Chess will never be solved, here's why

@9487

"still will have only played about 1 position out of every 1,000,000,000,000,000,000,000,000,000,000 unique positions (i.e. 10^13 vs. 10^43)."
++ This mistake keeps coming up: it is not necessary to visit all legal positions to weakly solve chess as Schaeffer did for Checkers. Besides, the vast majority of the 10^44 legal positions can never result from optimal play. Look at 3 samples: https://github.com/tromp/ChessPositionRanking multiple underpromotions from both sides.
Therefore Gurion's 10^37 is a better estimate.
https://univ-avignon.hal.science/hal-03483904 
Weakly solving needs only 1 black answer to the reasonable white moves, not all black moves. Hence a square root.
That leads to 10^17 positions to weakly solve Chess.
In that light 10^13 is not that far from 10^17.

@9488

"The current measure for "Accuracy" is derived from human and engine play, which are both imperfect."
++ Human or engine evaluations (like +0.33) mean nothing in absolute terms.
However, each position can only be a win/draw/loss. That is the objective evaluation. It becomes apparent when the 7-men endgame table base is reached, or a prior 3-fold repetition.
Optimal play is play without errors, i.e. without moves that worsen the game state from a draw to a loss.
There have been fewer and fewer errors in the last years of ICCF correspondence play and hence fewer and fewer decisive games.
Now they are at 105 draws out of 105 games, i.e. perfect play.

tyg trying to use an accuracy to push something false.
Yes - some positions wouldn't need to be analyzed.
Like any position with K+R against K that isn't stalemate.
Or Q-down positions where the down side has no compensation - and similiar.
But that doesn't mean that there aren't many others.
He wants a very small ratio - maybe trying to argue that the percentage of possible lopsided positions is gigantic.
But its not so easy for computers to count up the number of positions where there's 'compensation' and even harder to 'solve' all of them.
-------------------------------------------
We know there's an upper bound on the number of possible legal positions.
That number is easy to make a first approximation of.
And that number is subject to more reducing approximations.
Like - two Kings only of opposite color - max of 16 pieces of each color - max of 9 queens of either color - max of 8 pawns of either color - max of 48 squares for pawns - max of 60 squares for either king - max of 10 of any other piece-type of either color.
Although such reductions greatly reduce the initial upper bound (which is 13 raised to the 64th power) the number you're left with is still just too unmanageable.
tygxc probably wants to eliminate 'ridiculous' positions with nine queens and the like - because they 'couldn't happen' ... or are obvious wins for one side or both.
but can they calculate minimums on those? if they could -
the numbers you're left with are still too daunting.

Even if supercomputers can find exact huge numbers to subtract - that part would be strongly solving - and the rest would be unsolved because there's too many.
How do I know? Because the supercomputers struggle with even just 9 pieces.
And that's with castling disallowed. That's how pathetic it is. They can't even allow that ... which is not 'solving'.
There is no 'weakly solving'.
Time investment to remind tygxc about him being wrong:
I unfollowed this forum a long time ago.
If I was going to live another 1000 years it might be worth a little more 'investment' ?
but it still has a little intellectual value. And chess value.

@9503

"We know there's an upper bound on the number of possible legal positions."
++ Yes, there are 10^44 legal positions and 10^37 positions without promotions to pieces not previously captured.

"the numbers you're left with are still too daunting."
++ Yes, it takes 10^17 positions to weakly solve chess, that still is a daunting number.

"that's 'strongly solving'"
++ Strongly solving Chess is a 32-men table base and is beyond current technology.

"There is no 'weakly solving'."
++ Of course there is. Schaeffer weakly solved Checkers.
Please do read Games solved: Now and in the future by Prof. Van den Herik.

Why make such baseless, false, transparently uninformed claims? This thread is at 476 pages and most of it is similarly ignorant worthless nonsense.

https://www.researchgate.net/publication/231216842_Checkers_Is_Solved

"There are three levels of solving a game
(6). For the lowest level, ultra-weakly solved, the perfect-
play result is known but not a strategy for achieving that
value (e.g., Hex is a first-player win, but for large board
sizes the winning strategy is not known (7)). For weakly 
solved games, both the result and a strategy for achieving it
from the start of the game are known (e.g., Go Moku is a
first-player win and a program can demonstrate the win 
(6)). Strongly solved games have the result computed for 
all possible positions that can arise in the game (e.g., Awari
(8))."

"This paper announces that checkers has been weakly 
solved. From the starting position (Fig. 1A), we have a
computational proof that checkers is a draw. The proof 
consists of an explicit strategy that never loses – the
program can achieve at least a draw against any opponent, 
playing either the black or white pieces."

They did not strongly solve it--there is no complete game tree.

What a uniquely brilliant insight. No doubt no one on the previous 475 pages of this discussion ever considered it.

"Your judgement that chess is not infinite is at question."

Not by anyone rational.

"I'm suggesting that where there's a difference between a literal interpretation of infinite and a practical one, the human interpretation is the useful one."

It's not useful in a discussion about the solvability of chess.

"That's because our thinking is designed to be useful in interpreting the World around us."

But the solvability of chess is not part of the midlevel experience that our cognitive heuristics were evolved to handle. Nor is mathematics or modern physics or computer science or a lot else that we now deal with, especially where "we" are the intellectuals who address these problems.

"So getting stuck and being unable to get past a literal definition which is also unhelpful isn't useful in a practical sense, whereas accepting that a practical definition is useful whereas a literal one isn't is useful in a practical sense."

Blah blah blah. This sort of vague handwaving is indicative of people who don't understand the problem at hand and aren't interested in solving it.

gotta love how tygxc goes only after the low hanging fruit and utterly ignores the many ways he's been proven wrong.

tygxc, stop acting like you know the differences between levels of solving, considering how you tried to use statistical evidence as "proof"

Of course the bot isn't going to make bad moves on the assumption that you will blunder, and neither would a competent human player.

the "five years" bit is because tygxc misread a random paper and double counted a computer's efficiency by a factor of 100 million FYI

So you're a megalomaniacal narcissist? Who else would think that they can "end the argument"?

You should just get over yourself.

do you have autism?

I haven't read the arguments from either side that that is prima facie implausible.

There was nothing passive about my response to your smug hypocritical nonsense.

The argument is "chess is solvable =draw"

They are trying to disprove that since we don't know that yet since computers can't actually solve it

Most of the arguments are them repeating themselves infinitly

Optimal play is not determinable by either you, or engines. It will be determinable once chess is solved, though, were that ever to occur. This is not news to you.

The mistake is yours. 10^17 does not hold up.

I will note here that once again you are using Tromp's numbers to try to support your claim...a claim that Tromp himself dismissed out of hand when you tried to extrapolate waaay too much using his work as a foundation.

Evidence is not proof. Solving a game means a proof, not just evidence.

If this is indicative of your thinking then it's no wonder that everyone disagrees with you.

You are missing the point. Both strong and weak solutions provide an algorithm for answering any response by the opponent with a move that maintains the game value (1/0/-1). Mere "evidence" of the game value of a move such as 1. g4 is not a solution, weak or strong. It's empirical, not analytical -- solutions (= proofs) are analytical.

You don't understand what words mean. No wonder no one agrees with you. The only mystery is why people continue to debate you when you are wrong on basic semantics, let alone the math (which I haven't looked at, but there's no point in bothering).

P.S. You and BC are made for each other.