Chess will never be solved, here's why

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OctopusOnSteroids

Yeah almost anything can indeed be done, I'm aware of that. Great point by you as always. I'm sure youd have a good time summarizing it to every new comer that stumbles into the thread.

Elroch
Optimissed wrote:

I should have thought that any opposition to the premise that chess will never be solved must be based on the premise that chess is a game of perfect information or that it may be made into such by means of what seems like a minimum of processing the patterns which we see and yet do not fully understand!

It's not a "premise" that chess is a game of perfect information, it's a fact easily proven from the axioms, using the correct definition of the term.

And no "I want to use the standard term to mean some other thing" is not a worthwhile input.

OctopusOnSteroids
Dubrovnik-1950 wrote:

I have no problem in articulating and summarizing the arguments from both sides.

You actually have a problem that you may not be aware of, which is that you dont understand the arguments from both sides

OctopusOnSteroids

I'm actually all for challenging stardard terms. If they dont function logically in a relevant context they can be challenged.... However, I'm not saying thats the case here yet.

This leads me to ask Optimissed the following question:

If we want to change the definition so that a game where we havent been able to access all the information yet isnt a game of perfect information... When approaching a task of solving a game, how do we distinguish games where the its impossible to achieve a solution that guarantees a theoretical result (poker) and a game where its theoretically possible given solved state, chess? If both are games of imperfect information, how do we determine what the solution could offer us... Does the question make sense?

OctopusOnSteroids

Yes Optimissed, the discussion here is based on chess being theoretically solvable. If we were to define it as a game of imperfect information are we saying that we were wrong to think its solvable in theory?

Elroch
Optimissed wrote:

I would respectfully suggest that a definition which defines chess as a game of perfect info is ridiculously wrong.

Your lack of understanding of the usefulness of the property embodied in the definition - a property which chess definitely possesses - is of no importance.

In fact your response only informs people about your pathological arrogance.

Yet some things are held as truth by some humans, even though others do think they're ridiculously wrong .... and probably vice versa.

Here you reveal that you don't even understand the difference between a definition and a proposition - unless you are seriously saying you don't think chess satisfies the definition, which would simply be a foolish mistake?

When you say that chess is "theoretically capable" of yielding a solution to its complexities, surely, that is what this thread is about? Surely, the "theory" only exists on the basis of chess being (wrongly) diagnosed as a game of perfect information?

Just for information quotation marks are used to quote something someone has said, which is not the case here. Chess is in principle solvable (you can quote me using that exact phrase) in the same way as checkers was, before it was solved. Checkers and chess are both games of perfect information (PRECISE COMPLIANCE WITH A PRECISE DEFINITION), enabling a similar approach. The difference is the computational requirements.

Please correct me if you think I'm wrong.

Done.

At least to me but I think also to you, openness to others and their ideas is all important. That is not to be confused with acceptance and belief in them. I know I'm always capable of winning arguments where I'm right, provided that the rules are followed. However, people here tend to dodge the arguments which are supplied to them. They are only holding themselves back. Because I know this, I will always try to adjust my standpoint if necessary.

Try to get into your head the idea that being a game of perfect information is a precisely defined concept, easily shown to be satisfied by chess, checkers, tic-tac-toe, go, etc. Indeed, go and learn what the definition is.

Elroch

No, you are not in a position to impose your poor understanding on the entire field of game theory.

To help you get started understanding I can express the definition in a simple way. Do say if there is anything unclear to you.

A game of perfect information between two players is characterised by these things:

  • at each step it has a state visible to both players
  • some of the states terminate the game with a specified value for each player
  • players move alternately until the game reaches a termination state (or, for practicality, players agree on the result)
  • a move is determined by the state it leaves the other player with
  • the states determine the moves available
Thee_Ghostess_Lola

...not me.

but i do feel like chess is out there for doG & e/o to view right ? each & every move. perfect info ? ...seems like it to me. forget all the defs. theres no interpretation of the move (sans e.p.). they say poker is way less a game & way more a negotiation. cuz not all is known as the hand goes forward.

Thee_Ghostess_Lola

did MA say let them eat cake or let them eat candy ? (or neither !) ...seems like semantic thingy on deffing GOPI.

ditzyqueen
Optimissed wrote:

Anyway, we're talking, in part, about falsifiability, meaning that if your proposition that chess is a game of perfect information is unfalsifiable, then in turn that means that it cannot be based on evidence and it therefore has no basis as a scientifically valid proposition.

That's why "falsifiability" is a good test for what is scientifically based and what isn't. If your proposition IS falsifiable, which is a criterion which must be met to place it within the realms of scientific understanding, then why are you insisting that you have no need to refute criticism?

Unless you answer my argument about Enigma, you lose your own argument.

You're a pompous limey. No wonder Russia wants to nuke the UK

EndgameEnthusiast2357

A good explanation of why chess can't be solved with "mathematical rules" is look at how many puzzles can't be solved by engines because of how bizarre, subtle, and/or counterintuitive the solution is. Just look in the "mates difficult for engines" and/or "too difficult for computers" threads for examples. How could any mathematical representation account for them given how obscure the moves are that could only be realized through logical reasoning/stumbling upon the solution randomly through a pruning search?

Elroch
Optimissed wrote:

Answer my criticism regarding the Enigma. Can't?

I have not been involved in any discussion related to the off topic subject of (I guess to be) the Enigma machine. You must be confusing me with someone else.

Moreover, anyone with their head screwed on straight can see that an unconnected topic has to relevance to the helpful facts I have provided for you.

OctopusOnSteroids
EndgameEnthusiast2357 wrote:

A good explanation of why chess can't be solved with "mathematical rules" is look at how many puzzles can't be solved by engines because of how bizarre, subtle, and/or counterintuitive the solution is. Just look in the "mates difficult for engines" and/or "too difficult for computers" threads for examples. How could any mathematical representation account for them given how obscure the moves are that could only be realized through logical reasoning/stumbling upon the solution randomly through a pruning search?

I don't see this as a serious argument because the engines we have today can't be used to determine what is doable. They can struggle with some positions that are simple for humans. It's a given that some positions are much more complex and maybe not feasible for mathematical rules.. However, the process being a hybrid of brute force and AI abstracting rules based on that data is better than only brute force and again, we don't know whats doable because we dont have the tools.

Elroch
EndgameEnthusiast2357 wrote:

A good explanation of why chess can't be solved with "mathematical rules" is look at how many puzzles can't be solved by engines because of how bizarre, subtle, and/or counterintuitive the solution is

Yes. chess has very arbitrary rules.

The key thing is that those rules do not lead to any known (or any likely) large computational short cuts. Maths is about proving very powerful general results in a relatively compact way. Very different to the main demands of solving a game like chess or checkers.

Interestingly, go is a bit more mathematical. The endgames in go can be analysed in a way which is of mathematical interest, and the game provided the inspiration for a branch of game theory. Eg here is a thesis on the subject.

MARattigan
Elroch wrote:
...

Try to get into your head the idea that being a game of perfect information is a precisely defined concept, easily shown to be satisfied by chess, checkers, tic-tac-toe, go, etc. Indeed, go and learn what the definition is.

From Wikipaedia.

Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, but no secret information, and games with simultaneous moves are games of perfect information.

I'm no expert on game theory, so, it being from Wikipaedia, I can't say whether that is true. But all versions of chess I've come across allow for simultaneous moves, if you count a move as any action under the rules that changes the game state, e.g. simultaneous resignations. Computer versions will serialise all such actions, so, for example producing a win for one (random) player, rather than a win for both as under FIDE rules, in the example quoted.

(Actually FIDE may be moving slowly towards specifying a zero sum game (but not a sequential game). From the laws 2018:

5.1.2 The game is won by the player whose opponent declares he resigns. This immediatelyends the game.

From the laws 2023:

5.1.2 The game is lost by the player who declares he/she resigns (this immediately ends the game), unless the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. In this case the result of the game is a draw.

So now if you step into a dead position simultaneously with resigning the game is drawn, but nobody wins. If the players simultaneously resign in a position which is neither dead nor half dead both now lose instead of both winning as before.)

Elroch
MARattigan wrote:
Elroch wrote:
...

Try to get into your head the idea that being a game of perfect information is a precisely defined concept, easily shown to be satisfied by chess, checkers, tic-tac-toe, go, etc. Indeed, go and learn what the definition is.

From Wikipaedia.

Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, but no secret information, and games with simultaneous moves are games of perfect information.

This merely refers to the broadening of the term in some work. Chess and checkers fall into the most restrictive definition - no uncertainty and no simultaneous moves. (So even if you use a variation on the definition, chess satisfies it).

So while it is relevant to the discussion of games more broadly, it is not relevant to this discussion.

The article you linked says "Games with simultaneous moves are generally not considered games of perfect information", indicating that the earlier reference was an anomalous use of the term.

[I observe that allowing moves to be non-alternate is a fairly mild variation on the definition, because you can simply define a supermove as the whole sequence of moves played by the same player before the other player moves, turning such a game into one with the more restrictive definition].

MARattigan
Elroch wrote:
MARattigan wrote:
Elroch wrote:
...

Try to get into your head the idea that being a game of perfect information is a precisely defined concept, easily shown to be satisfied by chess, checkers, tic-tac-toe, go, etc. Indeed, go and learn what the definition is.

From Wikipaedia.

Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, but no secret information, and games with simultaneous moves are games of perfect information.

This merely refers to the broadening of the term in some work. Chess and checkers fall into the most restrictive definition - no uncertainty and alternating moves.

So while it is relevant to the discussion of games more broadly, it is not relevant to this discussion.

Where do we find the most restrictive definition (you give no link). Does it count "moves" as changes in game state or apply only to moves of some defined "pieces"? Presumably it applies only to two player games?

Elroch

You can say there is an "obvious comparison" between jelly beans and tigers, but that does not mean there is.

Elroch

That is two worthless, vacuous and erroneous posts.

To contrast, let me reiterate that chess satisfies the original, most restrictive definition of a game of perfect information (and all broader - i.e. weaker - definitions that encompass more varied games). And the only relationship of Enigma to chess is that some human beings who played chess were involved in cracking codes. I suppose you could add that both cracking codes and solving chess require a lot of brute force computation (but that a very weak connection, since the computations involved are quite different).

MARattigan
Elroch wrote:
MARattigan wrote:
Elroch wrote:
...

Try to get into your head the idea that being a game of perfect information is a precisely defined concept, easily shown to be satisfied by chess, checkers, tic-tac-toe, go, etc. Indeed, go and learn what the definition is.

From Wikipaedia.

Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, but no secret information, and games with simultaneous moves are games of perfect information.

...

The article you linked says "Games with simultaneous moves are generally not considered games of perfect information", indicating that the earlier reference was an anomalous use of the term.

Well exactly. If you take the term "move" in game theory to mean a change in game state then chess does have simultaneous moves. (The term must be read as one of the moves of the pieces in in the FIDE laws, but those contain several definitions which are not meant to be understood as what you always thought they meant.)

[I observe that allowing moves to be non-alternate is a fairly mild variation on the definition, because you can simply define a supermove as the whole sequence of moves played by the same player before the other moves].

But simultaneous moves can't be so separated.