Is Chess Something We Can Solve?

Make a reasonable case...with examples. Or don't float false equivalencies, your choice.

@383

"understand what he did" ++ He wrote his own Checkers program, Chinook and he compiled his own endgame table base, then he calculated with Chinook to his endgame table base. He wrote himself that perfect alpha-beta pruning leads to exponent 0.5. He only reached 0.67. Chess engines have evolved much more than Chinook. Moreover Chess is easier to prune than Checkers. So for Chess the exponent will be closer to 0.5 than to 0.67.

"you need to find a move to play against EVERY legal opponent move"
++ NO. Some moves can and should be dismissed right away because of logic.
Examples: 1 e4 e5 2 Ba6?, 1 e4 e5 2 Nf3 Qh4? 1 e4 e5 2 Nf3 Nc6 3 Nd4?
Also 1 a4 cannot be better than 1 e4, 1 Nh3 cannot be better than 1 Nf3, 1 e4 e5 2 Nf3 Nc6 3 Ng1 cannot be better than 3 Bb5 or 3 Bc4. Also 3 Bd3 or 3 Be2 cannot be better.

"If promotion was illegal."
++ No: if underpromotion to a piece not previously captured were illegal.
All master games in a database and all ICCF draws would be exactly the same if the rules were changed that way.
10^38 is the number of positions possible from 1 luxury box of 34 chess men: 32 chess men + 1 spare queen of each color.

A couple of comments...

- Tygxc's romanticised obsession with boxed pieces is tiresome and dovetails with his overvaluation of Sveshnikov. He doesn't just want to solve chess, he wants to show that the "wisdom" of his own era was the driver of it. Thus the shortcuts and the contortions. He's on a deadline to do this before he shuffles off this mortal coil and his imagined chance to "save" Sveshnikov is gone.

- Nobody should be changing definitions or adding terminology to coddle the crackpots. Weakly solved has been explained dozens of times. Nodes have been explained dozens of times.

If that means that 'weakly solved' and 'nodes' has been explained to tygxc and he is defying the actual definitions and misuse the terms and continuing to do so well that looks right.
I don't read through most of tygxc's posts because of mispremising.
Persons such as Elroch - Dio - Martin - MEGA - mpaetz - llama don't mispremise. So therefore I tend to read through their posts because of accurate premises they're basing their posts on.
I don't believe that 'nodes per second' can ever transcend 'operations per second'. Nor that 'taking the square root' of the number of possible positions could be valid in 'solving'. Nor that engines of the same strength drawing each other 'proves chess is a draw with optimal play'. It doesn't. Because its not 'optimal play'.
The endgame tablebases have some claim to 'optimal play' but they're incomplete.
The 'doesn't factor in castling' could be partially let go because castling wouldn't be legal anyway in many of the positions and those where it might be possible could be set aside. Like setting aside the 50 move rule and the 3-fold repetition rule.

I think its worse than that.
His pretense of 'smarter' is only part of it.
Plus him 'making sure he is correct' is almost nonexistent.
He is often pursuing the opposite of that.
Deliberate falsehoods are part of trolling.
Especially the most common form of trolling.
Which I call type 3 trolling. There's at least 8 distinct forms.
---------------------------
Regarding the forum subject (which O isn't really interested in)
the idea of 'getting' from 31 pieces to 32 pieces on the board with a hypothetical that 31 is already 'tablebased' (a huge leap that might never be actually accomplished) sets up some points regarding 32 pieces and 'tablebasing' them.
For example - at that point it might actually be 'useful' to actually consider the number of possible 'games' from the initial position?- to reach all possible positions with 32 pieces up to all points where no capture has occurred.
But Martin keeps reminding us about the 50 move rule and other rules.
The number of such games even with no captures yet would be infinite without a repetition of position rule.
And if the 3 fold repetition of position rule is in effect - then the number of 'games' with no captures having happened yet would still be much larger without a 50 move rule too.
----------------------------------
Point: even if you only consider games with no captures yet - those rules still 'needed'.
But even there - there's still 'big 'number' problems.
Even there - 'game analysis' would still seem to be daunting - even with all positions with 31 pieces or less 'tablebased'.
Because for one thing - 'adding a piece' doesn't 'map' into 'reverse capturing'.
They don't have to correspond.
There's more positions than that with 32 pieces. Far more.

@Elroch your post there might deserve many replies. And much rereading.
Seems I have it right about combinations of two or more black pawns or any repeated piece type.
The available squares get multiplied together and then divided by the factorial of the number of identical pieces involved.
You still get a big number though.
-----------------------
Regarding illegal positions there's an issue of the ratio of illegals. Would the illegals be more than half of positions? I would think it would be far under half.
---------------------------------
Regarding 'graph' yes I could read up on graph theory forever.
But is there no simple answer to the two variables you're addressing on the 'graph with nodes'?
---------------------------
"In terms of absolute computing time, I think the 32 piece tablebase would take more time than all of the others put together, but not a large multiple"
that has occured to me too. Years ago.
But then it also occurred to me that the hardest situations could actually be in the middle of the progression.Something analagous to when you see a sum expressed as a sum of a finite series of polynomials (with or without factorials on the bottom) but with the biggest terms actually in the middle not at the ends.
Sometimes with one biggest term in the middle - sometimes with two.
Analagous. Not 'similiar'.
You're probably familiar with the kinds of series I'm talking about.
And probably more familiar. Much moreso.

"I understand that you don't have intuition that works for this "
@Elroch I also tend to think that is the case for tygxc.
But I'm not 100% certain. Far from it.
If his position is a kind of lawyer position (or even 'debate team' position) that such intuition doesn't help his case then he will set that aside as opposed to 'not having it'.
Lol!

MEGA
I don't know if it was coincidence or not 
but it was 'eery' just now that Elroch kind of also suggested what I was suggesting about 32 pieces. Kind of because I suggested that the '32' would be so large.
Elroch just now suggested that 32 could actually take longer than all the tablebases before it combined.
But I also pointed out that it could be instead more like a finite series with one or two terms in the middle being the biggest terms.
Some things might 'narrow down' towards 32 pieces.
For example - all positions with promotions would be impossible.
Illegal. Or rather Are. You can't have promotions with 32 pieces on board.
That's a lot of positions the computer can just eliminate fast.
You just couldn't have five knights or more on the board anyway.
Nor two or more white lightsquare bishops.
Because 32 pieces means no captures yet.
Which means promotion is impossible because every pawn would be blocked from the promotion square by its opposite in front of it.

Well spotted about the biggest tablebases having limited numbers of promotions. The 32 piece one may not be the biggest. The reason is that it is rather "inefficient" to have so many pawns and no more than 2 of other pieces. For the biggest number of positions you really want to share the pieces out as evenly as possible over the piece types. You would have more positions with 3 of each of 5 pieces than 8 pawns, 2 rooks, 2 bishops, 2 knights and 1 queen.

But on the other hand, having more pieces also increases the number of positions, so there is a tradeoff.

I think Tromp has worked this stuff out (or could have as part of his analysis). His work is very impressive - see https://www.chess.com/forum/view/general/on-the-number-of-chess-positions

Note that before the legality check the calculations are really quite simple - just a big combinatorial counting exercise.

It's essentially a set of nested for loops specifying the number of each piece (with consistency constraints - you can't have more promoted pieces than the number of missing pawns, and there also have to be enough captures to make the number of promotions possible), with the final count for a class of piece counts being high school combinatorics - a calculation with a lot of factorial functions in it!

"The 32 piece one may not be the biggest."
Looks like we're in some agreement there Elroch.
I was also thinking about - could you have 31 piece arrangements in the original opening position - with just one pawn or piece 'missing'.
The short answer is yes.
Both sides bounce their knights - with one side first advancing its knight and 'filching' a piece or pawn on its 7th or 8th ranks and then sneaking back to home.
Such positions would be Ridiculous of course.
-------------------------------------
And maybe there would be some efficient 'approximation' way for the engines to exclude them?
Would be tough.
Even with the repetition rule and 50 move rule ... the numbers of ways the knights could do that stuff would be daunting. Point is it would be tough for the computer to find them all.
It has to find them to exclude them.
tygxc - to his credit - is apparently arguing (in a favorable interpretation of what he's doing) that there should be a way to filter out ridiculous game sequences.
But apparently he's not putting it right.
Not putting the case for that forward - properly.
Enter O?
O would clutz it up. He always does.
Certainly the software engineers are pruning out that ridiculous stuff for game-playing but that's not 'solving' though.

"Some moves can and should be dismissed right away because of logic."

then by definition you arent solving the game. how hard is that to get through your skull

also your "logic" is just imperfect evaluations.

if its not a formal proof it literally doesnt count whatsoever.

""If promotion was illegal."
++ No: if underpromotion to a piece not previously captured were illegal."

how about you actually read the paper of the calculation. nowhere do they mention the distinction to a piece previously captured. man up and admit being wrong.

"examples: 1 e4 e5 2 Ba6?, 1 e4 e5 2 Nf3 Qh4? 1 e4 e5 2 Nf3 Nc6 3 Nd4?
Also 1 a4 cannot be better than 1 e4, 1 Nh3 cannot be better than 1 Nf3, 1 e4 e5 2 Nf3 Nc6 3 Ng1 cannot be better than 3 Bb5 or 3 Bc4. Also 3 Bd3 or 3 Be2 cannot be better."

you have no proof that the moves are better beyond engine evaluations and general knowledge. that isnt logical deduction, that's just you making unfounded assumptions.

"10^38 is the number of positions possible from 1 luxury box of 34 chess men: 32 chess men + 1 spare queen of each color."

Read the paper, which directly contradicts your delusion.

its sad that tygxc's calculations are not only wrong, but that tygxc doesnt even know what they mean even if they were correct. taking the square root of the relevant positions means that you are estimating the size of the weak solution game tree itself, NOT the number of positions needed to find the game tree.

"taking the square root of the relevant positions means that you are estimating the size of the weak solution game tree itself, NOT the number of positions needed to find the game tree."
that looks well qualified.

MEGA there's something that might happen now.
Can we do 'tygxc' better than tygxc does tygxc?
If we're talking about dismissing 1) e4 e5 2) Ba6 ....
is there a way to improve on the way tygxc is going at that?
I think we know what his idea is.
But it also seems clear he is not presenting his idea correctly in the context of 'solving'.
Chess engines would know to 'prune out' 2) Ba6 from their calculations because the evaluation of that move is just too relatively dismal.
I tried it just now in a separate chess.com browser window.
I hit the fourth button down on the left side of the screen and then chose Analysis from the drop-down menu.
I played the moves and it gave Black an advantage of 2.50 with a reply of Nxa6 - which I had forgotten about previously. I was mistakenly thinking bxa6 which is still dismal for white but not quite as bad.
------------------------------------------
And an advantage of 2.5 is Crushing.
But that's Gameplaying. Not Solving.
And it seems if you let the engines Prune for solving based on their own numerical evalutaions of the positions then that's a kind of circular reasoning.
It would produce a kind of computer diarrhoea.
Similiar with having the same level engines play themselves and trying to argue from there that chess is 'a draw with optimal play'.
I believe tygxc has far more than enough intelligence to know that he's wrong.
And probably does know.
But there's this idea of 'the client'. And 'the debate case'.

Nowhere do they mention it, but they should. I think @tygxc is right on that one.