Chess will never be solved, here's why

I was not addressing the general "you", but the specific you.

If you still don't get it, I don't know what to tell you, it's your own past anecdote I'm referring to.

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].

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. 

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. 

    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!

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.

Looking this up, Qb3 is relatively uncommon (c. 500 games) but perfectly reasonable, and e6 is sufficiently odd looking to make it extremely rare, but is only a minor inaccuracy according to an engine.

Infinity is not a number...it is a concept. pi and e are numbers that just happen to be irrational numbers, which means they cannot be represented by a fraction. However, both pi and e are EXACT numbers. Their exact values are known.....just not in ratio or fractional form. The "exact value" of infinity has no real meaning, because it is not a value. 

By the way, I happen to know ALL the digits of both pi and e........... just not in order.

Before what?

It is a long time since I first met John Nunn (ex world chess problem solving champion), Stephen Hawking (really stretching a point - I have been a yard from him in the DAMPT tea room) and several other mathematicians who merit the term.

But I think #1 for me would be one I did properly meet and talk to - Prof. John Conway. I was later given a copy of his two-volume work on game theory - Winning Ways - as a present. This is a beautiful investigation of a generalisation of numbers (called nimbers) which encompasses a large class of games.  But my awe for him came from the excitement he inspired about whatever mathematics he turned his hand too, such as knot theory (my first encounter) and his serious work on group theory - I still remember the sign over his office door which said "∃ M1" which referred to the recently proven existence of the largest sporadic simple group. Oh, he also invented the Game of Life (cellular automaton), which was eventually shown to be Turing-complete,  and is also quite well-known for the "free will theorem" which showed that, with not uncontroversial definitions, if a person has free will, so does an elementary particle. [Indeed, Conway has sparkling notions named after him in a wide range of math-related fields]

If, ridiculously, you don't recognise Conway as an exceptional genius, I refer you to his obituary from Princetown University.

What was that you saying, again?

For anyone interested (yeah, I know...that's a long shot), pi is the ratio of the circumference of any circle to its diameter (approx 3.14) and e (approx 2.71) is the base of the natural logarithms. Both show up in mathematics in many places and have many uses. e (named after Swiss mathematician Leonhard Euler) is much less known outside of the world of math and even most people who have need to use math beyond basic arithmetic use base 10 if they get into logarithms. In calculus, using base e makes the math much less unwieldy and simpler. 

What I'm saying here is not serious math knowledge. I don't have that. This level of math knowledge would be the equivalent in chess of explaining how the pieces move. 

@4880
e turns up in many problems, even in this thread.

As shown, analysis of variations with width w and depth d lead to
1 + w + w² + w³ +... + w^d = (w^(d+1) - 1) / (w - 1)
positions if there are no transpositions, and

1 + w + w²/2 + w³/3! + w^4/4! + ... = e^w
positions if all moves can be permuted

As shown, the number of errors per game can be approximated by a Poisson distribution
The probability P of having n errors in a game with average lambda errors per game is:
P = lambda^n * e^-lambda / n!

e answers the question:

what value of a (if any) has the property that the derivative of the function a^x is the function itself.

But it also answers the question:

what value of a (if any) has the property that a^(i theta) = cos(theta) + i sin(theta)?