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Chess will never be solved, here's why

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tygxc

#19
There is no infinity, there are no trillions of moves.
Each chess game ends in 5898.5 moves at most.
In each position there is a finite number of legal moves.
Hence there are only a finite number of possible chess games.
The number is large because of transpositions.
There are billions of ways to reach the position after 1 e4 e5.
The number of games is irrelevant, it is the number of positions 4*10^37 that counts.
#20
Each decisive game implies an error. Increasing the time reduces the error rate.
At 1 second per move: 88.2% draw rate hence 1 error per 8.5 games.
At 1 minute per move 97.9% draw rate hence 1 error per 47.6 games.
Extrapolating:
At 1 hour per move 1 error per 266.6 games.
At 60 hours per move 1 error per 1493 games.
Also the ICCF results support that chess is a draw.
https://www.iccf.com/event?id=66745 
The comparable results with stalemate = win show that stalemate = win does not increase decisiveness. This reinforces that classical chess with stalemate as an additional drawing resource is a draw indeed.
Engines are weak at openings without their opening books as positions with >26 men have too many legal moves.
Engines are weak at endings without their endgame table bases as positions with <7 men have too deep lines.

MARattigan
tygxc wrote:

#19
There is no infinity, there are no trillions of moves.

If there is no infinity a lot of mathematicians have been sorely misguided. I've heard of ultra-finitism, but the proponents I've read will usually concede trillions.
Each chess game ends in 5898.5 moves at most.

Not quite true. Every game played under FIDE competition rules ends in 8848.5 moves at most. This is a consequence of the mandatory 75 move rule. A game of this length is possible under those rules without breaking the mandatory 5 fold repetition rule. See https://wismuth.com/chess/longest-game.html. The figure 5898.5 would apply under those rules if it were not necessary to claim a draw under the 50 move rule. But it is.

Under Fide basic rules (which I explicitly mention in post #19) there are neither mandatory nor claimable rules limiting the length of a game, though with current medical technology the length of a game involving a human would in practice be limited by the expiration of one of the players and with most current theories about the evolution of the universe would in any case be limited by e.g. the heat death of the universe.
In each position there is a finite number of legal moves.
Hence there are only a finite number of possible chess games.
The number is large because of transpositions.
There are billions of ways to reach the position after 1 e4 e5.
The number of games is irrelevant, it is the number of positions 4*10^37 that counts.

Agreed. But that is of course not to say that the number of games that need to be considered is the same as the number of positions. It does give a limit on the number of positions that would need to be indexed in a full set of tablebases.
#20
Each decisive game implies an error. Increasing the time reduces the error rate.

Does that mean you've already weakly solved chess and it's a draw and also proved that AlphaZero's evaluation function doesn't suffer from minimax pathology? (http://izvolitve.ijs.si/Stacks/Articles/19805735.pdf


At 1 second per move: 88.2% draw rate hence 1 error per 8.5 games.
At 1 minute per move 97.9% draw rate hence 1 error per 47.6 games.
Extrapolating:
At 1 hour per move 1 error per 266.6 games.
At 60 hours per move 1 error per 1493 games.

But you have no idea how the data from which you're extrapolating corresponds with objectively perfect play. (I'm assuming the answer to my previous question is "no and no".) The difference between that and Haworth's extrapolations is that his are based on statistics from the Nalimov tabebases which do correspond with perfect play under basic rules.
Also the ICCF results support that chess is a draw.
https://www.iccf.com/event?id=66745 

Poppycock. They support nothing of the kind.

If you take a random game from the middle of the table in your link


 

you will notice that the draw reached is not a dead position. It's an agreed draw. This is irrelevant in respect of perfect play.

What has clearly happened is that the players have followed their respective opening books or that of their silicon aids for a couple of dozen moves, played on without seeing any forced mate for another dozen moves or so and then having no good ideas on how to continue in any advantageous way given up playing in a position which, while no doubt theoretically less intractable to solve than the starting position is still well beyond current resources. (They might as well have agreed a draw at the outset.)

This is exactly to be expected.

When equally matched players are out of their depth in a position the most common result is a draw. This has nothing to do with the objective evaluation of the position.

An example would be the KQKNN endgame which has for centuries been regarded as generally drawn. Nalimov says that around 75% of positions are actually winning for the queen. But in practice the general result is a draw. I've left SF playing itself in a number of times in such positions with mate depth over 45 moves and about 5 times out of 6 it draws under the 55  move rule.

For centuries humans have been weeding out lines that result in losses that they can fathom from move sequences following the starting position and for decades computers have been doing the same faster and more accurately. The result is that for equally matched players who have an enyclopaedic knowledge of opening analysis the opportunity to reach winning positions that are within their depth is shrinking and you can expect that the number of draws will correspondingly increase.

But that is not an indication that chess is objectively a draw, merely that players with limited look ahead are increasingly reaching positions where they're out of their depth.

The comparable results with stalemate = win show that stalemate = win does not increase decisiveness. This reinforces that classical chess with stalemate as an additional drawing resource is a draw indeed.

As I already remarked, without any way of comparing AlphaZero's play with accurate play when the tablebases peter out it shows nothing at all about accurate play, only about play at AlphaZero's level  (neither for normal chess nor stalemate=win chess).


Engines are weak at openings without their opening books as positions with >26 men have too many legal moves.

Engines without their opening books are weak against strong human players only because the latter carry their opening books around with them on top of their shoulders.

 

Engines are weak at endings without their endgame table bases as positions with <7 men have too deep lines.

 

Not anything like as deep as positions with >7 men (or even to a lesser extent =7 men).

But its not just engines.

In 2000 Topalov (rated #1 at the time) and Karpov (i.e. Karpov) reached a KNNKP endgame in a position the same as the one I posted in #20 but the pawn and blockading knight shifted one square NW.

In the next nine moves the players blundered three half  points between them.

 

 

tygxc

#22
There is no infinity in chess. The 50 moves rule, the 75 moves rule, and the 3 fold repetition rule and the 5-fold repetition rule all be themselves guarantee that the number of moves in a chess game is finite.

Chess is a draw is a conjecture believed to be true but not yet proven.

Of course the evaluation function of AlphaZero is flawed, otherwise it could never win a game against itself. However with more time per move the error rate asymptotically goes down.

ICCF grandmasters already analyse endgames when in the opening. They are allowed to use engines and table bases. When they agree on a draw it usually is because it is a draw.

Also in TCEC they have to impose slightly unbalanced openings to prevent all draws.

Humans misplay 7-men endgames mostly because they get tired and low on time. Engines without table bases misplay 7-men endgames because their evaluation function is flawed. They happily go for a +3 advantage in a fortress draw.

NikkiLikeChikki

Here's a thread that has almost 10,000 posts: https://www.chess.com/forum/view/general/true-or-false-chess-is-a-draw-with-best-play-from-both-sides

Here's one with almost 1000: https://www.chess.com/forum/view/general/will-chess-ever-die-out-once-its-fully-solved

Here's one with over 200: https://www.chess.com/forum/view/general/solving-chess-with-no-bs-moderated

There are dozens of other threads on the same topic and everything that can be said has been said and none of it is relevant to anyone who plays chess.

Gymstar

+1

MARattigan
tygxc wrote:

#22
There is no infinity in chess. The 50 moves rule, the 75 moves rule, and the 3 fold repetition rule and the 5-fold repetition rule all be themselves guarantee that the number of moves in a chess game is finite.

There is no 50 move rule, 75 move rule, 3 fold repetition rule or 5 fold repetition rule in the FIDE basic rules of chess. Those rules now apply only to games covered by competition rules. The 50 move rule and 3 fold repetition rule were removed from the basic rules in 2017, the other two were never in. Prior to removal the draws had to be claimed anyway so games of any length were permissible.

There is infinity in theoretical chess under basic rules in that its perfectly possible to specify an unending game that doesn't contravene any of the basic rules. E.g.

2n-1. Na3 Na6

2n.    Nb1 Nb8

for all n in the sequence 1,2,3, ... .

Obviously these are impracticable to play out (as would be also 10 trillion move forced mates).

MARattigan
tygxc wrote:

#22
...

Chess is a draw is a conjecture believed to be true but not yet proven.

Believed by who?

Of course the evaluation function of AlphaZero is flawed, otherwise it could never win a game against itself. However with more time per move the error rate asymptotically goes down.

Are you then saying you have solved chess and proved AlphaZero's evaluation function doesn't suffer from minimax pathology?

ICCF grandmasters already analyse endgames when in the opening. They are allowed to use engines and table bases. When they agree on a draw it usually is because it is a draw.

There are no tablebases covering the ICCF position I posted and unlikely to be for a very long time. What makes you think it's a theoretical draw other than you can't see any way to win?

Also in TCEC they have to impose slightly unbalanced openings to prevent all draws.

Probably for the reasons I enumerated in my post.

Humans misplay 7-men endgames mostly because they get tired and low on time. Engines without table bases misplay 7-men endgames because their evaluation function is flawed. They happily go for a +3 advantage in a fortress draw.

Up to SF8 at any rate if engines' evaluation functions are flawed that's because (hopefully wide awake) human programmers with plenty of time have coded the leaf positions that way.

There is nothing wrong with assigning a positive evaluation to a fortress position. The evaluations are intended to guide play, not provide an indication of the theoretical assessment of the position. If the opponent of the player with the fortress has good chances should the fortress be misplayed then the program would do better to opt for the position in preference to an outright draw. (All of which has no relevance to theoretically perfect play.)

 SF14 draws this Black to play and mate in 50 in 6 moves against the Syzygy tablebase. Have a good knight's sleep and see if you can win it (take your time). You can take the White moves from the top of the list in syzygy-tables.info but make your Black moves on the playing board board before playing the preceding move on the site. 


Black to play and mate in 50

 

If you can do that one, try this one with two more pieces on the board. (You'll have to play it under basic rules - just reset the ply count as necessary.)

White to play and mate in 549

 

Then think about which ICCF players you would trust to distinguish a forced mate in, say, a couple of million moves from a draw.

 

Gnaim

You can play chess in around 10 to the power of 120 different times

NikkiLikeChikki

Elon Musk is working on Neuralink, which is a quasi-telepathic CPU brain implant. Testing is going on now and the first test subjects are planned for next year. Solving chess isn't going to ruin the game, everyone walking around with Stockfish in their brains will. Why everyone is so worried about chess being solved being a problem when this clearly will ruin the game as we know it is beyond me.

xor_eax_eax05

Elon Musk, outside of SpaceX, is borderline charlatan.

 

And yes, Chess will eventually be solved, just like tic-tac-toe was solved. But the solution is not going to be unique - there will probably be billions of different ways to reach the endgame with absolute best play from both sides - just like there is not one unique position in tic-tac-toe and in reality it depends on how the opponent starts the game.

 

Will it mean anything for humans? No, there is no way any person will be able to memorise all those billions of solutions - and if someone deviates even 1 move from any of them, then the other person would also have to know all the most efficiently calculated ways to win the game.

That's never going to happen.

NikkiLikeChikki

Right... the electric cars, the batteries, the tunneling machines, the solar power... Tesla made a $1.1B profit last year and his tunneling technology is revolutionizing the industry... a complete charlatan. Others are working on the same kinds of technology as well, so it's just not Musk if you hate him. Solving chess, if possible, will involve advances in quantum computers that are as of now only borderline theoretically possible. Brain implants are on a much faster trajectory of happening and games like chess will become irrelevant. Chess will become a trivial as doing math on a calculator when all you have to do is access best moves by thinking about them.

tygxc

#27

Chess is a draw is a conjecture believed to be true but not yet proven.
"Believed by who?"
++ By Steinitz, Lasker, Capablanca, Spassky, Fischer, Kasparov, Kramnik, Carlsen...

"Are you then saying you have solved chess and proved AlphaZero's evaluation function doesn't suffer from minimax pathology?"
++ No: chess has not yet been solved and no: AlphaZero evaluation does suffer as otherwise it could not win a game against itself. That however does not matter. 97% draw rate even if stalemate = win is a clear sign.

"There are no tablebases covering the ICCF position I posted"
++ No, but the ICCF grandmasters already hit the table base with their analysis at that moment. "What makes you think it's a theoretical draw other than you can't see any way to win?"
++ Both ICCF grandmasters agree it is a draw because they do look that deep in their analysis. It is incredible how deep they look at 3 days/move. In the opening they already analyse endgames.

Also in TCEC they have to impose slightly unbalanced openings to prevent all draws.
"Probably for the reasons I enumerated in my post."
++ For the reason that chess is a draw and all games otherwise would end in draws.

"There is nothing wrong with assigning a positive evaluation to a fortress position."
++ There is something wrong: an engine prefers a +3 fortress draw over a +1 forced win. 

tygxc

#31
"Will it mean anything for humans? No, there is no way any person will be able to memorise all those billions of solutions"
It will mean something for humans.
If a human has access to an edition of the Encyplopaedia of Chess Openings with all error-free end exact evaluations win/draw/loss, then that human will select his repertoire differently: broader for white and narrower for black.
A human can memorize a collection of 1000 perfect games all ending in draws from his repertoire.

xor_eax_eax05

 Lol you do realise the difference between 1000 games and billions of positions, right? And the fact that if their opponent chooses to move out of the "book" on purpose into a position that has a slight disadvantage just to throw the opponent off, you'd have to have memorised all positions from those slightly advantageous position into conversion in order to win it, right? That's an impossible task for any human mind. 

 Opening prep may change but since players will never have access to a db with all the positions during tournament play just like they are not allowed to bring a Stockfish distro, and since they won't be able to memorise every single position beforehand, it does not mean anything. I mean, even today opening prep is changing based on computer analysis, so it's not something that does not already happen. It will more limited but this limitation already happens today. In what top level serious tournament do you see the bongcloud played and studied? Plenty of other openings and variations are probably being complete discarded even today.

 Just look at the endgame tablebases. Does that change anything, even at highest level? If it was the case, as soon as a 7 piece endgame is reached, both top players would just move away from the board and adjudicate the game right there. But they dont, they play them out, because they can't memorise them all. And it's just 7 pieces. Do you think they will be able to memorise every single position from move 1? Nah.

MARattigan
tygxc wrote:

#27

Chess is a draw is a conjecture believed to be true but not yet proven.
"Believed by who?"
++ By Steinitz, Lasker, Capablanca, Spassky, Fischer, Kasparov, Kramnik, Carlsen...

...

And not one of those gentlemen would do any better than SF14 on the two positions I posted. 

The starting position is immensely more complicated. Their opinion of the result with perfect play carries no more weight than that of someone who has just learned the moves.

MARattigan
tygxc wrote:

#27

...

"Are you then saying you have solved chess and proved AlphaZero's evaluation function doesn't suffer from minimax pathology?"
++ No: chess has not yet been solved and no: AlphaZero evaluation does suffer as otherwise it could not win a game against itself. That however does not matter. 97% draw rate even if stalemate = win is a clear sign.

.... 

Your answer makes no sense to me.

So far as I understand it AZ could win a game against itself whether chess is a theoretical win or draw if it's evaluation  function produces minimax pathology and the same is true if it's evaluation function does not produce minimax pathology.

Where's the connection?

97% draw rate even if stalemate = win is a clear sign that chess with stalemate = win is statistically a draw with AZ's level of play. Just as the tablebase wins in the simpler positions I posted in #27 are also statistically draws with AZ's level of play.

tygxc

#35
Psakhis memorised all Fischer games and became USSR champion.
Dorfman memorised all Zürich 1953 games and became USSR champion.
Alekhine memorised all previously played grandmaster games and became world champion.
A human having memorised 1000 perfect games with his repertoire would have an advantage.
As black he would know he still can hold the draw as long as he follows a perfect game.
As white he would know to look for a win as soon as the opponent deviates from a perfect game.

It would also change how we play.
Assume 1 e4 Nf6 and 1 d4 f5 were known to lose by force and 1 e4 e5 and 1 d4 d5 were known te be a draw. No black player would then prefer the refuted line over the known draw line.
Assume 1 e4, 1 d4, 1 Nf3, 1 c4, 1 e3, 1 c3, 1 d3 were all known to be draw. White players might  avoid the former ones where the opponent knows how to draw in favor of the latter ones, where the opponent might not know how to draw.

Elroch

Carlsen is reported to have almost perfect chess memory. He has perfect memory of at least 10,000 games.

tygxc

#42
A player may have several perfect games memorised where the Berlin draws, but he probably has no games memorised that draw against 1 c3. Objectively both are a draw, but subjectively 1 c3 may give more chances to win, i.e. more chances of the opponent to err, because it is less common / seems less logical and thus may be unprepared for.

tygxc

#41
Suppose Carlsen has 10000 flawed games memorised and XYZ has 10000 perfect games memorised.