Chess will never be solved, here's why

More proof that you hate the forum.
We'll see if you Ever comment on the main forum topic.

I did use 'we're' Lola.
And will continue to use it where I think it applies.
be 'careful'?
What are you worried about L?

from Elroch in a very recent post replying to tygxc
"There is another point you don't understand that almost of the essential analysis needed to solve chess is of imperfect play, because we don't KNOW it is imperfect until the analysis is done. You think you can do without the positions in the analysis! This is a blunder, and I think one which is beyond you to get past."
@Elroch yes. 'beyond'.
But it is 'beyond' tygxc by his choice.
And a type of blunder he repeats constantly.
Why? Because he can.
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"because we don't KNOW it is imperfect until the analysis is done."
Yes. Obviously. And very central to the forum topic.
But tygxc likes to 'skip over' such things.
He's on a mission. Something like Washi is.
But tygxc's mission is much more innocuous than Washi's and concerns an obscure subject. The forum subject.

HOW MANY PAGES BRO

623..

About 10^44 (near enough for jazz).

More than you can manage to read, I'm betting.

I like the 44.
Neat. Kool. Far out. Tubular. A Californ ah Ay number!

The number of positions in a game is dependent on both the game and the meaning of "position". In some games and with some meaning of the term, positions that look similar may be different depending on what trumps have been chosen, for example, but not in others (including most versions of chess). Games with different rules have different sets of positions with any sensible definition of "position".

Before you can assign a number to any set of things you need to know what set you're talking about. So when you talk about the number of chess positions you need to know what game you mean by chess (there are games with different sets of rules all called "chess") and what you mean by position.

One natural way to regard a game with rules is as a series of sets of events specifically allowed (a fortiori mandated) by the rules (where the events in each set are permitted to occur simultaneously) starting from a particular arrangement of any objects manipulated in the game and possibly terminating in a result assigned by the rules.

Then a natural meaning of "position" could be a lower segment of the series, i.e. where you are up to in a specific game. This, I believe, corresponds with FIDE's use in the handbook when they talk of positions arising in various articles. I'll call those "natural positions" and abbreviate it to "n-positions".

Another more useful meaning of "position" for theoretical purposes would be equivalence classes of n-positions which have the same arrangement of any objects manipulated in the game and can be completed by exactly the same set of upper segments to form a complete game each of which terminates in results, if any, that match, and if that set is empty any already assigned result matches. (Edit: Correction in red added.) I'll call those "forward play positions" and abbreviate it to "fp-positions". They correspond, I believe, with what Elroch has called "game states" and is what I generally mean by the undifferentiated term "position". It means any previous play that has no effect on how the game can continue is ignored as an attribute of position.

(Both types of position can be organised into trees by continuation and the term "game tree" appears to be ambiguously used to describe either in articles on game theory. There's an obvious homomorphism from the tree of n-positions to the tree of fp-positions. The term "node" appears to be similarly ambiguously used to denote a node in either tree.)

So what has Tromp counted?

It purports to be legal chess positions, but the term "chess" is ambiguous. FIDE describe a game in the handbook under the heading Basic Rules and a further game with several variants by adding extra rules in the section Competition Rules. ICCF add further rules (with at least difficult to predict effects in some cases) and TCEC chess can't be analysed. Then you have regional variants (USCF) and nonconforming computer implementations (chess.com).

The closest it comes is to counting FIDE basic rules fp-positions, but it doesn't exactly do that. For example it counts the n-positions ({e4},{e5,White resigns}), ({e4},{e5},{Black Resigns}) and ({e4},{e5}) as one and the same legal position, but they're elements of three different fp-positions.

You could say the number is the number of fp-positions in a simplified version of FIDE basic rules chess where the agreed draw and resignation articles have been excised. It doesn't have a lot to do with with other versions of chess, at least not with the meanings of "position" I've suggested.

Damn. Need to keep writing "basic chess positions" to avoid that!

There's not much point trying to solve more difficult rule sets before solving basic chess.

It's only the 50 move rule that might interfere with a weak solution of basic chess giving a weak solution of FIDE rules chess. And let's face it, the 50 move rule is an ugly kludge.

But we have you talking about basic rules chess and @tygxc talking about any version but in the same posts. And he is saying he'll solve more difficult rule sets before solving basic chess, in fact claiming that basic rules chess is unsolvable in principle (while, strangely, asserting that the 50 move and triple repetition rules have no effect on the game).

The fact that you can get around the triple repetition rule in weakly solving competition rules chess doesn't alter the number of positions. And they're still relevant when it comes to strongly solving. Nor does it allow you to assume Stockfish will work with a tree of basic positions, or positions in a version of chess with one or both drawing rules excised.

I agree about the 50 move rule. Don't think Ruy Lopez had any conception of how it would alter the game (the theoretical game that is).

When you say, "It's only the 50 move rule that might interfere with a weak solution of basic chess giving a weak solution of FIDE rules chess", you're borrowing @tygxc's big red telephone and assuming basic chess is a draw. Otherwise both the the 50 move and triple repetition rules rule would probably interfere with almost all weak solutions of basic chess giving a weak solution of FIDE competition rules chess (in a measure theoretic sense), though that would not apply to weak solutions produced by some specific methods of course.

If you take a simpler starting diagram in basic rules chess, for example.

Then it's easy to prove that the White strategy

Play the rook to any square not adjacent to the Black king for 4.85x10^44 moves (a convenient number to state) then follow the moves recommended on the Nalimov site from the position reached.

is a weak solution of that game. But it doesn't translate directly to a weak solution under competition rules, because the game would terminate in a draw under one of the rules when it should be a win.

Perhaps more to the point, with this diagram instead

The strategy

Play the moves recommended on the Nalimov site.

would be a weak solution, but wouldn't translate to a weak solution under competition rules, because the game would be drawn under the 50 move rule with correct defence when it should be a win. 

Basic rules chess is also FIDE rules chess by the way. They have multiple versions on offer.

pov: tygxc doesnt understand that alpha beta search doesnt halve the exponent.

to any observers, it is incredibly basic logic that tygxc messes up, it's just that hes twisted it behind fancy terms. the short of it is that tygxc just assumes that a computer will find the perfect move with no search time and no effort.

random question: Do you think that having a computer not analyze any moves per position will lead to to the computer being able to do perfect moves every single time?

So now you're calling me a liar, as well as all the other insults.

If you hate me so much, why do you keep replying to my posts?

Did not know that Ruy Lopez brought in the 50 move rule.
That was in the 1500's. He was the best player in Spain for a while.
Did some research.
Castling in its current form did not come in until the 1600's and started in France then long after Ruy Lopez. Have the game rules changed much since then?
Could not find out when the 3 fold repetition move came in or who got it started.
But in a game between Karpov and Miles Karpov claimed a draw by repetition and got that draw when he shouldn't have because castling rights had changed during the process.
Noting that to claim a draw by 3 fold the same player must be on move in all three positions.
But do you have to be on move to claim it?

Sounds like a strawman argument. Computers do analyse moves.

Reading through the recent discussion causes some things to be notable.
Martin had noted 1) e4 e5 white resigns and e4 e5 black resigns and e4 e5 game continuing with white on move if I remember correctly.
Three different 'positions'.
You could also have e4 e5 Draw Agreed.
So that's four.
And add three more 'attributes' if that's the right word.
e4 e5 White Flag falls and e4 e5 Black Flag Falls and e4 e5 Both Flags Down.
Now you've got seven different positions from the same arrangement of pieces with the same player on move.
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I think 1) Nf3 Nf6 does a better job on some of this because you can have even more 'positions' from that.
Nf3 Nf6 Draw by Threefold Repetition. Yes!
And you could have Nf3 Nf6 Draw by 50 Move Rule because the knights could have moved around the board not just bounced back to their stables.
So now you've got Ten 'positions' with the same arrangement on the table.
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But even Nf3 Nf6 doesn't allow for either player on move.
Black Cannot be on move there no matter how it got there.
You can triangulate a King you can't triangulate a knight to shift whose move it is.
Note that with a position of e4 e5 without knowing all the moves we can add more attributes.
The Kings could have moved and then moved back.
So then there's 4 positions with white pawn e4 black pawn e5 
Castling Illegal Both Sides.
But no way there to have Castling Illegal White Only nor Black Only.
Actually just occured to me there is.
One side could have bounced his f-bishop or Queen or even his knight while the other side bounced his King.
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Thought about it and realized you could switch whose move it is with white pawn E4 and black pawn E5.
Would that be good for a student?
Like this:
1) e4 e5 2) Ke2 Ke7 3) Kf3 Kf6 4) Ke3 Ke7 5) Ke2 Ke8 6) Ke1
Now its the same arrangement but Black's on move instead !!
So now you've got another 'Attribute' possibility on that position.
You could have done it with the Queens too or the f-bishops.
Without 'losing castling'.
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knight moving versus knight moving cannot triangulate ...
Queens moving can 'switch' and so can bishops or rooks. And Kings.
Pawns can't do it and it looks like knights can't either.
Knights can't 'lose a move' while going back to wherever.
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Later in the game with more pieces moved from their originals all the attributes become possible with the same arrangement on the board.
How many potential 'positions' does that make possible with the same piece arrangement?
Could be large when you multiply some of the attribute possibilities by each other (some of them won't multiply properly) 
The product could move up over 100 with the same arrangement on the board?
Beginning to look like it.

it sounds like a strawman argument, but that is legitimately what tygxc claims with his "calculations."

tygxc assigns exactly one computer node per position on a weak solution game tree.

however, tygxc's game tree only has one move for one side, meaning that he selects the perfect move every single time without even LOOKING at alternative moves.

Again, this is not a strawman.

Noting that a bishop can 'lose a move' when compared with a knight - with the knight helpless in some endgame situations.
Because it can't do the equivalent of triangulation.
The knight can be 'in phase' or 'out of phase'.
Maybe its the only piece with a 'rhythm'.
I haven't got the classic ending for that handy.
Involves a King stuck on the promotion square in front of its edge-pawn.
The other King has to keep it locked in.
Say - black King on c7.
If white's knight is checking at c7 ... that's it.
Draw.
No matter how the knight tries to 'shuttle' the black King keeps bouncing c7 c8 and back.
But if the knight is 'in phase' hitting c8 instead with black to move - then black can Resign right there. But it wasn't. Draw.
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then try it with instead a bishop checking c7 ... Kc8.
Slide the bishop a square continuing to hit c7.
Black can head to the showers right there. Loss.
He is Excommunicated by that bish.

the algorithm that tygx refers to, the "Alpha-Beta search", is a pruning method to leave an desired value for one side's moves in response to every possible play. intuitively it could be understood as "white tries every possible move in each position, black responds to each white move with a singular move)

https://www.geeksforgeeks.org/minimax-algorithm-in-game-theory-set-4-alpha-beta-pruning/#

(is a source, but this is a very code heavy explanation)

The number of positions left over after such pruning is approximately the square root of total positions.

So, Perfect would mean that no alternative moves are even looked at besides the desired ones.

you'll notice how tygxc just ASSUMES that it's perfect here. Tygxc even lies about the source he cites. the game tree size that schaeffer actually considered was only 10^7, and took 10^7

"Roughly speaking, there are 10^7 positions in the stored proof tree, each representing a search of 10^7 positions" - https://www.cs.mcgill.ca/~dprecup/courses/AI/Materials/checkers_is_solved.pdf

you can clearly see that schaeffer doesnt run the search over all of checkers 10^20 positions from reading this and instead connects a search tree from the start to engame tablebases.

in reality the tree he pruned came from space of around 10^14

heres the full context of tygxc's 'halve the exponent' claim.

"An alternative would be to use only computing—i.e., build a search tree using the alpha-beta algorithm. Consider the following unreasonably optimistic assumptions: number of moves to consider is eight in noncapture positions, a game lasts 70 ply, all captures are of a single piece (23 capture moves), and the alphabeta search does the least possible work. The assumptions result in a search tree of 8(70–23) = 84^7 states. The perfect alpha-beta search will halve the exponent, leading to a search of roughly 84^7/2 ≈ 10^24"

you'll notice how this completely contradicts tygxc's claims that you can just halve the total positions.

you'll also notice how a perfect alpha beta search is unrealistic.

(part of it due to tygxc just randomly assuming that equivalent positions will always be factored out even though that takes enormous computing power to ensure)

you might be wondering, arent these all pretty technical and just minor mistakes that just add up? no. tygxc is just using these citations and technical terms to mask the fact that hes calculating only the size of the game tree of a solution instead of the size of the calculations necessary to FIND the game tree. Everything else is tygxc just layering fallacies to disguise this basic delusion.