Chess will never be solved, here's why

No. I wouldn't agree.

Consider the following two player game.

At the start of the game the index is set to 3.

White moves first and chooses a positive natural number.

If in a set prearranged time Black can find another positive natural number such that when the two numbers are raised to the index and added the result is some other natural number raised to the same index he wins.

Otherwise the index is increased by 1 and Black moves next with the roles reversed.

Thereafter the players alternate moves, the index increasing by 1 each time.

It was suspected for a long time that the game was drawn and some results were established such as, like chess, the game could not be won on the first move. But relatively recently the game was completely solved as drawn.

Note that the game tree, game states and branching factor are all infinite.

But the solution was not found by a BFI routine run on a computer. It was, in fact, a fundamentally different strategy.

I think if chess is ever solved the same will probably be true.

Edit: Now I think about it, it is trivial to prove the game I outlined is drawn, but still by a fundamentally different strategy.

came to this thread cuz i got a notif that opti got muted again, got jumpscared when i saw yall talking about tygxc lol.

but i do want to correct this, @tygxc's claim of the 5 year 'solution' is actually explicitly based on that method/solution for checkers. Yall mightve forgotten and have accidentally sanewashed him, but no, that was literally what tygxc was claiming. he just straight up assumed that not only was the chess engine involved going to be perfect, but that it would be perfect with only 1 node of computational power allocated per position.

tygxc never said ' that it would be possible by five years of effort to become more convinced about the answer we already believe, without getting anywhere near a true solution. He obfuscated this by obstinately misusing the term "solve"'

tygxc genuinely claimed that his methods (like discarding positions without actually looking at them, having enough strong engines reaching draws) were a rigorous logical proof.

ex: in response to "It's safe to say chess still can't be rigorously solved."
++ No, on the contrary it is safe to say chess can be rigourously weakly solved.The 17 ICCF WC Finalist and their servers are doing it now.110 games out of 110 that redundantly link the initial position in average 39 moves to certain draws. - Tygxc.

Yes. It's subtle difference.

@tygxc claimed that his proposed "solution" would complete in the foreseeable future and he also claimed that his proposed "solution" was along the lines of the checkers solution. Both were false. My meaning was that he had never claimed that a solution that was actually along the lines of the checkers solution would complete in the foreseeable future (only his own, which was not).

@MARattigan - I don't think you got the points I made.
For one - many bishops moving on the same color squares - not 'all bishops'.
For two - that isn't talking about 'won' positions.
For three - I didn't say 'all bishops'.
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I haven't taken the time yet to read over all recent posts by worthy posters such as yourself Martin and Elroch and Dio.
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But I did have some conversation with Grok just now about 'alternative solutions of chess'.
Various points were covered. Thousands of words 
Obviously I'm not going to do a 'Dubro' and kneejerk the entire conversations with Grok.
But there are salient points.
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First I had to get the concept across to Grok about tablebase endgame projects that concentrate on adding to won positions already established by Syzygy ...
then I had to get it to understand that this would not be done by retrograde move additions.
And I added that that would be hopeless in the way 'game tree' from the front already is.
No gametree analysis.
Not necessary. Once a position is established as a win because of lopsided material advantage - and you add any piece to the winning side - you only have to do another stalemate check and perhaps a couple of other relatively very minor checks like making sure an addition of a piece doesn't make winning impossible.
Which is extremely unlikely against lone king.
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then I started asking questions about a ratio of lopsided material wins to minimal wins (not book wins) ... and has anything been published about this?
Grok and I agreed that chessplayers and mathematicians would have considered such things both before and after the development of computers - and Grok mentioned about 'alternative solvings' of chess ... And I had to make it clear to Grok I was asking about published theories not 'published alternative solvings' whic hof course don't exist anyway.
As in not yet.
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Grok mentioned Moore's law and 'Haworth's law' (which isn't a law)
The point is there's apparently been no formal work done on computer projects to solve positions by adding material to won positions that are wins because of lopsided material advantage. Nor has there been formal published theory on that either.
As in - not anything that Grok found when I asked it.
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Grok liked the idea - and gushed. But it often does. The idea is to ignore that.
Grok - like Chatgpt and Copilot is built with an idea that it must err on the opposite side of cricizing its users.

Hi MEGA 
you got here just in time to miss Dubrovnik getting muted for the kind of thing that Opto has been doing for years.
And 'crazyrat' (who has two C-Rat accounts and is also an ibrust account and does O-worship) getting muted although he's back from that mute.
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Conjecture about the number and ratio of lopsided material wins within John Tromp's number.
A legitimate way to cut it down.
John Tromp's number is a big cutdown from 13^64 and from the even bigger Shannon number.
But part of future solving might involve a process of further legitimate cutdowns.

I think maybe you're missing the point.

You're proposing not to investigate won positions with a large discrepency in material on the grounds that they're won. The gaping flaw is - how do you know they're won without first solving?

Of course I can give you lots of examples of positions with large discrepency in material that are won and fit in with your "For two", but the whole point of the example is that it isn't a win.

And the Bláthy example has only one bishop.

What algorithm would you propose to avoid assigning a value of winning to general positions with large discrepency in material that are not winning. How are you going to recognise the exceptions? Stockfish won't reliably tell you.

MAR - you're still missing the main points.
Are you suggesting that doing a stalemate check is harder than solving a position?
Your Blathy example is of something not applying to my suggestion.
Why would you want to include positions that add to a-apawn endgame draws?
Martin's a good man though. (tempted to make a pun based on Swiss Family Robinson and Swisss Army knife but that got cancelled before Season 1.)
Yes - Martin's a good man. I do mean that.
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Martin did you see my Philidor joke?
Lets try an even shorter version of it.
GM instructs E player how to checkmate with K+R versus K ...
'E' masters it fast - but then asks 'what about three rooks'?

Seems like I am.

Answer to first is "no", but I see no relevance.

As I understood it Bláthy example was exactly applying. You'd better explain it again, because I think @Elroch understood it the same way.

Added further to my previous reply posts just now. By editing.
Your Blathy position doesn't have 'won position' elements.
Where/what is the won position in it that was 'added to'?
Not an explanation but rather 'resistance'.
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Idea: Start with positions that Syzygy has already solved and classified as wins.
Add material to the winning side.
But do a stalemate check. That's the 'algorithm'.
Not just if its stalemate - just make sure that the winning side can avoid stalemateing.
Which isn't a deep thing.
Note that it wouldn't be considering positions already stalemate - anyway.
Because its only considering positions that are already wins.
It just has to make sure that if and when its on move that it can avoid stalemating.
And things like perpetual check - with either side to move.
Pretty hard for the losing side to check - with Lone King.
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I was mildly surprised when Grok indicated there was nothing published on this.
But Grok agreed with me that many would have thought of it already.
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Martin - if you want the Python script for this - and the API calls for asynchronous rollbacks and also the stack pointer considerations ... then maybe that could be a wait.
No full Monty breakfast nor Monty Python script available.

How about - 
Pretty hard for Lone King to perpetually check ...
and you can take that to the Swiss bank.

Hiiii

looks like Dubro is using an alt account?
Dubrovnik-1950 closed his own muted account apparently.
And seems has replaced it with a new AVRO-1938 account so as to beat the mute.

Oh really you think so? What ever asylum those messages are coming from, they shouldnt allow devices.

@MARattigan you're still talking about stuff I didn't say.
I put up a very simple example.
Did you see it?
K+R versus K. No stalemate positions because those would not be considered.
(Obviously the tablebase projects know which K + R positions are wins and which draws.)
So then somebody asks about K+R+R versus King - in other words adding another rook.
What is your issue with that Martin?
You can add as much material to the winning side as you like - add to the rook that is -
and as long as its not stalemate and the winning side can avoid stalemate when on move - then its still a win.
I wonder why you're not acknowledging this Martin.
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We could start with K+Q versus K too.
In fact all wins for the side with extra material besides his King versus lone king -
and again - so you don't forget - Syzygy has already solved all such positions with up to seven pieces on board.
We don't have to start with book wins.
The tablebase has already generated a big base to start with.
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Martin I think what is happening is you're looking at your own stuff instead of what I've been presenting to you.
The Blathy position is very irrelevant.
Compare it with positions that incorporate K+R versus King and then more material is added to the winning side - to any or every square - that doesn't produce stalemate.
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I admit I'm surprised you didn't get this. 
If I had been asked to guess in advance how fast you'd catch on - 
I would have picked 'about two seconds'. Elroch too.
Prediction: O and Octo will try to jump in and pretend its 'jumbled' or something like that.
In other words - pretend that K+R versus K is 'jumbled' but lets see if they can avoid being predictable.
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For those interested in using their own brains (AI assistance is fine, but not to the extent of delegating all thinking to the AI).

Reading the technical details about Schaefer's solution of checkers made me think of a relevant concept. This is to consider the notion of a modified version of chess, a one player game with an enhanced objectve.

The idea is the player is the agent trying to construct an optimal strategy and their objective is to do so with minimum computation. The agent has to pick strategy moves and these moves need to both achieve the optimal result and minimise computation.

There is a rather simple recursion associated with this because of the nature of an optimal strategy: in simple terms the computation needed is the sum of the computation needed for the positions reached by each legal move by the opponent.

It's best to think of this starting from terminating positions. A move that achieves the optimal result immediately is as good as it gets. If the optimal result is a draw, this would be a move that stalemates or one that reaches a position that reaches a position that has already been incorporated in the (tentative) strateg. Dealing with the latter entails no additional computational demand, because it already has to be dealt with.

Of course this extends to positions where we can force one of the above positions in 2 moves and so on.

This is just some incomplete thoughts, Schaeffer must have developed something like this more in order to use it in strategy construction. But I doubt he had what I would imagine here - some sort of machine learning algorithm to estimate the computational cost of each candidate move.

On another matter, can we have a consensus that fiction is spam here?

Your post #15468 put forward two distinct ideas.

A. The idea of computer projects seeking to solve chess by shortening the process with no further handling of positions that are obviously wins (corresponds to 'resign' in chess games) is a valid one.

and

B. I like this next idea:In all the solved tablebase positions (in other words all 7-piece or fewer legal chess positions) that have been found to be wins for white or for black - Each won position has a further algorithm run on it - where adding more pieces to the winning side in all ways that do not interfere with that side's win - is considered - but with no further evaluation - they are simply counted and added and a number of such is determined.

I didn't see anything to suggest the two ideas were connected.

The Bláthy position and the two immediately preceding positions I posted in my response and the positions I've subsequently posted are talking about A not B. You keep talking about B instead.

In fact in #15468 you say

tygxc took a little run at that but in a hopeless way.
Like for example wanting to reject all further analysis after e4 e5 Ba6.
It 'looks' valid. But the plus of a bishop isn't always enough to win.
Even with 'ceteris paribus' factored in.

The positions I posted are aimed at showing the plus of anything isn't always enough to win.
Even with 'ceteris paribus' factored in. 

In fact you're making exactly the same argument as @tygxc did. You have suggested some conditions to restrict the positions that can be assigned as won without further analysis, but they're too vague to implement in any such analysis without further detail and it's fairly apparent that any similar set of criteria that doesn't cover all the positions considered for skipping will probably result in some positions being erroneously assigned a win evaluation, either because they're drawn or won for the opposite side.

Can we first agree on A then we can discuss B, which is more of interest. My response to #15468 already commented on it, but further discussion is possible.

If you think I'm being slow on the uptake it's because your responses to my posts are talking about something unrelated to the subject of the posts you're responding to. And my posts have been talking about something you did say, namely A above.

If you reread my posts on the understanding that the topic is A, we can probably agree that A is dead. Can you confirm?

@AVRO-1938

Any chance of you getting into your own and Grok the world's Smartest AI's thick skulls that all versions of chess have a lot more than 10^43 positions and 10^120 games?

You're probably in a negative feedback loop. The more you post Gronk's duff figures, the more it's going to read your posts and believe it's right and the more it's going to repeat them to you and the more you're going to believe them and the more you'r going to post them ...