Chess will never be solved, here's why

@11068

"the implementation of solutions are specific to each game"
++ Yes, like for Chess prune 1 e4 e5 2 Ba6? right away.
Weak solutions of Connect Four (by Allis), Losing Chess, and Checkers used game knowledge. Weakly solving Chess needs even more game knowledge.

"elimination of 27 orders of magnitude is larger than all of checkers by 10 million times"
++ Larger game, larger reduction.
Besides from 10^38 to 10^17 is 21 orders of magnitude.

@11141

"where on Earth does 10^120 come from?"
++ It is the erroneous Shannon number

"count a position as reappearing only if the possible forward play is the same in both cases"
A diagram = place of men on the board
A position = diagram + side to move, castling flags, en passant flag

That's your idea of a position, but it's irrelevant to solving FIDE competition rules chess or ICCF chess by a forward search because it doesn't include enough information to determine what continuations are posssible in those games.

A node = position + history + provisional evaluation

A node is the vertex of a graph. When referring to chess, that could be the game tree or a reduced version of the game tree where (real) positions that have the same possible continuations are coalesced so that nodes with the same possible continuations are not duplicated.

The attribute "history" would alone be sufficient to identify the nodes in all cases in either graph. It determines the attributes you include in position and the actual evaluation. You don't say what "provisional evaluation" means, but if it's anything to do with your big red telephone it can be ignored.

The full history is a many one map to the nodes. Sufficient, and in most cases necessary, to determine forward play is the board layout, side to move, castling flags, whether the last move was an initial pawn move and if so which, and, for FIDE competition rules chess or ICCF chess, a list of positions with the same material that have already occurred together with the number of times that each has occurred. 

For correct operation your originally proposed vehicle, Stockfish, which is designed for FIDE competition rules, requires a PGN from the last ply count 0 position to continue play. That is sufficient to determine the attributes I mentioned in the previous paragraph.

The number of nodes in the the second graph I mentioned above are the relevant values for weakly solving with a forward search. A value of 4.8x10^44 would be correct under FIDE basic rules (and the same number would also allow a weak solution of the other games I mentioned via tablebase construction). Under FIDE competition rules or ICCF rules the number of nodes is VASTLY greater. How many is difficult to say, but when I asked for an estimate of just those in KRK you didn't manage an answer.

As @Elroch pointed out these can be reduced from ludicrously vast to merely vast with the correct approach to the forward search but you have not yet explained how using Stockfish would effect that. 

'9.2.3 Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:

9.2.3.1 at the start of the sequence a pawn could have been captured en passant.
9.2.3.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.'
Laws of Chess

Naturally there is no such thing as an actual repetition of a position with all attributes of a position or it wouldn't be a repetition, it would be the actual position. So the "repetition of position" rules must pick out the attributes of a position whereby different positions can be considered the same. The rule doesn't magically produce a 1-1 map of that collection of attributes to the nodes in the second graph I mentioned above.

As my previous post explained, this implicitly assumes the tree of games is the same as the tree of positions. Because there are reversible moves in chess, the number of positions is way smaller than the number of games. 5 x 10^44 versus ~10^120

This means that positions dodged by only looking at one white move often reappear later.

My comment about cube root was a joke.
But the square root idea looks like its a joke too.

I would not call it a joke...it's a "common" enough methodology, used in checkers, finding prime numbers, etc. The problem is that Tygxc has not even begun to show that it would be applicable to chess, and that if it is, it likely applies to all possible games, the Shannon number 10^120, not unique positions.

You're about as creative as Dio.

Stand in the corner.

The Shannon number is not and never was intended to represent the number of all possible games. Not even under competition rules (it's obviously infinite under basic rules).

But with far less frequency in FIDE competition rules chess and ICCF chess if you count a position as reappearing only if the possible forward play is the same in both cases.

And where on Earth does 10^120 come from?

When you're trying to be clever it's better to get things right.

I didn't think I'd been asked again after the first time I gave my reason. Essentially, Cantor is positing the existence of finite numbers with special properties, in that they are finite but also infinite.

No. The DEFINITION of the adjective INFINITE is "NOT FINITE". This logically precludes any number from being both finite and infinite.

You need to first get enough understanding to avoid making obviously nonsensical statements.

I didn't think I'd been asked again after the first time I gave my reason. Essentially, Cantor is positing the existence of finite numbers with special properties, in that they are finite but also infinite. His mistake is that they are unknown finite numbers, since the series of infinite numbers is endless. It has a beginning but no end. If we choose to include negative numbers in the infinite series, again there is ambiguity, since we can choose to begin the series at zero.

Hence there are finite numbers within the infinite series which are unknown. He has chosen to call them "transfinite numbers" since they would be defined as any finite number outside the series of known finite numbers. Known finite numbers are considered to be normal (in that they have been used in calculations or whatever .... not a very good reason) and unknown ones are ambiguous and hence trans-finite. It's rather similar to Schroedinger's cat. Schroedinger originally invented the idea of a cat which is not known to be either alive or dead as a joke, intended to discredit speculation regarding superpositioning or ambiguously live states and dead states in the kind of primitive or childish interpretations of quantum theory which had started to become current. However, such interpretations have tended to gain currency, not because they have any merit, except that they appeal to some kinds of speculative creativity.

Cantor was merely using his imagination and attempting to demonstrate numerical hypothetical series. He was considered by many to be insane and ideed he did become certifiably insane. Also his ideas have absolutely no real use or no use in reality.

I'm very used to Elroch and others like him, trying to impose their will on the thoughts of various people here. I have no doubt that he will tell me that I'm wrong and that I don't understand a, b, c, and/or d. That kind of speculative dismissal is meaningless. Elroch habitually supports whatever he wishes to support and is usually unable to give coherent arguments. His qualification is in statistics and this is pure mathematics. You can make a set of anything, including of bananas, but someone who understands set theory is not an expert on bananas because of that.

Whether 10^120 is the exact number is not really important...what's important is the distinction between 10^44 unique positions and the (much) larger set of possible games, and whether Tygxc is properly applying his reductions or not. Not to say he isn't, but his cut and paste explanation that we've all seen several dozen times is not doing the job.

10^120 is a rough estimate of the game tree complexity. The wiki article gives 10^123.
When the game tree is a tree without considering the history of a move and when the leaf positions are unique, the game tree complexity is similar to the state space complexity (number of positions).

<<<No. The DEFINITION of the adjective INFINITE is "NOT FINITE">>>

Thinking that giving a definition of infinite makes your case is nothing more than an admission of your lack of ability.

If you were referring to the game tree complexity why did you call it the number of games?

You are entirely right that the two numbers are distinct in chess and I was wrong to conflate them. Thanks for drawing attention to this.

In games where there are no irreversible moves and no transpositions, the number of legal games is the number of leaf nodes. For example hex. These are the games where the idea that weak solution has the square root of the size of a strong solution makes best sense. But even here the game tree complexity is not the same as the number of leaf nodes, as I understand the definition.

I don't have access to the link you provide.

I linked it incorrectly, it seems. Here it is.

And the number for chess is later in the article, here.

Can you sketch an argument for why the game tree complexity would be 10^123 (presumably for basic rules chess since you quote 10^44 as the number of positions and that can only be understandable, if some way adrift, for basic rules chess). It could certainly be relevant to the thread.

I merely quoted the value from the article, having seen others previously. To me it cannot make sense for basic rules chess, since a tablebase has complexity ~10^44 and that strong solves the game. 

I think you missunderstand a few key details. I dont know what you mean with finite but infinite numbers. As for negative numbers its just a question of how we order them.

1= 1/1,

2 = 1/2 × -1,

3 = 1/2,

4 = 1/2 × -1,

5 = 2/1,

6 = 2/1 × -1

Do we agree that list contain all rational numbers, and that the list is infinitly large?

Now do we agree that at one point you come to number x = 3,14, and then later y = 3,15

Now you alternate between adding to this list, and a second list that contain all the real numbers. All the numbers of the first list will be on the second list so that x = 3,14 still on both lists. But when we come to y =3,15 on the first list the number pi will be on the second list so that on the second list y + 1 = 3,15

In this example there is no finite but infinite numbers. The list includes negative numbers. Both list are infinite, but one list is larger.

If all this is true then not all infinites are the same size.