Chess will never be solved, here's why

If you say so... Anyway thank you for your answer about the cost.

About your idea of project, I insisted so much on the game-theoretic value of the game, because it is crucial for your theory. As I said the percentage of drawn games is not a sufficiently strong evidence to assume that the game-theoretic value is a draw. More importantly, it is not sufficient to give a reliable estimation of the error rate per move. To do that, you start from the assumption that errors are statistically independent... Now, let's say that an engine is playing in autoplay, it is White's turn at move n of the game and the engine analyzes the position P, reaching depth d; then it plays a move M which is a mistake, and turns a draw into a loss for White. After that, the engine takes Black and analyzes the new position P₁ at depth d (on average). It already analyzed the line starting from P₁ in the previous turn, but now one other ply has been played; nonetheless, with some approximation we can say that reaching depth d at plycount 2n-1, gives for the line the same evaluation as depth d+1 at plycount 2(n-1) and it is well known that the difference between an evalutation at depth d and one at depth d+1 is on average smaller and smaller, the larger d. That means that very likely an engine does not recognize at plycount 2n-1 an error made at plycount 2(n-1). Most of the times these mistakes can be exploited only playing a very precise move, hence the engine will likely play another wrong move, that does not exploit the error, when the evaluation is still wrong. Even if the engine is lucky and play the right move at plycount 2n-1, it would face the same problem at plycount 2n+1, 2n+3... So if an engine makes a mistake in autoplay, likely with the other colour it will very soon make another mistake that will rebalance the game. That's why, even in the case that engines are becoming more accurate and the game value is a draw, it is still not possible to say whether they make 0, 2, 4, 6 or more errors, in general: they are not statistically independent.

You used simple maths to do your calculations, yet you think we cannot understand it. Did Tromp make such calculations to estimate the error rate per move? If that's not the case, do you think he too is not capable enough to conceive those calculations and arrive to your very conclusion?

I predict that @tygxc will fail to be convinced.

Hilariously, he thinks Sveshnikov solved B33 in the game theoretic sense a decade before computers reached the strength of the best (puny) humans! (Note carefully that what they need to do is converge on the standard of play of a 32 piece tablebase. They are presently woefully short of reaching the level of a much smaller tablebase).

I am now going to solve C67.

It's a draw, by example. Ta da!!

[irony]

#3251

"As I said the percentage of drawn games is not a sufficiently strong evidence to assume that the game-theoretic value is a draw."
I mentioned 5 kinds of evidence:
1) General consensus of expert opinions in this century
2) AlphaZero autoplay even with stalemate = draw and more draws with more time
3) ICCF WC even with 7 men table base wins > 50 moves without capture or pawn move
4) TCEC even with imposed openings intended to be slightly unbalanced
5) human classical world championship matches prepared by teams of grandmasters & engines
Maybe 1 of the 5 is not sufficient proof, but all 5 taken together are.

"you start from the assumption that errors are statistically independent"
++ Like I hang a piece and you fail to notice it and so you do not take it. Yes, errors in AlphaZero autoplay could come in pairs: in ICCF, TCEC, human WC they are independent.

"You used simple maths to do your calculations, yet you think we cannot understand it."
++ It is only high school math, but yet some do not even understand simpler proofs.

"it is still not possible to say whether they make 0, 2, 4, 6 or more errors"
++ For the ICCF results it is the only way to explain these. It does not even need the assumption that chess is a draw: that follows as the only way to explain the data.

"Did Tromp make such calculations to estimate the error rate per move?"
++ Tromp estimated the number of legal positions by induction.

#3253
"he thinks Sveshnikov solved B33 in the game theoretic sense a decade before computers"
++ That is what Sveshnikov himself said. It is his variation.

"They are presently woefully short of reaching the level of a much smaller tablebase"
++ Humans get tired, get nervous in time trouble, get disheartened by previous losses.
Even ICCF grandmasters fall ill and then blunder from their sickbed.
Otherwise 99% of ICCF WC draws are ideal games with no errors, i.e. perfect play.
Human classical WC match games are close to perfect:
whenever a clear error is made it is in an otherwise still drawn position.
All 4 games Nepo lost to Carlsen were by blunders in drawn positions.

The general consensus is that the game is not ultra-weakly solved, in fact no one but you say that the game is ultra-weakly solved. Third time I repeat that, and your "objection" so far is: "I do".

As for games between humans or different engines, we have to understand that all of them use in fact some sort of "evaluation function", that does not encompass all the possible situations, and therefore they are biased: they use rules of thumbs that give statistically the best outcome. Same strength, similar biases.

To make a very simple example, let's say that we are playing a videogame, and in a particular type of situation we can only play two moves, A and B; the outcome can only be 1 or 0 and we want to maximize it. A gives 1 80% of the times and B gives 1 20% of the times. Which is the best strategy? Without other informations, it is: play always A, of course. Any other strategy would be "suboptimal", but two "optimal" players will both fail to treat properly that 20% of cases where the best move is B. Something like that, but with much more options, happens for chess too, so players of the same strength evaluates things in a very similar way, and therefore it's impossible that the errors made by one of them are completely uncorrelated with the errors made by the opponent, especially in case of engines, which are not affected by random disturbances like fatigue, emotions, etc.

I deduced the very same data you mention from premises not based on those data, see above. Third time I repeat that, but you just state your hypothesis, with no explanation at all: "most games end in a draw and most experts think it's a draw" and then the jump to the conclusion "therefore the game value is a draw", and the explanation is "because it's the only way to explain that", which is begging the question. Like: "The Apple iPhone is the best smartphone on the planet because no one makes a better smartphone than Apple does".

Is that an objection? Why do you ignore the core point? If that's not the case, do you think he too is not capable enough to conceive those calculations and arrive to your very conclusion?

"As I said the percentage of drawn games is not a sufficiently strong evidence to assume that the game-theoretic value is a draw"
Obviously true.
But the so called 'game-theory' with 'game-theoretic' value could be a red herring anyway.  Or become one.  Or has become one.
'Game theory' a kind of mini-religion with gurus and disciples again.
Conflicting with objectivity of math and with better science.

There was a prominent person in the US around the year 1900 who suggested that everything that could be invented had been.
That's right.
I could probably dig up the name.
Snake Oil isn't a new thing ...

@  Nerves ...
thank you for posting that !
It did seem rather ridiculous at the time I read about it several years ago  that the Patents official would make such an outrageous suggestion.
Which is why I posted about it here !  

So an issue - why would somebody at that time have alleged otherwise ?
And was that an allegation made at the time?  or much later for example after the internet was developed?

#3257

"The general consensus is that the game is not ultra-weakly solved"
++ The general consensus is that chess is a draw, but it is not yet formally proven.
I presented 5 kinds of evidence.

"As for games between humans or different engines, we have to understand that all of them use in fact some sort of "evaluation function", that does not encompass all the possible situations"
++ The key is not the evaluation function, but the calculation depth. The evaluation function can be as simple as "table base draw or not" or "checkmate or 3-fold repetition", or a rude count of material (K = 1000, Q = 9, R = 5, B = N = 3, P = 1). When a human or engine loses, it is not because of a worse evaluation function, but because of too shallow calculation. The side that has not looked deep enough loses.

"Same strength, similar biases."
++ No, that is not true. Human or engine players of the same strength have different biases. Some (Petrosian) will never sacrifice until completely clear, some (Tal) will always sacrifice if they see some chance. Some will always trade, some will avoid trades. LC0 has an elaborate evaluation function (thick nodes), Stockfish has a simpler evaluation function but calculates deeper (thin nodes).

"Without other informations, it is: play always A, of course."
++ I stress the importance of incorporating chess knowledge into the brute force method.
Without other informations do not sacrifice material. Some sacrifices need proper attention. 1 e4 e5 2 Ba6? needs no attention.

"I deduced the very same data you mention from premises not based on those data"
++ No, you did not: you said you cannot tell. 127 draws, 6 white wins, 3 black wins, what is a plausible distribution of games with 0, 1, 2, 3... errors? I say: 126, 9, 1. You say? 0 errors = ..., 1 error = ...., 2 errors = ..., 3 errors = ...., 4 errors = ....?

"Is that an objection?" ++ No, but I got criticised for using induction instead of deduction.

"do you think he too is not capable enough to conceive those calculations"
++ Of course Tromp being a mathematician is capable enough to conceive my calculations, but that was not his subject: he was interested in the number of legal positions.

#3262
"If a game lasts 60 moves, and at each move there's on average four main choices, the number of possible permutations or games is 4^120."
++ Again this nonsense. It is utterly wrong for 3 reasons.
1) An average ICCF WC game lasts 39 moves, not 60.
2) White tries to win, black tries to draw. Black succeeds to draw, white fails to win, so white has to try something else. Black does not have to try something else.
3) Chess has many transpositions: different move orders lead to the same position.
If all moves were interchangeable it would be 4^39/39!

Your response is utterly wrong for the following reasons.

1) @Optimissed makes a statement about the number of games (with some constraints) of length 60 moves. When you say an average ICCF game lasts 39 moves you merely show that these games are irrelevant to his assertion. That is your point shows only that it is itself irrelevant to the statement to which you object.

2) @Optimissed's constraints include no mention of the players' objectives, so this point also serves only to show that it is itself irrelevant.

3) Different move orders leading to the same position are different games irrespective of the final position, so again this point serves only to show it's own irrelevance. This is particularly true under competition rules with your own stated meaning of position (diagram + side to move), with which meaning different games leading to the same position will almost never reach the same game state. (The accuracy of the calculation is about par compared with other calculations you have posted - severely deficient.)

#3275
Your response is utterly wrong for 3 reasons.

1) The length of 60 moves implies it is representative. An average ICCF game lasts 39 moves and that is relevant as 99% of ICCF WC draws are ideal games with optimal moves from both sides, i.e. perfect play and thus relevant to weakly solving chess.

2) Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition. Hence black tries to achieve the draw and white tries to oppose against the draw.

3) The same position reached by a different move order is the same position and has the same evaluation. There are enough chess positions, it is bad to assess the same position multiple times. The 50-moves rule plays no role, as it is never invoked in positions >7 men in ICCF, TCEC, human world championships etc. Chess has already been strongly solved for positions of 7 men or less.

The 10^72 is ridiculous: even for strongly solving chess i.e. a 32-men table base only 10^44 legal positions need consideration. For weakly solving chess 10^17 legal, sensible, reachable, and relevant positions need consideration.

#3125
"Checkers was not weakly solved by Marion Tinsley"
++ Yes, that is right. Checkers and Losing Chess were weakly solved by mathematicians and computer scientists. Most of their work was to establish an endgame table base for their game. That is a task for computer scientists. For chess 7-men endgame table bases have been generated by computer scientists, not by grandmasters.
The second part of solving Checkers or solving Losing Chess requires more game knowledge. Chess has discretionary captures and requires even more game knowledge to set up openings and to terminate a search when the outcome is not in doubt like in most but not all opposite colored bishop endings.
That is why weakly solving chess with Stockfish - as chess equivalent of Chinook that Schaeffer used for Checkers - should be done by (ICCF) (grand)masters. Somebody like GM Sveshnikov was most qualified for such a task.

#3277

"You claim that only 10^44 legal positions need consideration"
++ That is not my claim: Tromp proved there are 10^44 legal positions. So that is what is needed to strongly solving chess i.e. a 32-men table base. It is not feasible with present technology. Only weakly solving chess is feasible with present technology. That needs far less legal, sensible, reachable, and relevant positions: 10^17.

"Your assumption that somehow, positions can be assessed by one engine-glance"
++ That is not my assumption: it is the contrary of what I say all the time. I say positions can only be evaluated by deep brute-force calculation until the 7-men endgame table base or a 3-fold repetition is reached. You are the one with the daft evaluation algorithm.

"just let the engine glance at the starting position and you've got it"
++ I say all the time that no evaluation algorithm can assess a position, the only way is deep calculation towards the 7-men endgame table base.

"In reality, games hundreds of moves long have to be checked."
++ The longest ICCF draw was a perpetual check after 102 moves. The average is 39 moves and the standard deviation 14 moves. So 60 moves is exceptionally long.

#3281
So you would let a 1381 rated player decide which lines to analyse and which endgames not to analyse further.