Chess will never be solved, here's why

Freedom of speech is non-negotiable with me....I appreciate the appeal to kindness and relevance, both of which I value. But when those things are placed ahead of freedom, too much power is placed in the hands of the authorities, and some form of tyranny is inevitable. 
I'll do my best to be kind and relevant, but I'll never compromise my freedom of speech or ask anyone else to. 

Kindness and relevance are best applied by culture rather than by force. 

I feel unconfortable being part of a consensus but in this case it seems there's a natural, justified consensus. tygxc's participation is to repeat what can be described as propaganda for a point of view, which can only be described as unthinking. It's unthinking to continue to adhere to the beliefs of a supposed authority figure, long after they've been shown to have been a probably drunken boast, incapable of being supported. That's beyond doubt to those who know sufficient about this. My own expertise on the subject is far less than that of btickler, MARattigan and Elroch. Yet although I don't claim expertise, I was a very keen software hobbyist in the late 80s and early 90s. I wrote number-crunching programmes and worked out for myself, from first principles, algorithms to find prime numbers, which coincided with what turned out to be the standards in the field. I was concerned with programme space and execution speed at a time when that was wrongly seen as less relevant and when the thrust of programming was proceeding, to me wrongly and stupidly, in the opposite direction, which was to produce norm-conformity and interchangeability in a discipline which was too new for that, so that what was happening was counter-productive in the long run. I accepted that my future did not lie in programming and all my supposed brilliance didn't have any future there. After passing, with very high marks, the first year of a computing degree, I swapped to a degree in philosophy and also gave up computing as a hobby.

Even so, I can still think in Boolean terms, if the need arises; and I know that tygxc is definitely doing that (thinking in Boolean terms) where it's entirely inappropriate. All his complaints about off-subject posts ignores the fact tthat he steadfastly refuses to address all the arguments which show him to be wrong. He pretends they don't exist and we can and perhaps should draw our own conclusions from that.

Let's see if @tygxc can learn what deductive reasoning is.  He states that the proposition that 1. Nh3 can be ignored is "deductive knowledge".

This means that there is a sequence of logical deductive steps starting with a set of axioms and additional definitions and ending with the desired proposition as a conclusion.

Let's sketch out those steps.  Of course we start from the axioms that define the game of chess as a combinatorial structure, together with the definitions we need.

The required conclusion is:

PROP 1:  the value to white of the position after 1. Nh3  <= the value to white of the position after 1. Nf3

I hope we all understand what "the value to white of a position" means. This has a definition that is included in the set of axioms and definitions we start with.

I am personally unable to fill in the gap between the axioms defining chess and this definition and the conclusion that @tygxc claims is "deduced" (doing this would be of very similar difficulty to GENUINELY solving chess), but I merely have a couple of relevant degrees and many years of relevant experience and further knowledge to draw on, so I will have to hand over to him to sketch the way to fill the gap with DEDUCTIVE steps.

Over to you, @tygxc. Sketch the deductive proof of PROP 1 above.

This should be good. There has to be an axiom or set of axioms which may be reduced to

"1. Nf3 is, in all senses, superior to 1. Nh3, such that any continuation after 1. Nh3 cannot lead to a superior result for white than 1. Nf3, given best play by both sides".

Wonder if he'll realise that. Whoops, I've told him the answer.

wdirwd ^

I mean, edited ^

Not sure what you mean or whether you are being serious, but it's simply a proposition that requires proving. A very familiar situation to those who have experience of mathematics, computer science, game theory and all other rigorous disciplines.

<<Is the twin prime conjecture solved?
 
 
The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved.>>

Fascinating, although not as fascinating as Cecil Blanche Woodham-Smith's book on Queen Victoria.

I don't think an axiom, such as the one I outlined, which is necessary for his hypothesis to be true, can come before at least a partial solution of chess. Yet tygxc seems to conclude that the proof can precede the partial solution. He has therefore partially solved chess, in his own mind.

It is essential that @tygxc responds to post #6465 to support his previous claim.

You see, to tygxc "deduction" means à la Sherlock Holmes (to say the best); it is not a strict process like in mathematics or in formal logic. He pretends, imo, to not understand that such type of reasoning is inadequate for solving games.

     What you define as "clearly worse" is, in many cases, what I define as "what the committee of GMs don't like", as their opinion is what you propose using to determine better and worse.

     Eliminating so many possibilities is what makes me unsatisfied with any solution reach through this method.

@6474

"What you define as "clearly worse" is, in many cases, what I define as "what the committee of GMs don't like", as their opinion is what you propose using to determine better and worse."

++ Let us look at a few examples, where humans save engines irrelevant calculations.

1 e4 e5 2 Ba6? is clearly worse than 2 Nf3. It even loses to checkmate in 82.
It loses a whole bishop and all the rest is the same i.e. there is no compensation of any kind.
So the move 2 Ba6? can be safely discarded.

https://www.iccf.com/game?id=1164313 This was agreed a draw because it is a fortress.
Engines can go on for many moves until a 3-fold repetition.

https://www.iccf.com/game?id=1164259 This was agreed a draw because the opposite colored bishops make it impossible for either side to win.
Engines can go on for many moves until a 3-fold repetition.

@6465

"a sequence of logical deductive steps starting with a set of axioms and additional definitions and ending with the desired proposition as a conclusion." ++ Yes

The set of axioms are the Laws of Chess. https://handbook.fide.com/chapter/E012018 

"PROP 1:  the value to white of the position after 1. Nh3  
<= the value to white of the position after 1. Nf3"

++ This is what this paper did https://arxiv.org/abs/2111.09259
It was fed with no human input but the Laws of Chess i.e. axioms,
and it only performed boolean operations i.e. logic. It arrived at:
d4 > e4 > Nf3 > c4 > e3 > g3 > Nc3 > c3 > b3 > a3 >
h3 > d3 > a4 > f4 > b4 > Nh3 > h4 > Na3 > f3 > g4.

In human terms it requires a set of intermediate theorems deduced from the Laws of Chess.
One such intermediate theorems is that control over the center increases the value.
The center functions like high ground in the military: if you hold it the opponent fights uphill.
From the Laws of Chess follows that
Queens, Bishops, Knights, Pawns, and Kings control more squares from the center.
Thus control over the center increase the value.
That is the same in other games:
in Checkers the center is more important, in Losing Chess only 1 e3 wins,
in Connect Four only 1 d1 wins, in Nine Men's Morris: the best starting moves are b4, d2, d6, f4.
1 Nf3 controls 2 central squares and 1 Nh3 zero.
A knight on the rim is dim.
2 > 0, thus 1 Nf3 has a value >= 1 Nh3

Another such intermediate theorem is that greater mobility increases the value.
That is also true in other games like Nine Men's Morris. If you have played b4, d2 and your opponent f4, d6, then it is better to play d7, d5, e4, or g4 that limit your opponent's mobility than a4, c4, d1, or d3 that limit your own mobility.
In the initial position white has 20 legal moves.
After 1 Nf3 white has 23 legal moves.
After 1 Nh3 white has 21 legal moves.
23 > 21, thus 1 Nf3 has a value >= 1 Nh3

There is a hierarchy in the intermediate theorems:
King safety > material > center > mobility
A lone knight can defeat a whole army with a smothered checkmate.
King safety also explains why
Nf3 > Nc3
g3 > b3
c4 > f4
b4 > g4
c3 > f3

"I merely have a couple of relevant degrees and many years of relevant experience and further knowledge to draw on" ++ Me too

So there we have it.

@tygxc doesn't know what "deductive logic" means and doesn't know what "relevant degree" means either.

Perhaps I was wrong to think he would be one of those who understood what the value of a position is. For clarity: V(given position) is defined in three simple stages:

Let W be a white strategy and B be a black strategy (always assumed to be deterministic)

V(W, B) is defined as the (deterministic) result when these strategies are played against each other.

V(W) is defined as minimum over all black strategies B of V(W, B),

V(given position) is defined as maximum over all white strategies W of V(W)

@6478
There is no contradiction of any kind.
Your formalistic descriptions simply mean 'the outcome if all participants play optimally.
So V = min [V(W)] is indeed no higher for 1 Nh3 than for 1 Nf3. q.e.d. 

This is a good example of verbal reasoning being far better than the attempt to depict it algebraically, which we see here. I could portray it verbally. It would be much clearer and without need for further explanation. One thing I don't understand is this: why is the interplay of strategies deterministic? What's the reasoning behind that, because I think it's incorrect?

It is more difficult to believe that someone with a relevant degree would forget what deduction is. A bit like a literature graduate forgetting what a noun is.