@11068
"the implementation of solutions are specific to each game"
++ Yes, like for Chess prune 1 e4 e5 2 Ba6? right away.
Rather, like the implementation of solutions (remotely resembling your non solution) is specific to FIDE basic rules chess, FIDE competitio rules chess, ICCF chess etc.
Allis' weak solution of Connect Four, the weak solution of Losing Chess, and even Checkers all used game knowledge. For Chess that is necessary even more.
All using proven knowledge to verify (as opposed to expedite) the solution, no mention of a big red telephone anywhere.
"elimination of 27 orders of magnitude is larger than all of checkers by 10 million times"
++ Larger game, larger reduction.
Don't think you quite grasped what he said.
Besides from 10^38 to 10^17 is 21 orders of magnitude.
I think he was basing it on 4.8x10^44 which is appropriate for basic rules chess. With 10^38 you've already started your silly reductions. You already conceded 4.8x10^46 (still a vast underestimate) for FIDE competition rules chess at the start of the thread before immediately forgetting about it, so you should accept 29½ orders of magnitude at least for that and ICCF chess (though it's out itself by many orders of magnitude).
You gave no reasoning why you could ignore the triple repetition rule for versions other than FIDE basic rules, You failed to put any upper limit even on the number of positions in KRK under FIDE competition rules. We don't currently have even an ultra weak solution of all positions in that endgame, nor any proposal for producing one.
Isn't the musing about the repetition rule a red herring for solving chess (as opposed to playing an imperfect opponent)?
The reason is quite simple: if there is a forced win, there is a forced win without repetition. So consider a repetition of position to be a loss if you like (handily pruning forward analysis - there being no problem with the tablebase end) and seek a winning strategy. If there is none you can be 100% sure there is no winning strategy.
Having verified this for both sides, you can do the same but counting a repetition as a win. You are likely to find both sides will be able to achieve this, making the result a draw.
The problem, of course, is that this solution remains computationally intractable on account of its size.
That depends entirely on the method used.
If it's a tablebase construction 4.8x10^44 collections of position attributes is perfectly adequate for a weak solution of competition rules chess because they can be built by a method that excludes repetitions and sequences exceeding 50 moves (Syzygy actually considers wins frustrated by the 50 move rule, but that's not necessary).
But if you're using Stockfish (or ICCF contestants who take the moves from Stockfish) it doesn't prune the search in the manner you suggest. This is SF playing White.
No comment there from Elroch about the ridiculousness of taking the square root - not a gigantic reduction when you're talking about small numbers to start with ...
but with big numbers like 10 to the 34th to start with it gets more and more ridiculous. Its like he wants to 'extract' one position from each 100 million trillion positions and then go by that one.
that root is tygxc's 'magic carpet' to Nirvana-claims about 10 to the 17th.
He will get much attention.
Another 5000 posts thus coming up ...
But O likely to be the only jealous one. Foolishly jealous. As always.
@tygxc says that while the square root approximation was woefully over-optimistic with checkers (a game where all the play is irreversible until promotion occurs) it it enormously pessimistic with chess (a game where most moves are reversible from the outset to the end). Exactly the opposite of what the differences would suggest (with complete reversibility being the ideal case for reducing the complexity).
Of course, he relies on the fact that chess is so simple compared to checkers that an imperfect player can ignore 90% of the moves as irrelevant without a valid reason and be 100% sure nothing has been missed.
All wrong, but seems to make sense to someone who doesn't know the difference between playing chess and solving chess.