Chess will never be solved, here's why

@4591
"Poisson distribution doesn't work here" ++ How do you know?

"because if chess happened to be a forced win for white,
likelihood for the first error would be bigger than for the second error."
++ If you refine the distribution, then the result might slightly change, but not drastically.

"You cannot predict the amount of errors because each error has a different probability."
++ If probabilities of errors slightly differ, then the result will slightly differ, but not drastically.

"to avoid an error there are x amount of available lines that maintain current evaluation and the x varies from position to position." ++ That is right, but I look at the big picture, at 136 or 210 games with each like 50 moves or 100 positions.

"We cannot know the probability for the errors and we cannot make predictions for errors."
++ Yes, we can. That is the fundament of statistics.

Making comparisons is always tricky, but I try one.
Say you want to answer the question:
'How low can I make a door so all humans can pass under it upright?'
Now you cannot measure all 8 billion people.
The usual way is to measure a sufficient number of people, calculate the average and the standard deviation, then use the Gaussian distribution to calculate how high the door must be so all 8 billion can pass under it.

Now you retort: 'Gaussian distribution does not work.'
Men are generally taller than women so it is a bimodal distribution.
Adults are taller than children, so it is a skewed distribution.
In some countries people tend to be taller than in other countries.
Basketball players tend to be taller than marathon runners.
We cannot decide how high the door must be.

The comparison highlights the problem we're having. Humans could vary from say 5ft to 8ft. We have good data on how much they vary to make predictions.

Again in chess there are always x amount of lines that maintain current evaluation and avoid an error. Say that with best play there are 2 available lines that force a win for white. Once an error happens and evaluation changes from a win to a draw, there are now 19 available lines to force a draw with best play. 

We don't have accurate data on how much "x" varies to make any predictions on errors per game. We could have 136 games where the first error occured in 100% of the games and the second occured in 15% of the games. There is no way to reliably make predictions

@btickler it doesn't need you to accept it, but the hairs of your head are all numbered.

Mathematics is a lame human made discipline.

For example, there are algebraic transcendental functions which solution can't be written but is possible to draw the solution graphically.

So long as you have a welly sharp pencil.

@4593

"Humans could vary from say 5ft to 8ft. We have good data on how much they vary to make predictions." ++ We use the Gaussian distribution, though we know it is not exact.

"in chess there are always x amount of lines that maintain current evaluation and avoid an error." ++ Yes, that is right.

"Say that with best play there are 2 available lines that force a win for white.
Once an error happens and evaluation changes from a win to a draw, there are now 19 available lines to force a draw with best play." ++ Yes, that is right. But what does that mean?

Let us assume chess is a draw. In the initial position there are 20 possible white moves. Most of these lead to a draw as well. 1 g4 probably loses by force. So white has say 19 moves that draw.
Now black has 20 responses to each of the 20 white moves. To 1 e4 1...e5 probably draws, 1...c5 probably as well, 1...e6 or 1...c6 maybe too, maybe not, 1...Nf6 probably not, 1...b5 and 1...f5 surely not. So black has a narrower choice of good moves that hold the draw.
It is this phenomenon that explains why white wins more often than black:
white has a broader choice of moves that hold the draw and black has a narrower choice.

"We don't have accurate data on how much "x" varies to make any predictions on errors per game. We could have 136 games where the first error occured in 100% of the games and the second occured in 15% of the games."
++ Statistics on the 136 ICCF WC games show that the 127 draws are > 99% sure to contain no error and the 9 decisive games are > 99% sure to contain exactly 1 error.

"There is no way to reliably make predictions" ++ Yes, there is.
We can even reliably predict what door allows all 8 billion people to walk under it upright.
We do so using the Gaussian distribution, of which we know it does not work exactly.

"Yes, that is right. But what does that mean?"

It means your error distributions that are based on probability are not accurate, because each error has a different probability depending on the position that you cant calculate.

@4598
"It means your error distributions that are based on probability are not accurate"
++ It need not be accurate. We know the Gaussian distribution of size of humans is not accurate, and yet it is accurate enough to use it in many practical probems.

There is no fundamental difference between solving chess and solving a chess problem. You can convince yourself of the solution of a chess problem, and you may be right (if you are fortunate), but you have not solved it rigorously and with certainty until you have dealt with EVERY LEGAL MOVE BY THE OTHER SIDE. No excuses, even if lack of rigour is your lifetime habit.

I wrote this 6 weeks ago, on an identical thread. It basically seems to have killed that thread. It was my initial contemplation of the problem brought about when you believe these game theorists, basically when I was realising that the people who are trying to cling onto the incorrect ideas, such as "weak solutions etc" are just inviting confusion. After I signed off last night, I realised that many people mustn't understand what Game Theory is. They probably think that it's theory of games.

To repeat, Game Theory consists of the application of the theory of games to real life situations, where srategies are worked out and outcomes are scored, the RL situation being played through, as if they were a game, to find strategies that achieve the highest scores. Everything Elroch is saying points to the probability that he doesn't understand that chess can be directly compared with an RL situation, whereas it cannot be simplified in the way that Game Theory demands.

Consequently GT is inapplicable to chess. There isn't any doubt ... if you disagree, you just don't know what Game Theory is or don't understand it. I know it's fashionable now but I've been playing about with Game Theory since the 1960s. Anyway, this is what I previously wrote.


" (to tygxc) I think that your mistake is to refer to strategies. A strategy is a plan, overview or method.

<ultra-weakly solved means that the game-theoretic value of the initial position has been determined>

That's fair enough. Chess is a draw with best play from both sides. However, humans tend to understand that already. There are some exceptions, because although it's understood to be a draw, it hasn't been determined, by deductive reasoning. "Ultra-weakly" very clumsy, so you'd do better to call it the "game-theoretic value" or the "game-theoretic result". Not "The ultra-weak solution is that it's a draw", because it's completely unnecessary to use such jargon.

<weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition>

You're already in trouble. That's the problem with jargon. You can always use it to sell ideas or confuse the opposition. Here, you've evidently confused yourself.

Looking at the layout of the solution from top-down, with the game theoretic value being the top of the tree (effectively "the user interface"), that cannot be determined without understanding the stategies that may be used to achieve a draw in all circumstances {"against any opposition"). This is why you're much better off speaking in English and not Jargonese. Forget the idea of "stategy", because in any case it gives the wrong idea, since any full solution of chess is tactical only. You need to accept that the only "strategy" is the exploration of all tactical lines which may be relevant, not forgetting to allow considerable leeway for examining surprising lines, which may otherwise be missed but may lead to a conflicting result.

Deciding which lines may be relevant is an incredibly complex task. Your belief that Stockfish can achieve it, with the assistance and guidance of three GMs, is incredibly naive, if taken seriously. If those trying to argue against you deserve criticism, it's for allowing your ideas to achieve any credibility at all. Your ideas are wrong. There's no doubt about it. It isn't up for argument and you'd do best to realise that, no matter how belatedly.

Taking on board what I'm suggesting is the only way you will be able to communicate effectively and, more importantly, to start to get your thoughts in order. There isn't anyone else, commenting on this thread, who seems capable of pointing out the problems you're causing for yourself, by using terms which you don't seem to properly understand, even in the context in which you're trying to use them."

@4600
"There is no fundamental difference between solving chess and solving a chess problem."
++ That is right, solving chess is solving 'white to play, black to draw' for the initial position.

"You can convince yourself of the solution of a chess problem"
++ Yes, by looking at all relevant lines.

"you may be right (if you are fortunate)" ++ It has nothing to do with fortune

"you have not solved it rigorously and with certainty until you have dealt with EVERY LEGAL MOVE BY THE OTHER SIDE."
++ This is wrong. You do not have to look at every legal move from the other side only at the reasonable moves. You can rule out some moves by knowledge and logic.

Yes, you can rule out some moves by "knowledge". And in some cases you will be wrong to do so. That is the nature of imprecise inductive knowledge.

If the generation of boredom by repetition of falsehoods based on poor understanding was a valid proof method, you would be well on the way to solving chess.

@4603

"Yes, you can rule out some moves by knowledge".
++ That is also what van den Herik wrote: 'Next to brute-force methods it is often beneficial to incorporate knowledge-based methods in game-solving programs.' 5.2 p. 303
https://www.sciencedirect.com/science/article/pii/S0004370201001527

"And in some cases you will be wrong to do so."
++ No, then it is not knowledge. That is why the good assistants need to be (ICCF) (grand)masters. They can simplify and prune, but only if they are certain they are not wrong.

"That is the nature of imprecise inductive knowledge."
++ No, that is the power of precise knowledge and logic.
The 20 first moves have been ranked. The best moves are 1 e4, 1 d4, 1 c4, 1 Nf3.
If the 4 best moves cannot win, then the 16 worse moves cannot win either.
That allows to collapse 20 * 20 = 400 possibilities to 4, e.g. 1 e4 e5, 1 d4 d5, 1 c4 e5, 1 Nf3 d5

1 e4 e5 2 Ba6 can be discarded at once: loses a piece without any compensation.
1 e4 e5 2 Nf3 Nc6 needs to look at 3 Bb5, 3 Bc4, 3 d4, 3 Nc3.
It is again useless to look at 3 Ba6.
It is useless to look at 3 Na3: cannot be better that 3 Nc3.
It is useless to look at 3 b4: loses a pawn without any compensation
It is useless to look at 3 Nxe5: loses a piece without any compensation.
It is useless to look at 3 Ng5 or 3 Nh4: loses a piece without any compensation.
Do not let 'rigour' stand in the way of progress by ignoring knowledge and logic.
Do not confuse 'rigour' and 'stupidity'

@4604

"the moves in ICCF games are generally SF's moves" ++ No, not at all. You do not know ICCF.

"agreed draws and resignations represent possible blunders"
++ No, ICCF (grand)masters are not forum dwellers.
They resign when lost and agree on a draw when it is a draw. They often play on for months in drawn positions hoping in vain for an error (?) by the opponent.

"accounting for most of the results in your sample." ++ All wins are by resignation, draws are by agreement, by 3-fold repetition, or by claiming a 7-men endgame table base draw.

"These do not occur with a constant probability mass throughout the game but always at the end." ++ 127 of 136 games are error-free. When an error is made in 9 out of 136 games, the side who made the error realises this next move and resigns. That is why the few errors usually are at the end.

"You count a full point blunder as two errors (half point blunders) but why should this correspond with the square of the probability of a half point blunder." ++ That is a reasonable assumption. It does not even matter. ICCF has no blunders (??), only 9 errors (?) in 136 games.

"the full point blunders are clearly not independent."
++ There is only one error (?) per game in ICCF, so independent or not does not matter.

After a full point blunder the chances of another full point blunder before the next half point blunder are greater than after (impossible immediately after).
++ Does not matter for ICCF: only 1 error (?) in 9 out of 136 games.

I really don't rate your ability. If you had more of that elusive stuff, you wouldn't be on a par with btickler. Do you really like being on a par with him? Without doubt the most conceited and stupidest person to be commenting here? One grunt for yes, two for no.

On the other hand, don't think you won any points. I was agreeing with mpaetz and that is all. It was not addressed to you and it did not relate to anything I have been discussing with you.

If you don't know the difference between smalltalk and a logical argument, there isn't any hope for you. Ar least, no more hope than for that complete idiot btickler. He's still plugging away at the crap he talks.

OK put it another way.

I've just ranked them again; 1. g4 2. Nh3 3. f4 4.b4. How does your precise logic prefer the ranking you gave? Stockfish? Look at the examples I referred to in my previous post.

Total b*llocks. All of that.

@4608
"'I've just ranked them again; 1. g4 2. Nh3 3. f4 4.b4"
++ Now that is 'Total b*llocks'.

I did not give the ranking, but
1) Human knowledge e.g. Capablanca:
'From the outset two moves, 1.e4 or 1.d4, open up lines for the Queen and a Bishop.
Therefore, theoretically one of these two moves must be the best,
as no other first move accomplishes so much.'
2) AlphaZero Figures 5 and 31
https://arxiv.org/abs/2111.09259
The title is chess knowledge, not 'Total b*llocks'

Quoting for posterity.

Finally, the tacit admission that what Tygxc proposes is not a solution for chess at all...it's just modelling better play to "pretend" that chess is solved,  Why not just let engines keep improving and call it a day?  They will get to the same unsolved threshold anyway without "guidance".  This is kind of like the hubris of centaur players that consider themselves equal partners with their engines.  They are more like butlers for their engines .