Chess will never be solved, here's why

#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?

It isn't a mathematical system, because chess cannot be depicted or analysed by means of equations. I'm not entirely sure we can assume it's closed. It's rather ambiguous.

Not sure if game theory counts as mathematics? Maybe it does, because statistics also does. But game theory is more of a strategy to represent outcomes simplistically, in a way that can be totted up. The simplest form of game theory is the pro-con lists. List everything you can think of about killing elephants that's good and bad.

The effects of the current rules have been discussed extensively, here but more so in other threads on this subject. There seems to be a variety of opinions on how much it affects "solving" but I think the consensus, with which I agree, is that it doesn't affect it.

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.

4^16 is 4.294 billion.
4^ 120 =1.7668471e+72. 
That number is greater than the total number of atoms in millions of galaxies.
Chess can never be accurately solved.

Of course there's considerable redundancy there and some people have wasted a lot of time trying to calculate accurately how much redundancy. It shouldn't matter because it's still a lot of time needed to do it. Millions of years maybe and how do you store the results??

"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.

Imo it's just pretentious.

"Game-theoretic value" = normal outcome given best play. That means the theoretically optimum result of the rules of the game.

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.)