Chess will never be solved, here's why

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playerafar
7zx wrote:

Lots of people know more about maths than you do. This tygxc person is probably one of them. Nothing conceited about that.

I didn't say me.
tygxc claimed he knew more than anybody here.
You didn't read properly.
But that's okay. I can ignore.

playerafar
Elroch wrote:

I feel we should try to keep this impersonal. In addition, let's ignore @tygxc's eccentric misuse of terminology such as "solve", "ultra-weak solve" and his obstinate refusal to acknowledge the key distinction between a proof and a probabilistic argument. While annoying it is just bad semantics.

Given that, it's worth emphasising that while it isn't solving chess in the well-established unique sense, probabilistic analysis can be interesting and worthwhile. An example of this is Tromp's valid probabilistic procedure for estimating the number of legal chess positions, with clearly quantified uncertainty.

A grand aim which may be more accessible that solving chess might be to determine a valid probabilistic estimate of the chance that chess is a draw. We have not seen this - only estimates that are invalid for well-defined reasons. The question is whether there could be any such method.

It is possible/likely that the very heterogeneous and arbitrary nature of chess would make such an aim impractical. But can we find any way to attack this problem?

I think tygxc's claim that he knows more than everybody here should not be ignored.
It reveals motivation.
Plus its a false claim.
Proven by others more knowledgable constantly. Or more logical. Or both.
I knew instantly years ago his claims were false as soon as he tried to claim that the fundamental speeds of computers involved 'don't matter'.
And again when he 'took the square root'.
--------------------------------------
My point is what his posts are really 'about'.
And when he falsely claimed 'knows more' - a big chunk of 'what its about' suddenly revealed. Very reminiscent of the 'absent person'.
He's still a 'foil' (in a positive sense) to the discussion though and unlike that absent person - keeps the forum mostly 'on topic'.
Its just that when anybody asks 'why is tygxc doing this' it seems he has now provided a lot of the answer.
As you say @Elroch it can be 'less personal' now - because that part has been partly 'solved' now. No pun intended.

Elroch
MARattigan wrote:
Elroch wrote:

Yes. I am suggesting consciously focussing on a different goal that isn't as clearly out of reach. The problem is not the computational demand, it's coming up with a procedure that achieves a valid estimate.

First, I think, defining the concept. It seems to envisage sampling a set of games, but any old games (e.g. Fool's Mate) won't do. So, what set? And would all games in the set count as equally probable? I don't quite get it at the moment.

I don't get it either. I believe there is probably no practical calculation. But I am not sure.

playerafar

Nobody has been able to figure that one.
In the meantime - a lot of progress with engines 'playing better' though.
Not perfectly. Just better. Better than humans can. Including faster.

Elroch

AIs kind of try to solve this. They learn the probabilities of each outcome for a position. This can then be applied to the first position. wink.png But their probabilities are more like practical outcomes than theoretical ones. Eg (click to enlarge)

MARattigan
tygxc. wrote:

...

It can only be either a draw, or a white win, or a black win. There is no uncertainty.

...

Yes, that's pretty well no uncertainty.

playerafar

I was also thinking - how do computers do against humans at poker?
Poker AI is quite strong. And the more a known human opponent plays a poker engine the better the computer plays against that human player.
But apparently AI doesn't have quite the edge in poker that it does in chess - although the poker engines continue to improve.
An article on it here:
https://www.reddit.com/r/askscience/comments/2d6my1/can_computers_beat_champions_in_poker/

456aleAa

la verdad solo se español

456aleAa

quien se une

456aleAa

comenten los que saben español

playerafar

Maybe he's saying 'the truth can only be known in Spanish'.

Elroch
MARattigan wrote:
tygxc. wrote:

...

It can only be either a draw, or a white win, or a black win. There is no uncertainty.

...

Yes, that's pretty well no uncertainty.

Yes, it's like a coin flip. It can only be a head or a tail. No uncertainty. Except the uncertainty whether it is a head or a tail. wink.png

playerafar
Elroch wrote:
MARattigan wrote:
tygxc. wrote:

...

It can only be either a draw, or a white win, or a black win. There is no uncertainty.

...

Yes, that's pretty well no uncertainty.

Yes, it's like a coin flip. It can only be a head or a tail. No uncertainty. Except the uncertainty whether it is a head or a tail.

I know this sounds inane - but the coin could stand on edge.
Or be vaporized on the way down.
Or land in quicksand.

Elroch

Always such relevant points...

Brilliant19

It is so easy to make money using this

MEGACHE3SE
tygxc wrote:

@12710

"keep this impersonal"
++ This thread is about weakly solving chess, not about my university degrees.

(which he was completely unable to provide)

"The chance that chess is a draw" ++ 100%. Chess is a draw.

if 100%, then chess has been ultra weakly solved. where's the proof?

oh wait you're just lying again.

It can only be either a draw, or a white win, or a black win. There is no uncertainty.

except for we dont know which, so there is uncertainty.

@12715

"So, what set?"

This is a good set: both strong and recent.

extremely bad set, as it only represents an extremely limited playstyle that is very likely to completely ignore possible wins to chess.

7zx
playerafar wrote:
7zx wrote:

Lots of people know more about maths than you do. This tygxc person is probably one of them. Nothing conceited about that.

I didn't say me.
tygxc claimed he knew more than anybody here.
You didn't read properly.
But that's okay. I can ignore.

Nice little passive aggressive insult there.

tygxc

@11323

"distinction between a weak solve and strong solve but it isn't relevant"
++ The difference is relevant. Checkers for example has been weakly solved, not strongly.

"a weak solve means only the games derived from perfect play are known but it still isn't known the exact result of every possible position reached through non-perfect play (ex computers solve that Ne4 in whatever position will result in a win, but doesn't know whether all other positions after not playing ne4 are losses or draws, but is nonetheless irrelevant)"

++ No, that is not true.
Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.

tygxc

@11317

"it's like a coin flip. It can only be a head or a tail. No uncertainty."
++ Indeed. Chess either is or is not a draw.

"Except the uncertainty whether it is a head or a tail" ++ There is no uncertainty: chess is a draw. You cannot say it is 99% sure to be a draw, because by definition there exists no real or thought experiment that yields 99 draws and 1 decisive game with optimal play by both sides.

Likewise you cannot say the Riemann Hypothesis is 99% true. It is either true or false.
Schrödinger's cat can be 50% dead, 50% alive, because you can open 100 boxes with Schrödinger cats and find 50 dead and 50 alive.

Truth and proof are distinct. Fermat's last theorem was true all the time since Fermat formulated it, and did not suddenly become true after Wiles proved it. Besides Fermat might have had a proof as he asserted in his marginal note.

Elroch
tygxc wrote:

@11317

"it's like a coin flip. It can only be a head or a tail. No uncertainty."
++ Indeed. Chess either is or is not a draw.

If you flip a coin in the dark, the value is UNCERTAIN until you switch the light on, even though the physical state is determined. The only valid STATE OF BELIEF is a UNCERTAIN one (a probability). If you disagree with this, you are daft, to be frank!

The same is true of any proposition which is not proven.

"Except the uncertainty whether it is a head or a tail" ++ There is no uncertainty: chess is a draw. You cannot say it is 99% sure to be a draw, because by definition there exists no real or thought experiment that yields 99 draws and 1 decisive game with optimal play by both sides.

Here you refer to a frequentist paradigm, which has no relevance to the question. A Bayesian probability - describing a state of belief - is an entirely different thing to a frequentist probability. Read literally anything by anyone who has a clue about the two paradigms to fix your catastrophically incomplete knowledge.

Likewise you cannot say the Riemann Hypothesis is 99% true.

The Riemann Hypothesis is unproven. The only justifiable state of belief about it is an uncertain one. Such an uncertain belief is quantified with a probability p STRICTLY between 0 and 1.

0 < p < 1

Even you should be able to understand that to suggest that a person has to be either certain the Riemann Hypothesis is true or certain it is untrue would be stupid.

Truth and proof are distinct. Fermat's last theorem was true all the time since Fermat formulated it, and did not suddenly become true after Wiles proved it.

This is true and irrelevant to the quantification of belief.

Besides Fermat might have had a proof as he asserted in his marginal note.

I would say this is ridiculous, but the appropriate Bayesian viewpoint is that there is a very, very low probability that this was so. It is just about conceivable that an exhaustive computer search could eliminate the possibility of any proofs short enough to meet the requirements and convert the appropriate Bayesian probability of this ridiculous possibility from very small to zero.

@tygxc, Bayesian probability - the only type relevant here, and not the Frequentist paradigm to which you refer - is about quantifying belief. Read that again and try to understand it.

You need to read the following carefully (and critically, if you wish, but I suggest not banging your head against a brick wall, so to speak) because it is clear to everyone that it is a gap in your understanding. You are unaware of Bayesian reasoning, and familiar only with the separate Frequentist paradigm, which is irrelevant to this discussion. While both paradigms refer to numbers called probabilities, these numbers refer to different concepts in the two paradigms - it's only the word (and some of the maths) that is the same.

At every point in time, you have a state of belief about the truth of a proposition. This is a probability ascribed to the truth of a proposition. This probability is a function of all of the relevant information you have (combined with a very uncertain prior belief from a position of zero or little knowledge). A good way to conceptualise the value is that it is the one which you would consider fair for having a bet on the truth of the proposition, the value for which you would be no happier on one side of the bet than the other.

It is inarguable that your state of justifiable belief changes in steps based on the information you receive. This means that the probability you ascribe to an event changes. (Bayes rule is a systematic way of changing your state of belief, the only consistent one with general conditions, but we do not need to delve into the technical details).

A key point is that it is very hard to justify moving from a state of uncertain belief to a state of certainty. It can only occur when the belief becomes a logically proven consequence of known facts (Boolean logic is an extreme special case of Bayesian reasoning).

This can occur for example at the end of a mathematical theorem when the result is proven. The same occurs when a weak solution of a game is completed. This can be viewed as the completion of a logical deduction - it is the point when every single possible counter has been covered and there is none left to be concerned about. To be very precise, you can think of the step from uncertainty to certainty as occurring when the number of nodes left to analyse falls from one to zero.

You claim certainty about the result of chess. Initially you had no reason for certainty about the result - all you knew were the rules of chess and the results that could occur. You could only have had a guess at the result. So of course, the justifiable state about, say, whether the game was a draw was some probability p, with 0 < p < 1. Those inequalities are strict.

The above, with no assumptions about Bayesian reasoning, means that in order to reach a state of certainty, you would have had a state of uncertainty and then received a single piece of relevant information and became certain.

What was that step? If you cannot identify it and justify that this single piece of information had the pivotal significance necessary to cause a radical change in belief state you have confirmed that you are fooling yourself and confusing strong belief with certainty. Given the facts about the problem, this is the only conclusion available. If not, tell us what that magic step was.

You can choose to learn a powerful concept and principle from this. I am sure you will not - you will remain obstinately and arrogantly wrong.