Chess will never be solved, here's why

On the note of solving chess, here's a 10 minute game I just played, which is a lot of fun. It's a new idea in the Russian Grunfeld where, as white, I played Qb3 a move earlier than normal. My opponent responded with e6, which is the first time I've seen it. I immediately tried to take advantage of what I thought is a weak move and nearly got into trouble myself. I'm far from being an expert on the Grunfeld and haven't even worked out which system I prefer against it.

Yes, of course. I used to enjoy solving paradoxes. That is, spotting the thought-flaw. Similar can also occur in such things as Ontological Arguments for the Existence of The Supeme Being, where many people cannot spot the place where the new premise is smuggled in or, and this is the analogy with the idea of infinity in maths, where an old premise very subtly changes its meaning.

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)?

John Nunn. One of my early chess opponents was someone who was studying at Lancaster University. Forgotten his name but can picture him. It would be circa 1975. He told me that he might have won the London Junior Chess Championship except that someone else was competing that year. He had expected to win it, I think and I think that someone else what John Nunn. But I could compete against this person, whose name I've forgotten, and probably got about 33% against him. Since I'd never studied chess at all, maybe I could have been good if I'd taken it seriously, joined a chess club and studied it. I was 36 before I started to take it seriously and at that time was too busy to put much effort into it.

I should like to have a talk with this Professor Conway. If he has anything to do with this Weak and Strong solving routine, together with the inapplicable idea of "strategy", I should like to find out in his own words why he's got it so wrong or at least to let him argue for his point of view more persuasively than you ever managed to. Some professors and other academics I have met have been brilliant and others maybe not at all. Some are carried away with the idea of their own invulnerability. If you could argue why you think this routine, which you so strongly support, is OK for solving chess, rather than just taking it on someone else's authority, then my opinion of you would change, even we were still in disagreement.

My own reaction to it is that it's a facade. And an extremely simplistic one at that. These ideas of weak and strong solving don't add anything, when they are so ill-conceived. As for the idea of strategy, you still haven't told me why you think it's a good one. I think it's banal and just wrong.

Good, and thanks for clarifying that we're talking about the same things.

I didn't play it well and in a proper game I would never have played that way. I would normally develop, to try to take advantage of the light square weakness around my opponent's king. But this was a 10 minute game and the first one of the day. I usually lose the first game I play and in any case, one of my learning strategies is to deliberately play an interesting continuation that may be wrong. It turned out my opponent could have broken up the centre with a timely Nxd5 and white would have been on the worse side of equal.

I used to use 4. Qb3 out of preference to the more normal 4. Nf3, experiementing perhaps with ways to try to play f3. I soon found that approach to be too difficult for white. The previous time I played 4. Qb3, my opponent seemed to move-order me in some way and I lost. My other approaches to the GF are 4. e3 and 4. Bf4. I tend to win them when I'm playing well and lose when I'm playing badly, whereas I find the Russian with 4. Nf3 and 5. Qb3 more solid, with the right balance of aggression and development.

@4887
As chess is a finite game, it can be solved.
Chess could be strongly solved to a 32-men table base with 10^44 legal positions.
Chess can be weakly solved in 5 years calculating 10^17 relevant positions.

Can you support this?

@4889
"Can you support this?"
++ as previously said: the number of legal positions in finite: 10^44.
https://github.com/tromp/ChessPositionRanking

Thanks to the 3-fold repetition rule each position can at most be visited twice.
Thus each chess game ends after a finite number of moves.
Thus chess is a finite game.

The state space of the version of chess with a repetition rule (traditionally 3-fold) is enormous whether there is or is not a rule like the 50 move rule.

The reason is that what has happened matters, not just the current position. Indeed, you need to keep a visit count for all positions that have been visited and that could be reached again by a legal sequence of moves. So the state space consists of objects that consist of a position (a la FEN) plus a list of other positions that have the property that the current position can be reached from them and they can be reached from the current position (another way to put this is that they are all in the same equivalence class as the current position, according to the partial order that is defined as the existence of a legal path between two positions).

Another way to define this state space is as a set of equivalence classes of partial games. The equivalence relation is that the current position is the same and the set of counts for all previous positions that could be reached again in the future of the game is the same.

Anyhow, this state space is mindbogglingly enormous. I have never even seen an estimate of it, but its size clearly has thousands of digits in base 10, compared with the mere 45 digits for the size of the state space of basic chess.

There is a simplification that helps to get around the size of the state space.  I assert that if there is a strategy that can reach a decisive result from a position, there is a strategy that can reach this result without ever repeating a position or allowing the opponent the opportunity to repeat the position. If this claim is true, solving the game becomes equivalent to solving a version of chess where any repetition of position is illegal (and if there are no legal moves it is a draw).

Actually that doesn't help much - we still need the list of previous positions that are reachable.

Always trying to say these two things together as if they are equivalent.

#1 is proven by study.

#2 is complete conjecture, by you.

You can't float #2 on by along with #1...

He claims it is achieved by ignoring all moves that have an evaluation below some number.

If I might interject, I think that perhaps you are thinking that without the 50 move rule, endless repetitions can occur and so chess is therefore infinite and could not be solved...but in terms of solving, an endless repetition is simply a draw, and the calculations move onward.

In the case of tablebases, they are built going backwards from checkmate.  So, you cannot ever logically reach an endless repetition in a regression like this.  We're at 7 man tablebases right now, so for 7 pieces or less, if the position is *not* forced mate and not in the tablebase, it is therefore a draw.  Draws are inferred by exclusion.

@4891
"I have never even seen an estimate of it"
I have shown one: The number of possible chess games lies between 10^29241 and 10^34082
https://wismuth.com/chess/longest-game.html 

However, all of that is irrelevant. The 50-moves rule plays no role at all in solving chess.

Solve chess without the 50-moves rule. The same solution applies with the 50-moves rule.

We have over 1000 perfect games with optimal play from both sides: ICCF WC draws.
In none of these was the 50-move rule invoked.
Average game length was 39 moves with standard deviation 14, minimum 16, maximum 102.
7-men endgame table base wins were allowed including those that exceed 50 moves without capture or pawn move, but no 7-men endgame table base wins were claimed.
7-men endgame table base draws were commonly claimed in 10% of games.