Chess will never be solved, here's why

@6452
"whether I like insults or not, I would fight hard to protect the freedom to speak them."

++ "Please be relevant and be kind." is imperative.
Slinging insults, posting off-topic pictures and novel reviews is against the terms of service.

@6461

""Please be relevant and be kind." is imperative."

++ Being relevant and kind is desirable. Being free is imperative. 

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. 

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.

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.

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. 

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.

Happy to clarify that by adding a definition that was left implicit (I shouldn't have assumed it was obvious).

A deterministic strategy is one which always plays the same move in any specified position.

If you play two specific deterministic strategies against each other, you always get the exact same game and the same result.

@6482

After this formalistic intermezzo, can we now agree in your lingo that

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

and 

the value to white of the position after 1. e4 e5 2 Ba6  <= the value to white of the position after 1. e4 e5 2 Nf3

It's a definition that is used in the definition of the value of a position.

As chess players willing to take a good bet we could.

But game theorists trying to solve chess definitely cannot. These results are unproven, just like it is unproven that chess is a draw, and just like until recent history it was unproven that checkers was a draw (until it was proved).

You are the former.

@6488

Let us go back to your own previous post @6445:

"Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes
that are evaluated by the minimax algorithm in its search tree."

"It stops evaluating a move when at least one possibility has been found
that proves the move to be no better than a previously examined move."
++ 1 Nh3 is no better than 1 Nf3. 1 e4 e5 2 Ba6? is no better than 1 e4 e5 2 Nf3

"Such moves need not be evaluated further."
++ Thus 1 Nh3 and 1 e4 e5 2 Ba6? need not be evaluated further.

"When applied to a standard minimax tree, it returns the same move as minimax would,
but prunes away branches that cannot possibly influence the final decision."
++ The branches 1 Nh3 and 1 e4 e5 2 Ba6? cannot possibly influence the final decision.

I'm sorry, but your thinking doesn't make sense. A definition only needs to be valid, there is no notion of "accuracy".

Given the set S of legal states s in chess where white is to move, each s of which has a non-empty set of legal moves M(s), a deterministic strategy for white is a mapping f from S where f(s) is always a member of M(s).

That definition is valid because it determines whether something is a deterministic strategy for white or not.