Chess will never be solved, here's why

Yes, that looks right.

The numbers of pieces for different combinations of pieces are also strongly influenced by the distribution of the pieces. Eg the number of positions in the KNNNNNNNNk tablebase is surely much smaller than the number in the KQRBNkrbn one, because without considering checks the size of the latter would be 8!=40320 times as big, and the extra checks are not going to make up for that.

I still love to imagine that people click on this post expecting something really profound and are surprised when instead they get what is possibly the most downvoted post on the entire site

P9P : romans best movie imo was knife in the water. b&w's make the director work the shadows dont they ?

First of all you need a definition of "chess" that has only win draw and loss as results for either player where in all events a win for one player is a loss for the other and a draw for one player is a draw for the other, with the usual convention that for each player a win is preferable to a draw is preferable to a loss. Let us assume no resignation or agreed draw rules and also no iM or jR rules.

Let us take as a definition of "solve"

Provide one algorithm for each of the two players, such that the player using it can achieve at least the optimal outcome, regardless of the opponent's moves, from the start of the game.

posted recently on the thread.

Then the following algorithms for each player provide a solution.

For White on turn play move(D,'W','B',1+64!/(32!x2^6))[0] if it's non void

For Black on turn play move(D,'B','W',1+64!/(32!x2^6))[0] if it's non void

where D is the current diagram and move is the following function (vector entries starting at 0)

function move(d,f,s,n){

/* all variables local to the function */

..if n<=0 return [,0]

..if d is stalemate for f return [,0] 

..if d is checkmate return [,-1]

..r=[,-2]

..for legal moves m from d for side f {

....v->move(newd(d,m),s,f,n-1)

....If -v[1]>r[1] then r->[m,-v[1]]

....if -v[1]=1 then break

..}

..return r

}

function newd(d,m) return diagram after making move m in diagram d

Of course, if both players follow their algorithm the game could take some time and a lot of scrap paper, but there is no limit placed on either in the given definition.

Neither does the definition anywhere say you need to know the value of the initial position (though in terms of points it's (1+move(I,'W','B',1+64!/(32!x2^6))[1])/2 for White and 1+(1+move(I,'W,'B',1+64!/(32!x2^6))[1])/-2 for Black, where I is the initial diagram).

Neither does it say you need to prove that the algorithms work - it's sufficient if they actually do (though in this case you can prove it).

You may think that the quoted definition is a very bad definition.

If one player can force a draw that doesn't mean the other player can.
An idea - not a claim.
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Regarding 28 pieces on board having the most potential non-pawns and therefore the most positions of the 31-term series that defines all possible chess positions -
What would be the material allocation within that that has the most positions?
I think it would be under the heading of 12 pawns promoted and the other four captured.
Six pawns each promoted in other words.
But within that - for most positions:
four rooks each
four knights each
three queens each
two bishops each - the original two - in other words each moving on different colors
one king each. Of course.
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Can an upper bound then be worked out as to the number of positions that that allocation generates?
Yes.
3612 x (32 x 32 x 31 x 31 'for 4 bishops') x C(58, 3) x C(55, 3) x C(52,4) x C(48,4) x C(44, 4) x C(40, 4)
with the first two C (combinations) terms referring to the six queens
the next two C's referring to the eight rooks and the last two C's referring to the 8 knights.
Yes its going to be a gigantic number of positions just for that one allocation of material alone.
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I asked chatgpt to multiply out the expression and it pathetically kept blowing it.
So I then went to Gemini instead.
And it came up with a number of 187 octillion and change.
Which still looks high.
But there was also something 'suspicious' in the Gemini reply ....
187,998,376,838,888,888,888,800,000. 187 octillion. And change.
Uh oh.
Ten 'eights' in a row ???
Maybe it didn't row the boat right.

making my first comment for the achievement

Python did a more reliable job. Taking your formula as correct:

It has 40 digits compared to your 27.

The definition of ultra-weak solve requires a determination of the value of the game. Weak solving a game has always done so in practice, and the nomenclature would be horrible if it did not. So determining the value is a nice requirement for using the word "solve".

But the definition of "solve" I quoted doesn't require a determination of the value of the game.

Neither do the Wikipaedia definitions of weak and strong solutions (even with your quirky reading).

In fact the definition I quoted applies equally well to the game O I pasted some pages ago. The game doesn't have a value and not enough information to assign even an expectation. Nevertheless the algorithms, "carry on attempting to dispense a sheet of paper and staple it", for each player constitute a solution under the definition.

If you think that determining the value is a nice requirement for using the word "solve" that means it should appear in the appropriate definition. In fact there are a number of different possible meanings of the word "solve". If distinguishing between the different useful meanings results in horrible nomenclature then so be it. But my point above was referring to the content of the definition for a term already in use, not addition nomenclature to accommodate extra meanings.

For a weak solution this requirement is achueved by not only having an algorithm for each player that is provably correct (which at face does not necessarily tell you the result, even if in practice it is likely the writer of the algorithm knows if they are aiming for a draw or a win!), BUT also executing those two algorithms against each other in just one game!

Not a requirement in any extant definitions I've seen, but a previous Wikipedia definition gave the production of a provenly perfect game as an alternative definition of "weak solution". Doesn't appear to be any need for it. The algorithms need to work against any play by the opponent.

. the combination of:

1. knowing the two algorithms are optimal
2. knowing the result of one game between them

solves the game in the sense of determining the value.

2. is not called for in the definition I used above (but I did in fact quote the result).

This is appealing, as it removes the wooliness of "using reasonable computational resources". (Which happen to be my words ).

Unfortunately, "using reasonable computational resources", is a very large part of what this whole thread and pronouncements of games being solved in the public domain are about.

I did earlier in the thread give definitions which included the word timely, timely referring to the situation for which the solution is required. So for example the purported solution of checkers would not be a weak solution for a one minute blitz game. It should have referred to also storage and resources, so what should be defined is probably something like .

weak solution (t,s,r) for a player ... blaah blahh ... in time < t using storage < s with resources r.

weak solution for a player is weak solution (∞,∞,r) with some set of resources r. 

weak solution (t,s,r) of a two player WDL game is a weak solution (t,s,r) for both players.

weak solution of a two player WDL game is a weak solution for both players.

The "blaah blaah" should also mention proof. Very large numbers of @playerafar's wide swathe of substantially materially unbalanced positions could almost certainly be solved against any opposition by any one of the algorithms in the heads of chess players above a certain ability. But the proof is crucial.

Note that this still leaves a major distinction of ultraweak solving, as this does not have to provide any help for playing optimally. Interestingly, the common class of ultra-weak solutions called "strategy stealing" only provides a weak solution with certain extra conditions (eg a certain type of symmetry, and the axiom that playing a move is never a disadvantage).

[Wandering a little from the topic, it occurs to me that finding the value of a game/position by playing a single game between optimal algorithms resembles the approximate version of it that consists of an engine having at each stage in its analysis a mainline of best moves, with the evaluation of the final position reached being a possible choice for the evaluation of the initial position. Off the top of my head, I am not sure if top engines use this rule or whether they take into account uncertainty and use the evaluations of multiple leaf nodes to estimate the value of a position].

That's a bold claim! The idea of whether or not chess can be "solved" is a fascinating one, and there are indeed strong arguments to be made on why it's likely to remain unsolved for the foreseeable future, if not permanently. Here are some of the key reasons:

1. The Immense Search Space (Game Tree Complexity):

Branching Factor: At each move, a player has, on average, around 35 possible moves.
Game Length: A typical chess game lasts around 40 moves, but can go much longer.
Calculating the Possibilities: This leads to an absolutely astronomical number of possible game states. Estimates range far beyond the number of atoms in the observable universe (around 10^120).
Implication: To "solve" chess would require analyzing every single one of these possibilities, which is computationally infeasible with any technology we can currently conceive of.
2. The Computational Power Required:

Storage: Even if we could analyze the game tree, storing the results would require memory far exceeding any current or projected capacity.
Processing: The sheer number of calculations needed to evaluate each position and determine the optimal move at every stage is beyond the reach of even the most powerful supercomputers.
3. The Nature of "Solved":

Weakly Solved: Knowing the theoretical outcome of the game from the starting position (win for White, win for Black, or a draw) assuming perfect play from both sides.
Strongly Solved: Knowing the optimal move from any possible position.
Implication: Even achieving a weak solution seems incredibly distant. A strong solution is likely impossible.
4. Human Understanding vs. Computational Solution:

Intuition and Pattern Recognition: Human chess masters rely heavily on intuition, pattern recognition, and strategic understanding, which are difficult to fully replicate computationally.
Complexity Beyond Calculation: While computers excel at calculation, the strategic depth and nuances of chess involve complex relationships that aren't easily reduced to simple evaluations.
5. The Ongoing Evolution of Chess:

New Ideas and Strategies: Even after centuries of play, new ideas and strategies continue to emerge in chess. This dynamic nature makes it difficult to create a static "solution."
In summary, the sheer complexity of the game, the immense computational resources required, and the difference between human understanding and a purely computational solution make it highly probable that chess will remain unsolved. While computers have surpassed humans in playing strength, "solving" the game in the mathematical sense is a different and far more daunting challenge.

It's more likely that chess will continue to be a source of intellectual challenge and enjoyment for humans and a benchmark for artificial intelligence for a very long time to come.

um that was my own opinion tho

ive been translating my stuff to english and I guess it messed with it

...

i guess im just a bot lmaooooo