Chess will never be solved, here's why

@12789

"I only inspected and found none can result from optimal play by both sides."
++ You can verify yourself. Here is the random sample file of 10,000 positions without promotions to pieces not previously captured. The file is raw, before legality check, i.e. contains illegal positions. The file is labelled 'noproms', meaning no promotions to pieces not previously captured, i.e. it contains only positions from 1 box of 32 chess men, but some positions have e.g. 2 dark-square bishops on one side. I inspected the positions and found none that could result from a reasonable, let alone perfect game with optimal play from both sides.
If you think one of these could, then try to come up with a reasonable game that leads to it.
You do not have to prove optimal play, only present reasonable play.

"but not why you should be starting with 10^38 in the first place"
++ The number of legal positions is (4.82 +- 0.03) * 10^44.
However, the 3 random samples shown cannot result from optimal play by both sides,
as both sides have multiple underpromotions to rooks and/or bishops,
and such underpromotions only make sense to avoid a draw by stalemate,
and it cannot be optimal play for both sides to avoid the draw.

Per Tromp the breakdown of raw position count before legality check is:
promotions: 0 positions: 19201527561695835455154058755564594798074
promotions: 1 positions: 382355871178268365234183218244670372695068
promotions: 2 positions: 3666683498600457464891752992187014354136188
promotions: 3 positions: 22267499667290257736558400874926183060238400
promotions: 4 positions: 95095065373967146179514528215894174339720228
promotions: 5 positions: 300571414300527313744528888013946849776424304
promotions: 6 positions: 721668497316402902485416452421325823057710432
promotions: 7 positions: 1329934072135692805837128923570048899100334756
promotions: 8 positions: 1874962044164806332602085236357597905810647344
promotions: 9 positions: 1980800128935921108339671872170042183548439128
promotions: 10 positions: 1492529839915108301878747832838229979840571492
promotions: 11 positions: 722080907452760073481816196266539169729817880
promotions: 12 positions: 175351843526979273665005184194531833618491680
promotions: 13 positions: 7338473695924787177946719990630518998574920
promotions: 14 positions: 45087168602668580254351850721788483191140
promotions: 15 positions: 55323182237139471340692375109727946960
promotions: 16 positions: 11716401834002951530424702440978260
Total: 8726713169886222032347729969256422370854716254

Promotions to pieces not previously captured occur in master games and in ICCF WC Finals draws, but positions with 9 promotions to pieces not previously captured make up the lion's share of the (4.82 +- 0.03) * 10^44 legal positions.

No, they do not, according to your quoted numbers. The positions with 9 or more positions are similar in number to those with 8 or fewer.

That is why 10^44 is no good starting point.

Faulty premises give faulty conclusions.

A better starting point is 3.8521 * 10^37 from An upper bound for the number of chess diagrams without promotion.

That's great for chess variants where pawns cannot advance passed the seventh rank. Not for chess, though.

The 10^37 is too restrictive, as positions with 3 or 4 queens do occur in master games,
and in perfect games with optimal play from both sides as we know from ICCF WC Finals draws.

And the number of such positions is greater than those without (because the game starts with fewer queens than pawns)

I arbitrarily multiply by 10 to include such positions, leading to 10^38.
That is why starting from 10^38.

You're such a comedian! You didn't even do a dodgy calculation for that did you?

"what optimal play has to do with anything"
++ Weakly solving chess is about optimal play by both sides: positions that cannot result from optimal play by both sides are not relevant to weakly solving chess.

WRONG!

Positions that cannot result from ONE side playing moves THAT ACHIEVE THE OPTIMAL RESULT are not relevant to weakly solving chess. These moves may be suboptimal (draw instead of win) and the other players moves are restricted only by legality. THAT'S THE DEFINITION OF WEAK SOLUTION, regardless of your long held error.

The 110 draws out of 110 games of the ongoing ICCF WC Finals are examples of optimal play by both sides and constitute at least part of a weak solution of Chess.

What's that? About 5000 positions? Job nearly done then.

Moreover it is redundant, as it shows several strategies to achieve the game-theoretic value instead of the required one.

You correctly point out that not only is 5000 positions a bit short of a full weak solution, only a fraction of the positions can be in one, because they diverge. While a weak solution has to include the 20 positions after white's first move in the white strategy, it only has one move in the white strategy. To be more precise, if there are games where both players diverge between them, at least one of them is worthless to a weak solution. (eg no weak solution contains 1. d4 Nf6, 1. d4 d5, 1. e4 c5 and 1. e4 e5).

no, but you will be once im done

no, but you will be once im done

@12789

"I only inspected and found none can result from optimal play by both sides."
++ You can verify yourself.

You have a misconception about who is responsible for verifying the reduction you use.

It's your reduction so it's up to you to verify it yourself.

Originally you stated that none of Tromp's legal positions could be reached by sensible play which you defined in terms of the analysis page in chess.com with the version of Stockfish then available.

You were invited to show that even a single one of the positions was unreachable under that criterion and failed dismally.

You have now changed your mind and stated instead that not one of the positions can be reached by optimal play which has a well defined meaning, so I now invite you to prove that. A proof that even one is not so reachable would be a start.

Here is the random sample file of 10,000 positions without promotions to pieces not previously captured. The file is raw, before legality check, i.e. contains illegal positions. The file is labelled 'noproms', meaning no promotions to pieces not previously captured, i.e. it contains only positions from 1 box of 32 chess men, but some positions have e.g. 2 dark-square bishops on one side. I inspected the positions and found none that could result from a reasonable, let alone perfect game with optimal play from both sides.

Reasonable play is not necessarily perfect and perfect play is not necessarily reasonable (see example below). You failed to come up with even a sensible definition of the former nor a proof that even a single one of the legal positions in question was unreachable under the definition you gave.

If you think one of these could, then try to come up with a reasonable game that leads to it.

You do not have to prove optimal play, only present reasonable play.

No, sod off. It's your reduction - it's up to you to prove it. 

We don't know what's optimal without a solution and neither what is optimal nor reasonable (however you define it) is relevant. Only whether it will occur with your method during your search. You have to prove that none of Tromp's sample will occur. Best of luck. 

"but not why you should be starting with 10^38 in the first place"
++ The number of legal positions is (4.82 +- 0.03) * 10^44.

No.

That's the number of basic rules positions, taking the attributes of "position" that fully determine possible game continuations under FIDE basic rules, viz. diagram, side to move, castling rights and possible ep file. Those attributes determine the nodes of the FIDE basic rules chess search tree and you can call those attributes a FIDE basic rules chess position. 

You're talking about FIDE competition rules chess not FIDE basic rules chess.

The attributes included in a basic rules position are insufficient to fully determine possible game continuations under FIDE competition rules. Under those rules the attributes required are diagram, side to move, castling rights, possible ep file, and a list of up to 150 basic rules positions with the same material that have previously occurred (possibly including repeats). You can call those attributes a FIDE competition rules chess position. (It doesn't matter if you don't like the term, they are the nodes in Stockfish's search space.)

 @Elroch has suggested a way of drastically cutting down the size of the search space in a forward search solution of a type similar to what you originally proposed for a non solution, but you have not, so the number of nodes in Stockfish's search space is the number you should be starting with. That is the number of FIDE competition rules chess positions.

Nobody, so far as I know, has published an estimate of the number of FIDE competition rules chess positions, so I'll leave you to figure it out, but I don't think you'll fit it on the page without using two levels of index. 

However, the 3 random samples shown cannot result from optimal play by both sides,
as both sides have multiple underpromotions to rooks and/or bishops,
and such underpromotions only make sense to avoid a draw by stalemate,
and it cannot be optimal play for both sides to avoid the draw.

Per Tromp the breakdown ... irrelevant basic rules figures ...

Promotions to pieces not previously captured occur in master games and in ICCF WC Finals draws, but positions with 9 promotions to pieces not previously captured make up the lion's share of the (4.82 +- 0.03) * 10^44 legal positions. That is why 10^44 is no good starting point.

You have shown no reason to suppose that ICCF games should have any more relevance to solving even ICCF chess than a set of games between total beginners.

I agree 10^44 is no good starting point for the reasons above. It's probably far too low even for KNNvKP. 

On the other hand 4.85x10^44 is (slightly) more than adequate for constructing a retrograde (tablebase) solution, because that method can validly ignore all but the basic rules position attributes.

The reason I continue to include the factor 4.85 is that you have already acquiesced to that and also to a factor of 100 to account for the 50 move rule. These factors are very small beer compared with your ludicrous reductions , but if you had any belief in what you keep saying or any honesty you would at least be adjusting your original 5 year estimate to 5x√(4.84x100) = 110 years.

And the reason I keep referring to a non solution rather than a solution is that a weak solution is meant to give you the moves you need to make to get the best possible result from the starting position. If you put forward something that only says TSMYOYO if your opponent makes a move that tygxc or one of his handmaids didn't think was sensible or tells you how to draw if you've got a win, it's not very useful. In the words of the song, it's no bloody use to anyone, it's no bloody use at all.

A better starting point is 3.8521 * 10^37 from An upper bound for the number of chess diagrams without promotion.
'Without promotion' here is short for 'without promotion to pieces not previously captured'.
For some positions you can prove a piece is original, not promoted,
and for some positions you can prove a piece must be promoted, not original,
but generally you cannot tell from a position if it contains promoted pieces or not.
'Without promotion' means 'without promotion to pieces not previously captured',
or, in other words, positions possible from 1 box of 32 chess men.

The 10^37 is too restrictive, as positions with 3 or 4 queens do occur in master games,
and in perfect games with optimal play from both sides as we know from ICCF WC Finals draws.
I arbitrarily multiply by 10 to include such positions, leading to 10^38.
That is why starting from 10^38.

All of which might interest you but it's not germane.

What practical players do can't be related to perfect play in the absence of any solution and the non solution you would construct according to your original plan would only initially resemble anything Stockfish would actually play. Thereafter it would be a pastiche of bits of Stockfish non preferred moves and segments of Stockfish play with the latter on average getting shorter and shorter. 

"what optimal play has to do with anything"
++ Weakly solving chess is about optimal play by both sides: positions that cannot result from optimal play by both sides are not relevant to weakly solving chess.

Totally wrong.

A weak SOLUTION of chess is about optimal play by at least one side. Weakly SOLVING chess by a forward search can't be about optimal play by both sides because firstly you don't have anything that can do optimal play and secondly you have to take into account non optimal play by at least one side. 

As for optimal play the main line here is Syzygy optimal moves against me. It's not to be confused with what most people would call reasonable moves (you may differ).

The variation shown is the sample for the position from the Syzygy site. Look particularly at White's move 24.

You haven't shown that your non solution would be any more "reasonable".

The 110 draws out of 110 games of the ongoing ICCF WC Finals are examples of optimal play by both sides and constitute at least part of a weak solution of Chess.

No they aren't and no they don't.

Moreover it is redundant, as it shows several strategies to achieve the game-theoretic value instead of the required one.

It's only redundant if you and your opponent agree always to play only a proper subset of these 110 games.

it’s not his fault that argument after argument bit the dust.

true

Did optimissed get muted again he hadn't been online recently

Hey shig - tygxc doesn't have to shut up.
What are you doing here?

tbf it would be highly beneficial to all parties involved if tygxc DID shut up.

tbf it would be highly beneficial to all parties involved if tygxc DID shut up.

@12768

"The positions with 9 or more positions are similar in number to those with 8 or fewer."
++ No. 19201527561695835455154058755564594798074 / 8726713169886222032347729969256422370854716254 = 2.2*10^-6.

NO!

I am not sure if this was a deliberate deception or a blunder, but here you have divided the number of positions with 0 promotions by those with 9 promotions, which is of course not relevant to what I said.

Positions with 9 promotions to pieces not previously captured make up 22.7%.

Which undelines what I said.

"Faulty premises give faulty conclusions." ++ Valid premises give right conclusions.

Only when combined with valid reasoning. You fail really badly at the latter.

"chess variants where pawns cannot advance passed the seventh rank" ++ Cannot you read? 'Without promotion' is short for 'without promotion to a piece not previously captured'.

Which is NOT a rule in chess, except maybe among beginners who think that if a piece is not in the box you can't promote to it. The same set of positions is only relevant for such chess variants, not for chess.

Promotion to a piece not previously captured happens in maybe 1 game in 100, or 1 position in 1000.

So you are trying to find a 99% correct solution of chess now?

"the game starts with fewer queens than pawns"
++ But for a pawn to reach the 8th rank at least one capture is necessary.

True and not exactly news.Of course promotions happen,
but by the time promotion happens usually the desired queen is already captured.

So? You seem to think "usually" is a valid step in logical argument.Even more in the rare case of underpromotion, as there are 2 rooks, bishops, and knights and usually at least one of those is captured by the time a pawn promotes.

"usually"

"You didn't even do a dodgy calculation for that did you?"
++ Multiplying by 10 for something rare like 1 game in 100 or 1 position in 1000 is generous.

Another irrelevant guess that can't be used in valid reasoning.

"About 5000 positions?" ++ 8720 resulting from considering 10^17 positions.

From doing inconclusive analysis on all of those early in the game.

"no weak solution contains 1. d4 Nf6, 1. d4 d5, 1. e4 c5 and 1. e4 e5"
++ Those are 4 weak solutions:

You need to learn what a weak solution is. 7 positions is not a weak solution. A tree of 10^30 positions might be.

1. 1 d4 d5 and 1 e4 e5,
2. 1 d4 Nf6 and 1 e4 c5,
3. 1 d4 d5 and 1 e4 c5,
4. 1 d4 Nf6 and 1 e4 e5.
   If a pair of errors were found in 1 e4 e5, then 1 e4 c5 is available as a backup and vice versa.
   If a pair of errors were found in 1 d4 d5, then 1 d4 Nf6 is available as a backup and vice versa.
   The redundancy is unnecessary, but makes the weak solution fail safe against possible errors.

Hilarious!

Per Tromp the breakdown of raw position count before legality check is:
promotions: 0 positions: 19201527561695835455154058755564594798074
promotions: 1 positions: 382355871178268365234183218244670372695068
promotions: 2 positions: 3666683498600457464891752992187014354136188
promotions: 3 positions: 22267499667290257736558400874926183060238400
promotions: 4 positions: 95095065373967146179514528215894174339720228
promotions: 5 positions: 300571414300527313744528888013946849776424304
promotions: 6 positions: 721668497316402902485416452421325823057710432
promotions: 7 positions: 1329934072135692805837128923570048899100334756
promotions: 8 positions: 1874962044164806332602085236357597905810647344
promotions: 9 positions: 1980800128935921108339671872170042183548439128
promotions: 10 positions: 1492529839915108301878747832838229979840571492
promotions: 11 positions: 722080907452760073481816196266539169729817880
promotions: 12 positions: 175351843526979273665005184194531833618491680
promotions: 13 positions: 7338473695924787177946719990630518998574920
promotions: 14 positions: 45087168602668580254351850721788483191140
promotions: 15 positions: 55323182237139471340692375109727946960
promotions: 16 positions: 11716401834002951530424702440978260
Total: 8726713169886222032347729969256422370854716254