If the two strongest engines have a billion draws in a row and zero wins between them at very long time control on a giant array of CPU cores, it won't prove anything as far as weakly or strongly proven result for chess.jefk wrote:again a very definite statement, but eg. Prof Jaap vd Herik states that chess probably will be solved in a few decades, with the developments going faster than expected; that is, weakly solved, i presume.syzygy wrote: From a mathematical point of view, chess is a finite game and can be trivially solved by application of the minimax algorithm, but I don't believe you can produce a proof that chess is a draw which can be verified within our lifetime. Zermelo's theorem will in any event not be of help in tackling the computational effort. So chess may be "solved" according to some definitions, but it is not "weakly solved" within the normal meaning of that term.
Minimax ? i thought that alfa-beta is universal validity ? maybe not for some math purist, but for a weak solution that doesn't matter.
Then i don't think it's a pure computational problem, i once had this discussion with Bob Hyatt, showing him some games which have been solved without brute force computation. So i do think one of the theorems of Zermelo can be applied, at least in a common sense matter.
If you cannot find a winning advantage (from the opening) than it's a draw, simple as that. Look at some results H6 vs Kom11, only one win out of 33 games. We are approaching the dreaded draw zone...
That is because strong chess engines do unsound pruning because it wins more games. But for the same reason, these same engines can miss important tactical shots. Sometimes, to solve a problem, you have to turn off or at least turn down null move pruning, for instance.
One can argue that the game may be "practically proven" and in a common sense sort of way this is true. But to actually prove a game it has to be exhaustive. So, for instance, alpha-beta pruning can be used because it is sound, but null move pruning cannot be used in a proof.
The fabulous depths and results that you see with advanced chess engines is due to un-sound pruning. Mathematically, it does not produce the same result as a mini-max search {as alpha-beta does} which is to say it does not always produce the right answer. What it does do is to help find a really good, really deep answer really fast.