Chess will never be solved, here's why

@12070

"There are like 9999999...9999999 (120 9's) possible chess positions."
++ No. There are (4.82 +- 0.03) * 10^44 legal chess positions,
most with around 9 promotions to pieces not previously captured.
There are no more than 3.8521 * 10^37 legal chess positions without promotions to pieces not previously captured.
There are about 3*10^37 * 10.9456 = 3.28 * 10^38 positions without underpromotions to pieces not previously captured.
Of these 1.8 * 10^17 are relevant to weakly solving Chess.

@12048

"Tromp counts basic rules positions not competition rules positions."
++ There are only positions, and competition rule 9.2.3 defines it.

Competition rule 9.2.3

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. ...

doesn't define the term "position". It states when positions are to be considered the same for the purposes of rules 9.2 and 9.6. Since it refers to "positions", if were a definition of "position" it would be circular.

Elsewhere in the rules "position" makes sense only if it means a situation occurring in the game. E.g.

5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’.

Under competition rules two different positions (situations) can arise that are considered the same for the purposes of 9.2/9.6 but in one neither player can checkmate the opponent’s king with any series of legal moves whereas in the other one of the players can. Your understanding of position would make no sense in that context. 

The final positions (situations) in these two examples illustrate.

Under competition rules neither player can checkmate in the final position (situation) in the first example but White can checkmate in the second. But the FENs are identical in both, so the positions would be considered the same for the purposes of 9.2/9.6. 

Edit: I have revised the above examples, because the original versions of the first was dead on the penultimate move, as pointed out by @tygxc. The examples are now correct. The draw indication added to the second position by chess.com is in error. The info circle added to both is also in error. I played both colours under FIDE competition rules in both games and at no point did I claim under the 50 move rule. The first position is a draw because it's dead.

You confuse positions and nodes.

I don't. I mean different things by the terms than you do in the competition rules game.

You confuse the basic rules game and the competition rules game. And your meaning of "node" doesn't make any sense in either.

The node is a position + history + provisional heuristic evaluation. The history takes care of the 3-fold repetition rule and the 50-moves rule.

Which doesn't seem to have a lot to do with the nodes/sec figures issued by the SF developers. It needs only the history since the last ply count 0 node and it evaluates the nodes itself, they're not intrinsic to the nodes in the game tree. The nodes exist whether SF has evaluated them or not.

What counts as a provisional heuristic evaluation anyway? Is that a static evaluation or an SF evaluation after some random number of nodes?

"factor of two to account for side to move is too high, but I would suggest by very little"

++ Yes, likewise the factor 1/2 for positions to nodes is a bit off too.

Just a little bit. See below.

Generally 1 diagram = 2 positions = 1 node

"3.8521...e37 x 10.9456 = 4.2163...e38."
++ 3.8521E37 is an upper bound, the estimate is 3E37, see page 9

I stand corrected (I haven't actually checked your working.)

It still doesn't justify using it in the way you do.

"What factor of 1/2 for diagrams to nodes?"

Here are 2 diagrams, 4 positions, 2 nodes.

Your parents should normally teach you how to count when you're about two, but I'll do my best.

The answer depends on what is meant by "position" and "node", but let us use your definitions.

Let us list the "nodes" you've shown for your "positions".

( rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR w KQkq c6 , e4 c5 , ? )

( rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - , e3 c5 e4 , ? )

( rnbqkbnr/pppp1ppp/8/4p3/2P5/8/PP1PPPPP/RNBQKBNR w KQkq e6 , c4 e5 , ? )

( rnbqkbnr/pppp1ppp/8/4p3/2P5/8/PP1PPPPP/RNBQKBNR b KQkq - , c3 e5 c4 , ? )

The "?" indicates a "provisional heuristic evaluation" whatever that might be. I've assumed it's supposed to be a single figure in each case - if not you need separate lines for each value.

Notice that none of the lines are the same. That means there you've shown one, two, three, four of your nodes.

Unfortunately you've missed a few out. Here, for example, is a node you've missed for your first position.

That is

( rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR w KQkq c6 , e3 Na6 Nh3 Nb4 Bd3 Nc6 Ng1 Nf6 Be2 Nb8 Bf1 Ng8 e4 c5 , ? )

Which is obviously different from the node you showed for your position. If you think hard you may be able to find a few more.

Tell us how many you can find.

"[You appear to be] planning to use SF [either alone (in some posts) or by proxy through ICCF players (in others)]"
++ No. ICCF (grand)master + 2 servers each 90 million positions/s during 5 days/move.

Refer to original unmutilated quote I've reconstructed in red.

"I don't think SF exploits that symmetry in any way" ++ No, but the up/down symmetrical position does not happen. If it were to occur, the human would recognise it.

How do they do that while SF is searching at 2 billion nodes/sec and what are they meant to do about it if they could? And where is it mentioned in your detailed flowchart?

ICCF (grand)master + 2 servers of 90*10^6 servers, average 5 days/ply 

I don't see anything about it.

"SF is designed to play competition rules chess." ++ ICCF (grand)masters use it for analysis.

That's probably because they're interested in playing competition rules chess.

If they're using it for ICCF chess, it probably plays pretty crap when it's down to 8 men because it thinks it's aiming only for 7 man wins within the 50 move rule, when could actually go for wins that aren't. But then I suppose they all have the same handicap so it doesn't matter. 

"That is a diagram and a limited amount of history"
++ And a provisional heuristic evaluation, together a node.

Not with any sort of evaluation. The nodes in the game tree are there in the game tree whether they've been visited and evaluated by SF or not. That's SF's search space.

What's the definition of "a provisional heuristic evaluation" anyway? 

The engine recognises the 3-fold repetition of a FEN or the 50-moves rule from the PGN.

Yes, but it needs only the PGN from the last setup position with ply count 0. That is sufficient to define the game state. But different PGNs from possibly different ply count 0 positions define the same game state if the same 9.2.3 positions that can be reached within the 75 move rule occur each the same number of times (and in other cases as well).

"you seem to have omitted the case of two queens of the same colour"
++ Yes, 3 queens vs. 1 queen makes no sense.

But you just said two promoted queens; didn't say anything about that. I've seen 3 queens v 2 queens. Must have been inferior players.

In the absence of a more detailed description of your process than ICCF (grand)master + 2 servers of 90*10^6 servers, average 5 days/ply and the absence of any definition of "makes sense" it's impossible to say whether all or any of the positions visited during your process or occurring in your lack of solution will make sense or not.

That is why the /2 is there in addition to the /4 to select Q only and omit R, B, N.

Then you only propose to not solve chess with underpromotion disallowed? How do you let SF know that? It underpromotes to all of them quite regularly when I play it at KNNKP. 

"Where's the output?" ++ The core output are the 114 ICCF WC Finals draws.
The more extensive output are the records both ICCF (grand)masters kept.
'I maintain both manual and electronic records. When the move is received, I note the exact time, my candidate moves, records of all actions taken, and their results.' - Edwards

So if it's gone 1.e4 e5 2.Ba6 which of that lot should I be looking at?

"If someone wants to know what moves to play"
++ Follow an ICCF WC Finals draw for as long as possible,
then switch to ICCF (grand)master + 2 servers of 90*10^6 positions/s, average 5 days/ply

What if they're trying to win? What if he gives them a blunder? What if they can't afford his fees? What if he's busy with somebody else? 

"if as Black I play 1...e5 against 1.e4 and my opponent plays 2.Ba6 and I want to know what move to play, your solution tells me, Play ICCF (grand)master + 2 servers of 90*10^6 positions/s, 5 days/ply"
++ Yes, though for 1 e4 e5 2 Ba6?, lesser hardware and less time/move will suffice.

The blunder rate may be less with lesser hardware and less time/move , but that doesn't mean 0.

"different rules" ++ ICCF is more decisive than FIDE,
so a weak solution of chess per ICCF is a fortiori a weak solution per FIDE.

Non sequiteur. You're assuming chess is a draw without any evidence.

@12070

Of these 1.8 * 10^17 are relevant to weakly solving Chess.

ah yes, repeat long debunked claims instead of addressing the refutations.

@tygxc does seem to subscribe to the view that you can prove something by asserting it often enough.

I disagree. I would say that tygxc would take the position closer to that of if he believes something, he can assert it as proven fact.

elroch have you heard of terrence howard? tygxc reminds me of him a ton

'nodes per second' is invalid.
...

There is nothing invalid about nodes per second so long as it is understood what the nodes quoted are.

@tygxc takes the term to mean basic rules positions in his figures, which is invalid (though he prolifically gives a definition of node that differs from both that he ignores).

While the state space for chess with a drawing rule is enormous compared to that of basic chess, this does not make a weak solution bigger to the same extent.

...

@12080

"Under competition rules two different positions (situations) can arise that are considered the same for the purposes of 9.2/9.6 but in one neither player can checkmate the opponent’s king with any series of legal moves whereas in the other one of the players can."
++ No. Dead position takes precedence, ends the game immediately and independently of 3-fold repetition or 50-moves rules, which must be claimed.

Careless of me not to notice the first position was already dead on the previous ply. I've fixed it. See the edit.
My point is valid. A 9.2.3 criterion for when positions are to be considered equal for the purposes of 9.2/9.6 can't be taken as an intended definition of "position" in the FIDE laws.

"doesn't seem to have a lot to do with the nodes/sec figures issued by the SF developers"
++ It does, that is exactly what a node means for the engine.

No it's not.

A node is something an engine traverses in a game tree and assigns evaluations to as it goes along. They don't come ready evaluated.

There are two basic versions of the game tree. A full version and a fully reduced version. The fully reduced version has no repetitions of the same foliage at different points in the tree, which enormously reduces the number of nodes. The engine will attempt to traverse the latter by recognising nodes with the same foliage in cache and reusing the results, but if there is insufficient hash space it may traverse something in-between.

Your version with full history applies to the full tree. An engine keeps the full history only for the game record and probably only then if it has an integrated GUI. In processing it's interested only in the history from the last ply count 0 position and what castling rights exist.

"The nodes exist whether SF has evaluated them or not."
++ Yes, but the engine adds a provisional heuristic evaluation when it visits a node.

And if it adds the whatsit that you have so much difficulty precisely specifying to the node, the whatsit was obviously not part of the node.

"What counts as a provisional heuristic evaluation anyway? Is that a static evaluation or an SF evaluation after some random number of nodes?"
++ Yes, and for 2 purposes: alpha-beta pruning and best-first search.

Brilliant! "Is this an aardvark or an anteater?" ... "Yes."

"Tell us how many you can find."
++ That is what I say the whole time: chess is full of transpositions. Despite there being 35 legal moves in some positions, the average number of non-transposing choices per ply is 3, while 10^38 = 3^80.

It's not anywhere near as full of transpositions under competition rules as it is under basic rules. You've given many examples of transpositions under competition rules that aren't. Transpositions of your irrelevant 9.2.3 criterion positions don't mean anything under competition rules. It's transpositions of the nodes that count.

That's why I asked you to tell us how many "nodes" you could find matching your first "position" as you define it. You haven't answered. You might find it easier with sensible "nodes", but not much I would guess.

I add some detail here (between the initial and final red brackets) to clarify @tygxc's next cryptic snip.

["I don't think SF exploits that symmetry in any way" ++ No, but the up/down symmetrical position does not happen. If it were to occur, the human would recognise it.

How do they do that while SF is searching at 2 billion nodes/sec and ]"what are they meant to do about it if they could?"[ And where is it mentioned in your detailed flowchart?

ICCF (grand)master + 2 servers of 90*10^6 servers, average 5 days/ply

I don't see anything about it.]

++ Here is an example game between two humans, they play the up/down mirror image:

Wonderful! Answers what was asked in exact and explicit detail. Not.

(Not to imply any relevance, but I couldn't spot a single up/down mirror image in the whole game apart from the initial position which is only legal with White to play either.)

"The nodes in the game tree are there in the game tree whether they've been visited and evaluated by SF or not."
++ Yes, but the provisional heuristic evaluation helps for alpha-beta pruning and for best-first search. When the engine visits a node, it attributes a provisional heuristic evaluation.

If the engine attributes your whatsit to a node it visits, that presupposes the whatsit was not a part of the node in the first place. You do appear at last to have plunked for the static evaluation as your meaning for the whatsit.

"What's the definition of a provisional heuristic evaluation anyway?"
++ A figure like +0.33 given by the engine after the set time of calculation. It used to be in pawn units, but nowadays +1 means 50% chance to win and 50% chance to draw or lose.

Belay that. You haven't plunked for the static evaluation as your whatsit; you just haven't a clue. 

Is that meant to be a rigorous definition? You wouldn't get a definite answer even if you specified a set time a specific version of a specific engine a hash size and the exact machine to run it on (which of course you don't).

"I've seen 3 queens v 2 queens. Must have been inferior players."
++ Probably. What game? Even so it is too rare to influence the relevant position count.

Rare in what kind of play?

It has to be rare in the positions that will be searched by your process. Currently you have no definition of a process that will result in a solution.

"Then you only propose to not solve chess with underpromotion disallowed?"
++ The purpose it to weakly solve Chess as it is, but for the purpose of estimating the relevant number of positions to do so, the observation is that optimal play of chess as it is leads to exactly the same games and outcome as chess with underpromotions restricted to pieces previously captured.

That you need only an estimate is fair comment. 

Now you need a description of a procedure to solve a version of chess (and to decide which version) that is sufficiently detailed to determine the nodes it might visit for us to assess if your estimate is reasonable.

ICCF (grand)master + 2 servers of 90*10^6 servers, average 5 days/ply

is apparently the most detailed description of your procedure that you're able to post at this stage of the thread, but if it can be understood as a procedure at all, it's obviously not one for solving any version of chess.

There are almost certainly more weak solutions for competition rules chess or ICCF chess than, for example, Tromp's figure for basic rules positions. (For basic rules the number of weak solutions is most probably infinite.) In all probability nobody has ever seen a game that doesn't end in resignation or an agreed draw in a relatively short number of moves that corresponds with any of them. 

The positions that are included in different solutions could be markedly different. It is likely that some solutions include a significant percentage of positions with many promoted pieces on the board.

Syzygy has multiple solutions to the positions it covers, all perfect. 

Here is one.

You'll notice that on the move shown there are five knights on the board. That is optimal play if the phrase is taken to mean perfect play.

But what you've apparently failed to appreciate in all your gropings for a procedure to support your claim that you can solve chess in 0 or 2 or 5 years is that if you're to match up your nodes/sec quote with a forward search procedure, it's not the nodes that appear in your solution that determine the duration of your search but the nodes actually searched.

The number of those that contain multiple promotions or underpromotions couldn't be determined from the solution especially when you haven't obtained a solution, so you have to estimate them from the details of the search procedure.

If you wish to continue struggling to find a forward search procedure that would, in principle, actually weakly solve some version of chess, then your uncle Elroch has already given you some tips that might reasonably allow you to reduce your estimate of the number of positions with multiple promotions you are likely to encounter (as well as how you might cope with the humongous state space with the triple move rule in effect to get your solution to complete in the lifespan of one universe instead of gazillions). 

"How do let SF know that?" ++ No, estimating the number of relevant positions for weakly solving is different from the solving itself.

Fair comment. See above.

"So if it's gone 1.e4 e5 2.Ba6 which of that lot should I be looking at?"
++ 1 e4 e5 2 Ba6? is trivial,

But you've always been very coy when asked to show your straight ten wins as Black against Stockfish. Why would that be?

just like 1 e4 e5 2 Nf3 Nc6 3 Ba6?, 3 Nxe5?, 3 Nd4?, 3 Ng5?, Nh4?, 3 Ng1?. Those are moves that lose for white, they do not even try to win.

That you need to prove if you are to weakly solve chess. 

They do not oppose to, strive against achieving the game-theoretic value.

That also you need to prove.

We don't know what the game-theoretic value is, but unless it's a win for Black those moves would at least intuitively appear to strive against achieving it.

 If you want we can partition the weak solution of Chess into 2 parts:

1. weak solution of how to draw as black against drawing white moves
2. weak solution of how to win as black against losing white moves

I am only interested in part 1.

Neither part corresponds with the definition of weakly solving that you've posted ad nauseam. Have you given up on solving?

And

ICCF (grand)master + 2 servers of 90*10^6 servers, average 5 days/ply

does neither part 1 nor part 2.

"The blunder rate may be less with lesser hardware and less time/move"
++ 1 e4 e5 2 Ba6? is trivial.

See previous comment on the subject. We're still waiting.

"You're assuming chess is a draw without any evidence."
++ With massive evidence.
114 draws out of 114 games in the ongoing ICCF WC Finals, strongest chess on the planet.
White has an advantage of +1 tempo = +1/3 pawn, not enough to win.
Each further move dilutes the advantage.

"massive" apparently meaning zero.

What are we arguing about again? ICCF comp?