Chess will never be solved, here's why

#1750
""if nobody makes a mistake - its a draw" ++ True but not yet proven

Please, you cannot stretch things as you like. To claim that the game is weakly solved, one has  to prove that the game value is a draw, not infer that from the experience we have gathered so far. And one needs to prove that the optimal strategy provides at least the game-theoretic value against all the opponent's possible moves, not only the "reasonable" ones. Is "reasonable move" defined in game theory?

#1755
"To claim that the game is weakly solved, one has  to prove that the game value is a draw"
++ Chess is not yet weakly solved, but weakly solving it is feasible. Once it is proven that black has one move that draws against all (reasonable) white moves, then chess is weakly solved and the conjecture that the game theoretical value of chess is a draw is proven.
"And one needs to prove that the optimal strategy provides at least the game-theoretic value against all the opponent's possible moves, not only the "reasonable" ones."
++ Some logic is allowed. It is not necessary to work out 1 e4 e5 2 Ba6? to checkmate, we know that it loses. It is necessary to prove that black can draw against 1 e4 e5 2 Nf3, 2 d4, 2 Nc3, 2 Bc4. Once this is proven, then it is trivial to prove that black can also draw against say 2 Be2, or 2 f4. "a strategy has been determined" can borrow from the strategy of not hanging pieces or pawns without need like 2 Ba6? and also the strategy of developing pieces and playing for the center, not the wings like 2 a4 or 2 h4.
In the proof for Losing Chess they applied "heuristics on best-first expansion"
http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/ICGA2016.pdf 

@tygxc, we argue in circles and I don't know how to break them. You make statements as if they are proven, while in fact they are theories. That's the only problem.

You have already said that. But can you prove that game theorists agree with you that you can test a strategy only against "reasonable" moves, a concept you have not defined yet in a general way?

Only logic is allowed. But you do all by yourself. You have to convince game theorists and other scientists, not only those who play and know chess.

Imagine I claim I have weakly solved chess. Then another group, working on a similar project, challenge me to prove my statement against SF. "Of course!" I say. First game: SF plays 1. a3. "Oh no! I don't know how to draw against SF in this line"; I throw away my set of solutions and play with my brain and... I lose of course. Second game: SF plays 1. a4. "Oh no! These programmers have configured SF to play suboptimal openings! Well, but I know it's a draw", and I lose. You got it, the same thing can happen (and it would happen) for all the games, as White and Black, and I would not draw even a single game. The world would laugh at me.

That's why to prove chess is weakly solved, you have to test the supposed optimal strategy against all the possible opponent's replies, not only against what you decided is an optimal strategy. Otherwise, you use the concept of optimal strategy to prove a strategy is optimal, in a circle, you see?

#1758
There is nothing wrong with heuristics.
Use the same concept "heuristics on best-first expansion" as in the proof of Losing Chess.
That is also why Sveshnikov asked for "good assistants" and not only "modern computers".
First look to draw against 1 e4, then 1 d4, then 1 c4, then 1 Nf3 and if all that has succeeded, then the other 16 pose no problem.
After 1 e4 e5 first look at 2 Nf3, then 2 Nc3, 2 Bc4, 2 d4 and do not even bother to look at 2 Ba6?
The 'good assistants' should be knowledgeable in chess analysis, not in software or hardware.

Hey, I think if you get your funding we could do a deal here.

If you're only interested in loosely guiding the search to the 7 man tablebases I can generally get there in about five minutes and about half the number of moves it takes SF. So for, say, half the price per move of leasing a Summit machine for 60 hours, if you send me the positions I'll send you back the moves within quarter of an hour.

Save you the effort of recoding SF to use a very basic evaluation function as well.

You get it all done in 5/(4x60) years (just over a week) and save pots on the lease and I'm on a nice little earner.

What do you think?

When you try to prove that Black can draw, you start by testing for Black the best candidate move that an evaluating function provides, but you have to test it against all possible opponent's replies, because otherwise you cannot prove the supposed non-optimal replies would not win. As @MARattigan says, yours would be not a weak solution, it would be a loose one.

#1761
In principle you are right about that, but in practice some focus is necessary and the 'best first heuristic' makes sense. Make no mistake: weakly solving chess is still a large endevour. Chess is not as complicated as people used to think (10^36 positions, not 10^44, or 10^50, or 10^120) and weakly solving chess (10^17 positions) is easier than strongly solving chess, but 5 years on cloud engines = 5000 years on desktops is a huge task. 
Making a full game tree like you suggest is not even feasible as it would require too much storage. You mix up strongly solving chess with weakly solving chess. For Losing Chess or Checkers there is no full game tree either: these are weakly solved, not strongly solved. Chess is more complicated than Losing Chess or Checkers. You cannot impose more stringent requirements on a proof for chess than have been imposed on accepted proofs for Losing Chess or Checkers.

You are mixing up things: a strong solution would mean to provide an optimal move for all the legal positions, not only an optimal move for all the opponent's moves from the beginning. To claim you have weakly solved chess, you have to provide the game theoretic value of the game and, in reasonable time, an optimal strategy. So you can decide to not store some of the optimal strategies, to save space, but you must be able to provide them in reasonable time. So you cannot skip them as you please during the search, you are too confident.

I know that all this makes you feel uncomfortable, but you can overcome it. You can do it. Simply put, Sveshnikov did not use "solved" as game theorists do.

#1763
Sveshikov used 'close' chess, but I guess this is a poor translation of 'solve'.
I advocate heuristics.
Once 1 e4 and 1 d4 are proven to draw, then there is no doubt that upon request a similar proof with the same method and effort can prove the draw against 1 a4 and 1 a3.
Once 1 e4 e5 Nf3 is proven a draw, then there is no doubt that upon request a similar proof with the same method and effort can prove at least a draw against 2 Ba6. Even more it is not even necessary to go through that effort: we know for sure 1 e4 e5 2 Ba6 loses for white even without a full calculation to checkmate.

I see you have no doubt, just excuse us for not being so confident and expecting more. Maybe we do at least agree on what weakly solved means. Now can I ask you where did you find that, to solve checkers, only the square root of the search space has been checked?

• There is nothing wrong with heuristics for playing chess.
• There is nothing wrong with heuristics for picking moves for a candidate strategy, 
• There is no value to heuristics when applied to the moves of the opponent of a strategy. They all need checking rigorously.

All these are close analogies to the task of proving a solution of a chess problem is correct. Especially note the last.

Yes.

Care to articulate a full question?

Yes, it is

As a big fan of heuristics and Occam's Razor to refine problem sets, I still concur...and this is the the crux of why Tygxc will not get his solution.  At the end of his 5 year mission to seek out new positions and boldly go where no engine has gone before (but eschewing most of the ECO codes along the way ), all that will have been accomplished is to say "we're pretty sure that chess is a draw with best play"...which is where we already sit today.

True, that.

What what?

If you're querying the tens of trillions I have to admit to some unreliability on the back of my envelope. I've run it through Javascript and it should have read 3 trillion.

I'm going to be completely balanced and say that, in principle it is possible (but by no means obvious) that one side could generate a strategy that was not only optimal but also avoided large regions of the set of possible material balances (such as more extreme over-promotions).

The problem is that that is merely a hypothesis, based on inadequate intuition and may be false,

To give an idea why it might be false, it's really about the big numbers. Say you have 10^30 positions to solve (some part of the space of positions in your strategy and you want to avoid black having, say, 4 knights. This might be possible to ensure almost all of the time, but it's no good achieving it 99.9999999999999999% of the time. If the other side has one chance to be a pain and underpromote multiple times to knights (or more extreme examples) they need to be dealt with. It might be that the defender needs a million times more positions to be able to wangle another underpromotion in one of them. But if so, allowing 5 could be unavoidable with 10^30 positions.

What would be more likely to be achieveable would be to avoid unusual excess promotions on both sides. For example it seems reasonable that if there is a drawing strategy for a side, there is a drawing strategy that only involves promotions to queens (reasoning is that underpromotions appear fairly unusual in best play (<1% of games?), so unless the path to a draw is very narrow you can probably find a part of it that doesn't have any for you side. So that would reduce the range of material balance significantly, if nowhere near as much as a certain person here wants.