a 7-men endgame table base.
"weak versus strong solving are, for our purposes, essentially identical"
++ No, not at all. Strong = all white moves, all black responses.
Weak = all reasonable white moves, only 1 black response.
"response to your math error" ++ I made no math error, the math is correct.
you do realize that by definition you cant prove to me that black doesnt win with perfect play on black's end? by definition to prove that would be a weak solution for chess, of which does not exist.
@7812
"you need to prove that the game ends in a 7 men table base draw"
++ Look at this game: https://www.iccf.com/game?id=1164344 it ends in a 7-men endgame table base draw, so none of black's moves need to be questioned.
Alternatives for the white moves need to be explored to weakly solve Chess.
++ Checkers used Chinook and an endgame table base.
Chess has Stockfish and a 7-men endgame table base.++ No, not at all. Strong = all white moves, all black responses.
Weak = all reasonable white moves, only 1 black response.
both of those are factually incorrect.
checkers had simplification in addition to chinook.
weak is not all reasonable moves, it is all moves.
also, it is most certainly a math error. I am willing to bet $10,000 on it.
@7806
"for chess to be solved, an extremely strong engine needs to analyse an incredible 10^120 different games (estimation), a number higher than the number of atoms in the universe."
++ No. There are only 10^44 legal positions, of which 10^17 are relevant to weakly solving chess. There are between 10^29241 and 10^34082 different Chess games.
"you never know if the present engine's recommendations are truly the absolute 'best' moves"
++ We do know. If a black move leads to a 7-men endgame table base draw, then it is good enough to achieve the game-theoretic value of a draw.
As for white moves we need to explore all reasonable moves that oppose to the draw.
"We really should hope that chess never gets solved."
++ If it is desirable or not is a different question. Ask the Checkers, Nine Men's Morris, Connect Four and Losing Chess players, whose favorite games have been weakly solved.