Chess will never be solved, here's why

@5842

"it does not guarantee achieving the best result"
++ It does guarantee that. The best result is a draw.
Even after a mistake, e.g. 1 g4? black is winning.
That means in every position there is at least 1 move that keeps the win.
Even if a position is repeated once or twice, there is a way out with a winning move.

"Consider a rook ending. Every move that does not lose the rook or stalemate is winning.
So just picking one of these moves without consideration of the ply count to an irreversible move (mate in this case) can lead to infinite play without reaching mate."
++ Maybe some position gets repeated twice,
but then in a winning position there exists at least 1 move that wins and avoids the repetition.

"a draw rule like 3-fold repetition" ++ You can avoid the 3rd repetition in a won position

"or 50-move" ++ 50-moves rule plays no role in solving chess

"an infinite game (which is outside of combinatorial game theory but is clearly not a win"
++ The 3-fold repetition rule is essential

"all paths to mate pass through positions that have already been visited twice"
++ Then it was an error to visit the pivotal position twice.

Well it really depends on the situation and, most of all, how high confidence and certainty are respectively prioritised. But it CAN be huge.

@5844

Sigh.

"The discussion related to positions that were basic chess winning."
++ There is no such thing as basic chess. The 3-fold repetition rule is essential in solving chess. The 50-moves rule plays no role in solving chess.

In a position that is winning like 1 g4? or 1 e4 e5 2 Ba6? there is always a winning move that avoids the 3-fold repetition.

"the difference between high confidence and certainty is HUGE" ++ Chess is a draw is certain.

@5848

"This is a well-defined game"
++ No, it is not. 1 Nf3 Nf6 2 Ng1 Ng8 3 Nf3 Nf6 can go on forever without an x-fold repetition rule. The game cannot be decided without a repetition rule.

"only piece locations, castling rights and e.p. square."
++ Plus side to move. That is the definition of a position.

"basic chess is also theoretically strong solvable by a 32-piece tablebase"
++ Theoretically yes, but practically no. It can loop forever.

"chess with a 50 move rule is a different game"
++ The solution to chess without the 50-moves rule also applies to chess with the 50-moves rule. The solution of chess with the 50-moves rule does not need to invoke the 50-moves rule.

"In a position that is winning like 1 g4? or 1 e4 e5 2 Ba6? there is always a winning move that avoids the 3-fold repetition." ++ There is always a winning move that avoids the 3-fold repetition, otherwise it would not be a winning position.

Chess is a draw is certain. "People with inadequate knowledge of correct reasoning are often certain without fully adequate reason." ++ People with inadequate knowledge of correct reasoning are often incertain without fully adequate reason. This is an example.

There are many strong solutions also. Think about it.

@5850

"Not as a practical game, but an infinite sequence of legal moves is a well-defined object, like an infinite decimal." ++ That is abstract theory. For practical weakly solving of chess an x-fold repetition rule is necessary. 3-fold repetition is a major drawing mechanism, that occurs in 16% of perfect games with optimal play by both sides as we know from ICCF WC games.

"The tablebase contains all basic chess positions, all legal moves and the result (with moves to mate with speed-optimal play  for all winning or losing moves)." ++ A 32-piece table base that strongly solves Chess with 10^44 legal positions is out of reach of present technology. That leaves only weakly solving as viable, and weakly solving needs an x-fold repetition rule.

"Speed-optimal means the winner tries to mate quickly and the loser tries to get mated slowly."
++ There are no bonus points for winning quickly or losing slowly.

"You must mean strong solution"
++ No, I mean a weak solution, as a strong solution is beyond present technology.

"there are many weak solutions" ++ Yes, there may be more than one weak solutions. I mean a weak solution without the 50-moves rule is also a weak solution with the 50-moves rule.

"there are even basic chess positions that are drawn with a 50 move rule that are winning without this" ++ Yes, but such positions cannot be reached from the initial position by optimal play by both sides. There are chess positions that are drawn by the stalemate rule, but as AlphaZero showed Chess stays a draw even if stalemate is made a win. Both stalemate and the 50-moves rule are superfluous and could be removed with no effect.

An algorithm that "solves" (to be discussed later in this post) a game with the key properties of basic chess is as follows.

First elaborate what those properties are.

1. A finite number of positions
2. Alternating moves
3. Each position has a finite set of moves to other positions by the player to play
4. Some positions have known results (checkmates and stalemates, at a minimum, for chess). In general let's just assume there are >=2 possible ordered results)

And here is the algorithm

1. Form a database of all positions
2. Label all positions that are decided on the board (a stalemate or checkmate has occurred) with a definite value
3. Label all other positions with bounds that are the minimum possible value and the maximum possible value

Now execute a loop.

1. For all positions P that have bounds that are not as in 3 in the last list, update the bounds for all positions with a legal move that leads to P (you can be more efficient by considering if the "right" bound is non-trivial). The reason this makes progress, is that if you have a legal moves from a position, you can do at least as well as the relevant bound at the destination.

At some point repeating this loop changes nothing. Then you have discovered everything possible about the values of the positions.

Some have a definite value (both bounds are equal).

All others have only an upper bound and a lower bound on the value which are not equal.

In chess, with only 3 values, the latter always means that neither side can force a win however long the game goes on, so the natural value is a draw.

This reasonable definition gives a value to every basic chess position, dividing them into two sets where one side can force a mate in a finite number of moves, another two where neither side can force a win but one can force a stalemate, and another where none of the above are true, and optimal play would go on indefinitely without a result. The last three sets are seen as draws.

ok?

(Unless there is any technical error - I don't think so - it is nice to have something work out simply).

True according to the definition I have seen. A table-base provides all strong solutions, but a single strong solution might say "If white, play 1.e4. If black respond to 1.d4 with 1. Nf6", and thus never deal with 1. d4 f5.

The notion of providing the value for every move in every position is such a natural one, it deserves its own term. "Maximally strong solution" would be clear enough.

I was thinking from general principles, that the specific strong solution would have to be found. When I first thought of writing it, it was going to be a jest. A couple of seconds later I realised that it was quite reasonable.

As you know, I dislike weak and strong with a vengeance but it does seem that what you call "maximally strong" can never be achieved, because what IS completeness, in this context?

Much of this is not what I would call arguing. The essence of the discussion here is being conducted by some really smart, educated, and experienced people who are discussing very sophisticated concepts. I find it fascinating. When they disagree, I'm not nearly wise enough to pick a side, but I find it inspiring that people care about such things. The sun won't rise or fall on this and the world won't be changed much by the solvability question, however it's answered, but if you have any kind of analytical mind, you can't help but be intrigued. At least that's how I see it. 

To me, a full tablebase with info such as moves to mate and/or next irreversible move (might as well be both) does the job. Any other form would implicitly provide the tablebase.

The one advantage of Tygxc's misguided expertise is that unlike older threads with Vickalan and S23bog and Ponz, the arguments are about real theories.  It's like the difference between having to explain to someone that you can't just seed clouds to end a drought., vs. trying to explain that rain dances do not produce rain.

When I joined Chess.com, my first impression of this thread was "echo chamber" but after a while, you begin to see personalities emerge and how they function on an intellectual level. Although I can loosely follow what is being discussed, I have no inclination either way.

I just find the word battles intriguing...

I wouldn't know.....but to me, more important than any of that....tygxc has taken a fair amount of criticism for his arguments. Maybe it's entirely deserved.....but through it all, he has remained a class act, holding steadfast to his theory and not responding in kind even when the criticism has crossed some lines. No judgement here on that, but kudos to tygxc for the level at which he's conducting himself and the dignity he's maintained. We could use more of that here. 

I wish I could say I'm smart enough to assess whether tygxc is right or not, but right or wrong, I'm impressed with his arguments.....and the effort he's made to present them. I could say that about several others as well. 

Carry on.

Is this some example of you *not* wasting your life?  Because it seems a little forced.

tygxc completely ignores criticism, although I stopped reading his replies because he never seemed to respond properly. I think it's relativey easy to appear to be a class act if you don't acknowledge reality.