OK that's a fair comment but ty is entitled to his utter rejection of a mathematical approach. He says he has trained to be a mathematician. It is because my son is a mathematician that I do realise its importance and am willing to meet you halfway. Incidentally, son claims he is now a data scientist. He certainly has a wonderful array of large screens in the new office he just had their garage converted into. One of them is even curved, which is really impressive.
I thought he was an engineer, so I was mistaken.
@Optimissed, firstly, no, I am not stating my "opinion", any more than I would be expressing an opinion if I said that 1+1 is not 3, but is 2. The mathematical sciences are not made up of a set of opinions, they are made up of a set of things that are known to be true. Note that it is not only not an opinion, it is also not "mine". I am communicating what is known.
Are you familiar with the concept of a proof? Are you aware that a weak solution of a game is a proof of the game value? If you look at a paper on the first part of the solution of checkers, you will see a reference to the proof tree (which is the analysis that rigorously proves the result from a given position, by reaching a position with known value at the end of every line). A proof tree does not just deal with opponent moves that seem playable, it deals with all LEGAL opponent moves, because proofs are rigorous.
I am actually rather sure that you understand that @tygxc uses heuristics (vague positional understanding and rough rules) and empirical evidence (game results and unreliable evaluations) to support a conjecture, then describes this as "solving chess". You have drawn attention to this on occasion.
The real discussion between you and tygxc is on a higher level ... on a kind of meta-judgemental or interpretational level. You are stating what is known in the context of your approach to mathematics, which is that of a mathematical purist. tygxc is attempting to state what is known to him, as a scientist-pragmatist. One approach is not "better" than the other.
Yes, ty uses heuristics and they may not all be good. I'm equally sure that there is no possible solution of chess via mathematics. The only possibility is via a more pragmatic, scientific approach. You may disagree with that and you may not like it but I am also stating what is known, by a different process of "knowing" than the deductive one you prefer. All deductive judgements must still be judged to be appropriate and that's where the assumptive thinking may lurk for those who think that syllogistic logic is a be-all-and-end-all.
We're not in much disagreement. There does exist a "mathematical" (i.e. rigorous) solution algorithm - a computer program that would solve chess if it had the resources. It's just impractical to execute.
To be clear, the solution of checkers qualifies as such a mathematical solution, because it was designed to be rigorous and to reach certainty, not an approximation to this.