Chess will never be solved, here's why

I am not sure what you mean. If the rules of a game permit one to go on forever, it is excluded by definition.

If you meant something else, do say.

What is "perfectly obvious" to an ignorant windbag doesn't matter as much as you think it does.

With all due humility, I have a perfect understanding of the degree to which the relevant part of game theory is applicable to chess. It is as clear to me as the meaningfulness and value of the three definitions of types of solutions of games which all the cognizant people in these forums accept, which are well-established in the academic literature, and which you falsely asserted were made up for wikipedia!
With more appropriate respect for others and less unfounded arrogance, your understanding would improve greatly. [That's not a prediction].

I was trying to forcefully make the point that it may not always be appropriate fo "believe what you say". On this subject, especially w.r.t the application of T. of G to solving chess, you seem all at sea.

I could equally tell you that  you would very rarely go wrong by believing what I say.

Why you and not me? I also try to be precise, when the situation warrants it. You refused even to answer my points, which is a very clear indication that you cannot answer them. You call it a "body of knowledge" but there are various reasons why you are in error to call it that.

You have to answer my arguments because I can see very clearly that you are mistaken in this and that if you are following what is considered "knowledge" then you are incorrect to do so.

If you could define and explain "weakly solving chess" without resorting to other words that have to be defined, such as "strategy", and that means define it in an explanatory way rether than the obfuscatory way you have so far used, perhaps I could show you where I think you are going wrong. However, if you cannot or will not do that, then my criticism will have to stand.

This game was funny.

Wrong thread, I know but there's nothing to beat light relief.

So do the official rules of chess include a 50 move = draw rule? And if not, how can you claim chess is a finite game? And if it's not a finite game, why would the "Theory of finite games" apply?

I'm back to "There is no proof that an 'optimal' move exists in the general case".

Yes, Nerves of Butter, I understand that you can find me a specific case or two where there is obviously an optimal move, but that certainly doesn't prove that one always exists. And if you can't prove one always exists, you can't claim chess is solvable. 

Throughout this thread, some have mistakenly considered extremely large finite numbers to be the equivalent of infinity....."for all practical purposes".  This is a mistake. No matter how large a finite number is, it is not the equivalent of infinity....or even close.... period. And any logic or conclusions that follow that assumption are false. 

Well, we know the real meaning of infinity. Infinity is an ideal. That is, it's a concept of the mind only, with no real example that we can definitely say is infinity. Having accepted that, we can then use infinity in a metaphoric sense. There are ideas of quantities which we cannot say are infinite in reality but which are near enough, conceptually. As long as we understand that infinity is an ideal concept only, it seems fine to use it in any way we want, provided it isn't part of a mathematical equation.

That's because there is no absolute optimal move. Provided a move doesn't change the game result negatively, it is optimal in relation to a person who plays the move if it suits his or her preferred playing style.

Lol @ "Come to think of it".  You just didn't like the point I was making.  Where else did I mention tests?

If you are not obsessive, then what are you still doing in a thread where you keep telling everyone they cannot understand the problems or the terminology?  It seems like you have an issue...I mean beyond the fact that you said "goodbye" less than a week ago...

The concept of infinity has a very real, very useful,  and very specific meaning in calculus. 

I just read your ridiculously conceited epistle in its entirety.

My first observation would be that calling people an ignorant windbag may suit your ethical norms nicely, as well as your aesthetic sensibilities, so you're expressing yourself very well and showing who you are very perfectly BUT it isn't the best way to win an argument, because the only people who you will convince are other stupid people.

You may THINK you understand it and I think you don't. You make it obvious that you don't  because otherwise, you should find it easy to tell me where I'm going wrong. You deliberately obscure the subject and that is because you don't understand it. If you understood it, then you would be able to express yourself educationally and clearly.


<<It is as clear to me as the meaningfulness and value of the three definitions of types of solutions of games which all the cognizant people in these forums accept, which are well-established in the academic literature, and which you falsely asserted were made up for wikipedia!>>

Very good. The first thing is that you define those who agree with you as "cognizant". Not sure anyone does agree with you except tygxc, though. Some may believe you. That's different from agreement, so we can discard your use of "cognizant" as meaningless.

Secondly, I know it's on Wiki because I was referred there when this conversation began, as the source that was being used. And there it was: the erroneous set of definitions you're using. If you think those definitions are meaningul and yet you can't redefine them in a way that does not use the word "strategy", you're being dishonest with youself. I don't think that you're wilfully trying to deceive others: it's only that you're not intelligent enough to understand the relevance of the objections I have already made. You have a Masters Degree in stats. Being brutally honest, stats was always thought of as that branch of maths where those of lesser ability can stay afloat and find refuge. Previously, you deliberately decieved me and some others into the belief that you have a PhD. That's a bit pathetic, is it not? You aren't even honest so why should anyone give you respect? You don't give it to others.

I hope that people from your place of work are reading this. You know, the ones with the better minds than yours. There must be many of them.

Yes it does. Calculus uses the idea of incremental changes in one variable to calculate how that affects a dependent variable. I remember it being explained extremely well to us when we first learned it. Lots of curves drawn in chalk on the blackboard, being broken up into tiny strips, the ends of which would be curved. But it was explained that as the limits approached infinity, the error caused by the physical shape of the curves approaches zero. I enjoyed mathematics very much up to about first year university standard but I think ultimately my interests lay elsewhere. I'm not my son at all. He had the reputation at St Andrews of being a brilliant mathematician. I was never that or anywhere near but could calculate very accurately and fast in my head, which of course isn't maths but arithmetic. A prodigy, not a savant. I just learned to calculate using images in my mind. I could write a 10 digit number in my mind, do something else for a while and then read the number off, in coloured chalk. I could rub it out using a duster when I didn't need the number any more. All I can remember was that the calculations were visual and 3-dimensional, and I was doing two processes at once. And they depended on real time. That was vital. Any hesitation and it wouldn't work. I later worked out how the mind works, based on that.

I don't think Elroch ever met a true genius before. He can't cope! But the nature of the mind is that it changes through life and you have to go with it or lose what it gives you. It doesn't stay still.

Anyway, I did enjoy the pure mathematical basis of calculus. But although it has a real use, infinity is still a purely notional entity isn't it?

    Claptrap. The number of planets in the universe may be so staggeringly huge that we can imagine it as "infinite" when theorizing that this or that condition or phenomenon "must " exist somewhere, but this number pales in comparison with how many digits are in a computation of the exact value of pi--an infinitively-repeating calculation. 

     Of course you admit in your final phrase that your assertion is inexact.

Like many other things, yes. I was trying to illustrate that to a mathematician, infinity is not just a big number. It's a concept that is used every day and math beyond say, algebra, would be impossible without it. 
If you take the decimal .9999999999......... and extend those nines out to infinity, it equals one. Many people have a hard time with that. It isn't "almost" one. It EQUALS one.  Here's a simple proof:
1/3 = .3333333........ where the threes go to infinity. 

1/3 x 3 = 1. 

Therefore .3333333...... x 3 =  .99999999........   = 1. 

It's hard for non-math people to grasp that those 9's NEVER end. That's what infinity is. Our minds really weren't wired for this, so we have to kind of rewire to learn advanced math. I think the concept of solving chess challenges those same "muscles" in our brains. 

@4856

"So do the official rules of chess include a 50 move = draw rule?"
++ Yes in competition it is used, but ICCF allows 7-men endgame table base draws that exceed 50 moves without pawn move or capture.

"how can you claim chess is a finite game?"
++ Because of the 3-fold repetition rule.
Chess has a finite number of 10^44 legal positions.
As any of these can be reached twice only, any game of chess ends in a finite number of moves.

"There is no proof that an 'optimal' move exists in the general case".
++ As chess is finite, i.e. ends in a finite number of moves, it can only end in either a draw, a win, or a loss. Thus every position including the initial position also is either a draw, a win, or a loss.
In a lost position, there are only moves that lose.
In a drawn position there is at least 1 move that draws,
and there may be several moves that lose: errors (?).
In a won position, there is at least 1 move that wins,
there may be several moves that draw: errors (?),
and there may be several moves that lose: blunders or double errors (??).

"if you can't prove one always exists, you can't claim chess is solvable."
As proven above there is at least one optimal move in any position.

All I heard was something about MIRRORS!

So infinity is different in kind from pie or e. Would you agree with that or have I missed a fundamental which takes priority?

No, you missed my point entirely. As long as we understand that infinity is a notional idea, it is also possible to use that idea metaphorically.

It obvously isn't claptrap, since it's a point of view, which is completely valid in a World that is not dominated by one ideational paradigm at the expense of all others.

When we are talking about deductive reasoning - solving combinatorial problems (like the topic of this forum) and associated mathematical theorems, the difference between finite and infinite is far more than metaphorical - it has a large influence on what is true. The difference is so large that there are many examples that are viewed as "paradoxes" because intuition based on the finite can get misled when we move to the infinite.

As a model example, if you have a finite set of real numbers, one of them has a value less than or equal to that of all of the rest. If you have an infinite set of real numbers, this is not so.

This is relevant to game theory in at least one way (likely more). Say you have a game where the result is a real number, but this number is not limited to a finite number of possible values (as an illustrative example, chess has 3 possible values for the result).   This may cause problems with reasoning about strategies because you could have an infinite set of strategies where there is no strategy that achieves the "best" value - there is merely a sequence of strategies whose values tend to an unattainable value.

The theory of finite games deals with games that lack the property of chess that there is only a finite number of possible games (with a terminating rule relating to repetition and/or number of moves without irreversible change). It only requires that individual games are required to end by the rules and that the number of legal moves at each turn is finite.