Chess will never be solved, here's why

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tygxc

@4496
"it's impossible to win a lottery after X number of lotteries go by without a winner"
++ You do not understand the statistical argument and thus come up with a nonsense comparison.

DiogenesDue
tygxc wrote:

@4496
"it's impossible to win a lottery after X number of lotteries go by without a winner"
++ You do not understand the statistical argument and thus come up with a nonsense comparison.

Go ahead and explain how it's nonsense.  Also, your quote/snippet is out of context once you remove "This is kind of like concluding...".

tygxc

@4498
"Go ahead and explain how it's nonsense."
++ The comparison is nonsense.
Of course after X number of lotteries go by without a winner says nothing about whether winning the lottery is possible or not.
The argument goes that there is a certain probability of an error in a game, and that this probability can be inferred by observing the outcome of a sufficiently large number 136 of games of sufficient quality. It is impossible to fit 'chess is a win' with the observed data.

LogoCzar

Kotshmot
tygxc wrote:

@4498
"Go ahead and explain how it's nonsense."
++ The comparison is nonsense.
Of course after X number of lotteries go by without a winner says nothing about whether winning the lottery is possible or not.
The argument goes that there is a certain probability of an error in a game, and that this probability can be inferred by observing the outcome of a sufficiently large number 136 of games of sufficient quality. It is impossible to fit 'chess is a win' with the observed data.

If chess is a forced win for white, it would require an errorless game. An errorless game has not happened in your sample of 136 games. 

DiogenesDue
tygxc wrote:

@4498
"Go ahead and explain how it's nonsense."
++ The comparison is nonsense.
Of course after X number of lotteries go by without a winner says nothing about whether winning the lottery is possible or not.
The argument goes that there is a certain probability of an error in a game, and that this probability can be inferred by observing the outcome of a sufficiently large number 136 of games of sufficient quality. It is impossible to fit 'chess is a win' with the observed data.

No, clearly the argument doesn't "go" wink.png...you'll have to explain it in your own words.  Can you?

You should probably start off with the obvious...why you think that ICCF games can be proven to be of sufficient quality...and what exactly "sufficient quality" is supposed to represent, in this case.  Because it's completely circular as you have explained it on many occasions...if you cannot explain why ICCF games have reached some "quality" threshold that is absolute and not relative to current engine playing strength, and if you cannot do so without using engine-derived and/or engine-dependent statistics to prove that engines have reached this threshold (which is like asking toddlers to tell you if they can run fast, when their only frame of reference is a playground full of toddlers running around), then you have nothing.

tygxc

@4501
"If chess is a forced win for white, it would require an errorless game.
An errorless game has not happened in your sample of 136 games."
++ There are 3 possibilities: chess is a draw, a white win, or a black win.
Observed: 133 games = 127 draws + 6 white wins + 3 black wins.

Assuming chess a white or black win no Poisson distribution of the errors / game fits.
Thus chess is no white or black win.

Assuming chess is a draw, a Poisson distribution with mean value 0.070984 error / game fits.
The 127 draws are 99.74868% sure to be errorless.
The 9 decisive games are 99.9148% sure to contain exactly 1 error.
We can even pinpoint the 1 error: it is usually the last move.

tygxc

@4502

"why you think that ICCF games can be proven to be of sufficient quality"
++ A World Championship Finals, 17 ICCF (grand)masters with engines, 50 days / 10 moves.

"why ICCF games have reached some "quality" threshold that is absolute"
++ There is no such threshold.
Take the 1953 Zürich Candidates' Tournament:
210 games = 118 draws + 49 white wins + 43 black wins
Assume chess a draw.
Fit a Poisson distribution so the probability of an odd number of errors is (49 + 43) / 210.
Result: mean value = 1.044 error / game.
Games with 0 errors: 74
Games with 1 error:  77
Games with 2 errors: 40
Games with 3 errors: 14
Games with 4 errors:  4
Games with 5 errors:  1

Now assume chess is a white or black win.
Fit a Poisson distribution so the probability of an odd number of errors is 118 / 210. 
Result: impossible fit

Conclusion: chess is a draw with best play from both sides.

7zx

But there's no reason to suppose that it's a Poisson distribution.

If there is a forced win, nobody's figured out how to do it yet - probably because it involves deep calculations which are beyond the ability of existing players.So it wouldn't be surprising if everybody made the same 'mistake' of missing the win.

tygxc

@4505

"But there's no reason to suppose that it's a Poisson distribution."
++ There is reason, a Poisson distribution is derived from the Binomial distribution and applies to many similar stochastic processes.

"If there is a forced win, nobody's figured out how to do it yet" ++ OK

"probably because it involves deep calculations" ++ speculative

"So it wouldn't be surprising if everybody made the same 'mistake' of missing the win."
++ No, this would be extremely surprising. How would such a win look like? 1 a4? Even that has been played several times by grandmasters. It runs against all human and engine logic.

lfPatriotGames
7zx wrote:

But there's no reason to suppose that it's a Poisson distribution.

If there is a forced win, nobody's figured out how to do it yet - probably because it involves deep calculations which are beyond the ability of existing players.So it wouldn't be surprising if everybody made the same 'mistake' of missing the win.

Or as it was explained to me, as far as we know there has never been a game with no errors. 

 

Nicoquelicots
Optimissed a écrit :
tygxc wrote:


'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.' - Capablanca
AlphaZero corroborates that with no other input but the Laws of Chess: Figure 5 and Figure 31
https://arxiv.org/pdf/2111.09259.pdf
Also 1 c4 and 1 Nf3 merit attention.
Those are the 4 best moves, so solving chess can restrict itself to those 4.
If the 4 best moves cannot win for white, then the 16 worse moves cannot win either.


1. c4 is at least equally good and possibly fractionally better. 1. Nf3 also cannot be much worse than either of them. It may be about equal.

I wouldn't trust AlphaZero to be unbiassed, as I was explaining to Elroch.

Good morning,
Thank you for your answers to all. It is true that e.e4 and 1.d4 are unanimously cited as the first reference shot. But I also agree with 1.c4 which can be quite embarrassing for blacks.
I read that in machine-to-machine matches, to avoid draws, humans impose the first moves to force machines to play from various positions and thus sometimes unbalanced. And even like that there are about 3/4 of draws against 1/4 of blank wins. Which means that the advantage of the first shot of the whites can hardly be missed by the blacks and gives at best a draw for the blacks.
Happy end of days

tygxc

@4507
" there has never been a game with no errors"
++ They lied to you.
99.7% of ICCF WC draws are games with no errors.
Even Zürich 1953 had 74 games with no errors.

tygxc

@4508
"the advantage of the first shot of the whites can hardly be missed by the blacks and gives at best a draw for the blacks."
++ The advantage of 1 tempo is not enough to win,
so chess is a draw with best play from both sides.
You cannot queen a tempo.

Elroch
tygxc wrote:

@4505

"But there's no reason to suppose that it's a Poisson distribution."
++ There is reason, a Poisson distribution is derived from the Binomial distribution and applies to many similar stochastic processes.

Actually, we can be sure that this is a rather crude model that can be improved upon, and that the improved model would give different results (how much is unclear).  For example,  we could certainly use errors Poisson by move or errors Poisson by game, with the former being more natural to me. In the former case, there is surely a better model that takes into account empirical dependence of errors on game length. In the latter case there is surely a better model that takes into account the variation in error rates depending on the stage of the game (maybe errors are most common in the middle game). Both could be improved by incorporating any information on the strength of the two players etc.

Nicoquelicots
tygxc a écrit :

@4508
"l'avantage du premier coup des blancs peut difficilement être raté par les noirs et donne au mieux un nul aux noirs."
++ L'avantage d'un tempo n'est pas suffisant pour gagner,
donc les échecs sont un match nul avec le meilleur jeu des deux côtés.
Vous ne pouvez pas ajuster un tempo.

Yes, of course, but this one-shot advantage is decisive for machine-to-machine matches, which is why blacks do best with a draw. No?

tygxc

@4511
"this is a rather crude model"
++ Yes, I first calculated with an even cruder model with just high school math.
The result is about the same.
A more refined model may yield slightly different results, but no drastic changes.

"errors Poisson by move or errors Poisson by game"
++ Yes, you could use Binomial Distribution by move, but it would not make much difference.

"the variation in error rates depending on the stage of the game"
++ Yes, as chess is most complicated around 26 men, it is plausible that most errors occur around 26 men. It would not make much difference in the result: chess being a draw and the number of games with 0 errors.

"information on the strength of the two players"
++ No, that is not relevant. I take a sufficiently large tournament with a sufficient number of players of sufficient quality and then apply statistics to that. The last ICCF WC is suitable as well as Zürich 1953. From the statistics follows that only chess is a draw is consistent with the observed data and follows the number of games with no errors: 127 for the ICCF WC and 74 for Zürich 1953.

tygxc

@4512
"this one-shot advantage is decisive for machine-to-machine matches"
++ No, the first move advantage of 1 tempo is not decisive in machine vs. machine matches.
On the contrary: in the TCEC top chess engine competition they had to impose slightly unbalanced openings to avoid all draws.
The more time you give the engines or the humans, the more they draw.

Elroch
Optimissed wrote:


I'll try to explain it. You're a statistician and therefore accustomed to dealing with sets of events in the "macro". Considering a unique event, you will tend to see its outcome "a" or outcome "b" probabalistically, since as a unique event but still an event which is viewed in the context of the set, superficially outcomes a or b follow probability patterns. Within the context of the set, viewing all the events as a whole, each unique event is simply part of this or that subset as part of a statistical pattern. That tells us nothing about the event itself.

Bayesian probability is about the state of belief in a proposition that is uncertain (cannot be deduced by Boolean logic from the known information). It is well-known to be fully suited to dealing with samples of one, using all the inductive power available and no more.

An outcome on the chess board may be considered to have a definite result with best play: but it is one that may be unknown.

Correct. That is a situation where one wishes to quantify belief, and the only consistent way to quantify belief is Bayesian probability.

All probabilities that are assigned to it are therefore the result of guesswork based on inductive reasoning.

This is an inconsistent sentence.

The prior is the only thing that could be described as "guesswork" (though you would not use this word if you were familiar with the work in the subject, which often gives an answer to "what is the appropriate prior?".  And of course, inductive reasoning has no element of guesswork. Fundamentally it is the correct application of Bayes rule (difficult as this may be to formalise in a specific example).

That is effectively equivalent to basing them on error limits.

This is an incorrect comparison to something you are familiar with from frequentist statistics.
Anyway, that's my thinking. 

 

Elroch
tygxc wrote:

 

"information on the strength of the two players"
++ No, that is not relevant. I take a sufficiently large tournament with a sufficient number of players of sufficient quality and then apply statistics to that. The last ICCF WC is suitable as well as Zürich 1953. From the statistics follows that only chess is a draw is consistent with the observed data and follows the number of games with no errors: 127 for the ICCF WC and 74 for Zürich 1953.

It is relevant because it is available information that definitely affects the rate of errors. Weaker players make more errors. Players playing against stronger players make more errors (because stronger players are so because they provide more opportunities for the opponent to make errors). The only question is how relevant it is. Undoubtedly, like most things, you would be keen to make an absolute proclamation about this without any quantitative reasoning.