Chess will never be solved, here's why

@12336

"the square root formula is based on assumptions of constant branching factor, games of equal length and no transpositions"
++ No. The square root is only based on the assumption of perfect alpha-beta pruning.
So it depends on the efficiency of the engine: 0.67 for Chinook of Schaeffer for Checkers and close to 0.5 for modern Chess engines, which have evolved more over years.

Variable branching factor, games of unequal length and transpositions do not affect that.
To cope with transpositions it is enough to consider an equivalent branching factor of non-transposing moves. That is also how an engine works: if a branch reaches a transposition, then that branch is not calculated, but looked up in the transposition table.

"Transpositions are ubiquitous in chess analysis." ++ Yes.
As 10^38 = 3^80 a game of average 40 moves has only 3 non transposing choices per ply.

"all positions with promotions or multiple promotions"
++ No. Underpromotions are rare. Promotions to pieces not previously captured are rare. Underpromotions to pieces not previously captured do not occur in games with optimal play from both sides and can be ignored indeed.

"states can be reached in an ENORMOUS number of ways" ++ Yes, that is why positions, not games count. That is why a way to handle transpositions is necessary i.e. a transposition table.

"The square root is only based on the assumption of perfect alpha-beta pruning.
So it depends on the efficiency of the engine: 0.67 for Chinook of Schaeffer for Checkers and close to 0.5 for modern Chess engines, which have evolved more over years."

no justification given for the 0.5. in fact, most modern chess engines are actually far less efficient.

in addition, if you actually read the solution paper to checkers, you would have noticed how schaeffer points out that an alpha beta search does not prevent double counting positions.

tygxc is going to respond to this so im going to give you a heads up

tygxc's end claims here are not supported by any area of research, and ive actually shown tygxc's "logic" to dozens of math majors and math professors, and they all found the exact same errors that have been pointed out to tygxc many times.

"states can be reached in an ENORMOUS number of ways" ++ Yes, that is why positions, not games count. That is why a way to handle transpositions is necessary i.e. a transposition table." completely ignores the computing costs of using such a transposition table

its funny, i just discovered several new ways that tygxc makes errors.

"An alternative would be to use only computing—i.e., build a search tree using the alpha-beta algorithm. Consider the following unreasonably optimistic assumptions: number of moves to consider is eight in noncapture positions, a game lasts 70 ply, all captures are of a single piece (23 capture moves), and the alphabeta search does the least possible work. The assumptions result in a search tree of 8^(70–23) = 8^47 states. The perfect alpha-beta search will halve the exponent, leading to a search of roughly 8^47/2 ≈ 10^24"

alpha beta pruning is calculated from the game tree complexity, not from a stored positions table.

and i bet tygxc wont figure out why schaeffer did that calculation. but i figured it out.

this is why I'm partially convinced there's a sort of language misunderstanding on tygxc's end. nobody with a math education beyond middle school would call that a "proof", unless "proof" translates to something weaker in the different language that tygxc is native in.

I think I see what tygxc is now trying to say though.
He's apparently claiming that in 'optimal play' the advantage for either side will never approach 1.0 ...
but he's totally blind to the fact that that's today's engines against today's engines.
Has he yet responded to the fact that today's engines would beat yesteryear's engines?
Has he responded to the argument that engines of the future will be stronger than today's?
He's not looking at 'the big picture'.
And probably isn't going to.
'No cheddar' there for him.
But that's OK.
Its more like 'intellectual tunnel vision' than 'intellectual dishonesty'. 
Its the other guy that's dishonest.
Like claiming he's the only one discussing the forum subject.
Blatant dishonesty.

@12362

"in 'optimal play' the advantage for either side will never approach 1.0" ++ Correct.

"today's engines would beat yesteryear's engines?"
++ Today's ICCF World Championship Finalists with each 2 engines of 90 million positions per second at average 5 days per move have now reached 0 error, 110 draws out of 110 games.
In previous years there were sparse decisive games, thus some errors.

"engines of the future will be stronger than today's" ++ Yes, engines and humans of the future might reach the same 0 error in a shorter time than average 5 days per move.

Yes, he keeps making that same elementary blunder.

It's just like some flake saying "But science is just a theory" over and over again, even after you patiently explain to them what the word "theory" means in the relevant context. It must be some sort of combination of psychologically motivated dishonesty and lack of intelligence.

@12364

You keep denying the truth even confronted with massive evidence.
That must be some combination of psychologically motivated dishonesty and lack of intelligence.

Do you really not understand the difference between proving something and convincing yourself of something?

Have you never studied any mathematics past middle school?

Did you never even get to where you learnt what a proof was or were you such a poor student that you forgot it completely?

These are not rhetorical questions.

A solution is a proof. Convincing yourself is not one.

@12366

"Have you never studied any mathematics" ++ More than you.

"a poor student" ++ No, on the contrary.

"A solution is a proof" ++ You cannot impose your own puristic, agnostic opinions.
You cannot impose more severe demands on a weak solution of Chess than on weak solutions of Checkers, Losing Chess, Nine Men's Morris, Connect Four.

Chess is a draw.
1 e4 e5 2 Ba6? loses for white.
Those are facts. There is massive evidence. You are free to believe Chess is a white, or even a black win, or that 1 e4 e5 2 Ba6? draws or even wins for white.

I agree with tygxc except that "proof" should be replaced by "very strong indication" and "deductive" by "inductive". It isn't a deductive argument since there is no chain of syllogistic premises leading to that conclusion. Therefore it is a language problem. I think that "proof" is often used in a weaker sense, to imply a pragmatically acceptable proof rather than a rigorously deductive one. I have no problem with that but we should bear in mind how others use words. That is, both sides should bear it in mind.

@12368

proof = the evidence that compels acceptance by the mind of a truth or fact - Merriam-Webster

@12368

"there is no chain of syllogistic premises leading to that conclusion."

It is deductive.
White has the initiative, moves first.
White is up 1 tempo.
3 tempi = 1 pawn
1 pawn is enough to win: queen it
you can queen a pawn, but you cannot queen a tempo
Thus the white advantage of the initiative worth 1/3 pawn is not enough to win. Chess is a draw.

Yes, it is a language problem. @tygxc does not understand what "solving a game" means (as used in the peer-reviewed literature on the topic). On several occasions he has indicated he has false beliefs about the way peer-reviewed work uses the term (more specifically, the meaning of 'weak solution'). He has avoided fixing this despite patient explanation and referral to the literature.

It is important that people discuss the same topic rather than merely using the same words. Where ever some uses the same words to refer to something different, they only add noise and obfuscation by appearing to discuss the topic but in fact not doing so. There is even less excuse for doing this when an error has been pointed out.

Everyone should always be wary in general of incorrect assumptions that if a word is the same it refers to the same concept. Of course the very worst of all is when someone does not even know they are talking about a different concept or insists on using language incorrectly after this has been brought to their attention.

@12368

"very strong indication"
++ Those are weasel words. It is either true or false.
Chess is either a draw, a white win, or a black win.
The deductive argument as well as the 110 draws out of 110 games in the ICCF WC Finals compels the mind to accept that chess is a draw.

All well-defined propositions are either true or false. Very many of these are uncertain. So, as usual, your post is nonsense, with the exception of that latter point. We are well aware that your mind is compelled to be certain that chess is a draw because you are oblivious to the fundamental difference between a high probability and certainty.

I suggest you go for accuracy rather than a condemnation of anything that frightens you. Objectivity is the attempt to bring in and accurately relate all the variables. Go for it.

So yes, it is either true or false but we are trying to establish whether it's true or false and that doesn't include assuming that we know the answer already.

@12371

"what solving a game means"
++ Again:
"weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition" per Games solved: Now and in the future

I know you have a puristic interpretation of all opposition meaning all legal moves, while I have a more realistic interpretation of all legal moves that strive against achieving the game-theoretic value

to oppose = to strive against, resist - Merriam Webster

1 e4 e5 2 Ba6? does not oppose, i.e. strive against black achieving the game-theoretic value of a draw.