Chess will never be solved, here's why

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tygxc

@4054

More insults: "troll" "deceive".
Facts, figures, logic.
If you cannot produce any, better stay silent than project your own issues.

tygxc

@4056

"the sudden lack of ++"
++ I use ++ to clearly discern where my own comment starts after the "quoted phrase" I respond to. If I do not quote any phrase I do not need any ++

tygxc

@4060
You project your own issues.
Read post @4043 with plenty of facts, figures, explanations and then comment factually on it if you can at all instead of obscuring it with meaningless insults and accusations.
As the Facebook debating champion you know that ad hominem is the lowest.

japie33

I think chess WILL eventually be solved, but not until hundreds of years, engines are simply not strong enough yet.

Elroch
tygxc wrote:

@4036

"So the number of seconds in five years, divided by your figure of 17 seconds per position is a figure somewhat less than 10 millions."
++ In 17 seconds the engine calculates 17 billion positions.
You confuse the proof tree and the search tree.
The engine considers far more positions than it retains.
For comparison: Checkers has a proof tree of 10^7 positions and a search tree of 10^14.

Presuming you are not being deliberately deceptive, you misunderstand the relevance of the proof tree to the complexity of the proof.  The purpose of the proof tree is to bridge the gap between the opening position and a tablebase. In the case of the solution of checkers, the relevant tablebase was for all positions with 10 pieces or fewer. This tablebase contains about 3.9 trillion positions. As you can see, this is an enormously bigger number than those positions in the tree searched for the proof, never mind the pruned tree (total about 3 million positions) produced with the benefit of perfect hindsight (i.e. knowing the solution).

For chess you would need a much larger tablebase to reduce the proof tree to an analogous degree.  Let's look at the figures for checkers:

5e20 legal positions

1.5e7 proof tree (for 19 forced openings - checkers introduced these because the standard opening position got "boring".)

3.9e12 position tablebase

You can see that the complexity was reduced only by to a power of 0.6 (not as good as square root), just to calculate the tablebase used - tablebases can be generated fast while making good decisions in general positions is extremely slow. 

For basic chess, (10^44)^0.6 = 2.5e26, which is 250 trillion trillion trillion trillion, a complexity way beyond the world's computers put together. Similar log scaling would give a proof tree of 1.8 e15. This might appear not to be out of range. The problem is that it doesn't even exist without first calculating that far out of reach tablebase mentioned above.

For most facts, see Checkers is solved

tygxc

@4069

"For basic chess, (10^44)^0.6 = 2.5e26"
++ Chess has more ways to create nonsense positions than Checkers.
This is where the 10^44 legal positions stem from:
https://github.com/tromp/ChessPositionRanking

The 3 diagrams there represent randomly sampled legal positions.
Position 1 has 7 white rooks, so at least 5 underpromoted and 2 black dark square bishops, so at least one underpromoted. The only reason to underpromote to a rook or bishop is to avoid stalemate, i.e. avoid a draw. It is not sensible for both sides to avoid a draw, so at least one side must have made a mistake by underpromoting. So this position is not sensible.
Position 2: 4 white rooks, 2 black dark square bishops, not sensible.
Position 3: 4 white rooks, 3 black rooks, not sensible.

That is why 10^37 is a better figure
https://arxiv.org/pdf/2112.09386.pdf 

This does not include positions with 3 or 4 queens, which do occur.
So multiply 10^37 by 10 to include such positions: 10^38.

Now from a sample of 1000 positions included in the 10^37 observe that the vast majority of these by similar but more complicated arguments can only result from a game with errors too.
Tromp conjectured only 1 in 10^6 can result from a real reasonable game. That leaves 10^32 positions.

Now observe, that each pawn move and each capture render huge numbers of positions unreachable during the solving process. Let us assume we use a dedicated engine to look at 1 e4 only and investigates if 1...e5 draws for black. That engine never has to look at any position with a pawn on e2 or a pawn on e7.

The fact that we only have a 7-men endgame table base and that Checkers used a 10-men endgame table base makes no big difference. From table 3 of the above reference is clear that most chess positions are around 26 men.

Now apply the exponent 0.6 to 10^32 to reflect these numbers of positions unreachable during the solving process.

Now observe, that many legal, sensible positions reachable during the solving process are not relevant. 1 e4 e5 2 Ba6 is not relevant, does not try to win, is a sure loss, checkmate in 82. None of these positions leading from 1 e4 e5 2 Ba6 to checkmate is relevant and the engine does not need to burn time on it.

Also observe, that many positions are clear draws.
The final position of
https://www.iccf.com/game?id=1164259
is a clear draw. If the engine continues to calculate, it will eventually reach a 3-fold repetition draw, but none of the resulting positions is relevant.

Also note that weakly solving only calls for a strategy: 1 strategy. If it is proven that 1 e4 e5 is a draw, then it is not relevant if 1 e4 c5 draws as well or not, so the resulting Dragon, Najdorf, Sveshnikov etc. positions are not relevant.

That leaves 10^17 legal, sensible, reachable during solving, and relevant positions.

Weakly solving Losing Chess even only took 10^9 positions not 10^44 or 10^26.

 

lfPatriotGames
tygxc wrote:

@4034

"Why 5 years if the starting point is some unknown future time?"
++ How long does it take to build a house? When does that period start?
The starting point is when the money is there.
The work cannot start before the assistants and computers are there to start it.

"So it sounds like this Sveshnikov character is saying chess will be solved in 5 years."
++ Read again:

'Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess.' - GM Sveshnikov (+)

The 'give me' expresses the necessity of the assistants and computers as a prerequisite.
The 'good assistants' imply human assistance being essential. He even names them first.
The 'lastest computers' implies that they already exist.

You do not seem to know him
https://en.wikipedia.org/wiki/Evgeny_Sveshnikov 
https://www.chess.com/news/view/evgeny-sveshnikov-1950-2021 

This still makes absolutely no sense. Even if we assume the only problem with solving chess is money, and as soon as the money is available, it will take 5 years, that still makes the 5 year claim a steaming pile of road apples. 

So to answer your question, it takes about 9 months to build a house. Of course it could take a lot longer or a lot less, but that's about average. And you start building when the permits are secured, which is a lot more important than the money. The money part can change, drastically, with the economy and price fluctuations. So you don't have to have  the money to start, but you do have to have the money to finish. 

So you are STILL saying the 5 year period for solving chess starts when there is the money. Well, when is that? It could very well be no amount of money will matter, but even if it did, what if there isn't enough money for 300 years? I don't see the point in saying chess can be solved in 5 years if nobody has any idea when the 5 year period starts. 

stancco

Money? Don't make me laugh.

It takes an angel only, one who doesn't side satan's side, of course. That one lies.

Elroch
Optimissed wrote:

Of course, <<<<Also note that weakly solving only calls for a strategy: 1 strategy. If it is proven that 1 e4 e5 is a draw, then it is not relevant if 1 e4 c5 draws as well or not, so the resulting Dragon, Najdorf, Sveshnikov etc. positions are not relevant.>>>>

has completely lost me. It would very much depend on which side was trying to achieve a draw. If white is playing for a draw, it still may not influence white's opening move, since white may find a draw easier to obtain after 1. d4, even if 1. d4 were to win theoretically for black. If black wants a win. then black would play the Sicilian. It's such comments which made me suspect dementia.

You are right. If 1.e4 e5 is a draw it says nothing about whether either side has a winning strategy. For example, it does not prove that 1. e4 c5 doesn't win for black. Likewise, it does not prove that 1. c4 does not win for white.

If you are confident that chess is a draw and focus only on proving that this is so, and you have proven that 1. e4 e5 is a draw, you still need to prove that white can draw against 1. e4 c5, and that black can draw against 1. c4 (just as with the more open-minded viewpoint).

tygxc

@4078

"it does not prove that 1. e4 c5 doesn't win for black."
++ If 1 e4 c5 is a black win, then 1 c4 is likely to be a white win.
Moreover if 1 e4 c5 is a black win, then by strategy stealing 1 c3 e5 2 c4 is a white win.

"it does not prove that 1. c4 does not win for white."
++ 'From the outset two moves, 1.e4 or 1.d4, open up lines for the Queen and a Bishop. Therefore, theoretically one of these two moves must be the best, as no other first move accomplishes so much.' - Capablanca
This was corroborated independently by AlphaZero, with no other input but the Laws of Chess
Figure 31 https://arxiv.org/pdf/2111.09259.pdf 

To be sure 4 moves need investigation: 1 e4, 1 d4, 1 c4, 1 Nf3.

The possibilities that chess is a white win or chess is a black win go against expert opinions and empirical evidence from ICCF, TCEC, AlphaZero, human GM games.

There is also a deductive argument. To win a game of chess a direct assault on a king is only possible if the opponent neglects its defence. To win a game of chess involves queening a pawn. 'Any material advantage is enough to win' - Capablanca. In the initial position material is equal, but white is a tempo up. 1 pawn = 3 tempi. You cannot queen a tempo.

Suppose that a tempo were enough to win a pawn. Then it would be advantageous to play a gambit where white sacrifices a pawn to win 2 tempi, then convert the 2 tempi to 2 pawns, and then queen the extra pawn.

tygxc

@4076

"So you are STILL saying the 5 year period for solving chess starts when there is the money.
Well, when is that?"
++ I do not know. Chess can be solved in 5 years. If chess will be solved depends on somebody spending 3 millions to hire 3 grandmasters and rent 3 cloud engines for 5 years.

In 1961 President John F. Kennedy persuaded congress to put up money to set men on the Moon. In 1969 Armstrong walked on the Moon.
It took 8 years to put men on the Moon, but it depended on the money.

tygxc

Conclusion: chess can be weakly solved in 5 years,
but when or if depends on money to hire the grandmasters and rent the computers.

Elroch

The problem is the lack of people willing to spend $3 million to ask the question "is chess a draw?" and to get the answer 5 years later "we are now slightly more confident that it is but, in all frankness, didn't have a snowball's chance in hell of proving it. Thanks for the cash."

I feel there are slightly more attractive investments.

DiogenesDue
tygxc wrote:

Conclusion: chess can be weakly solved in 5 years,
but when or if depends on money to hire the grandmasters and rent the computers.

There is no such conclusion.

lfPatriotGames
tygxc wrote:

Conclusion: chess can be weakly solved in 5 years,
but when or if depends on money to hire the grandmasters and rent the computers.

I actually agree with that. Since you said the start of that 5 year period begins when the resources become available. I think you gave a housing analogy, which is also for the most part true. You have to have the money and resources (but most importantly permits) before beginning the 9 month period to build a house. So for a house that 9 month period may not start until 40 years from now. But it still takes 9 months to build the house.

And for chess, I agree, it could only take 5 years to solve. If the starting point is when resources become available. Which is probably at least 200 years from now. But even then my guess is it wont be solved, it will just be a more refined speculation. 

lfPatriotGames
Optimissed wrote:


It can't possibly be solved in 5 years. This has been proven by argument, since no proper argument has been given, nor will be given, to show that a solution will ever be possible. As for achieving it in five years from any point in the foreseeable future, we can reasonably say that current understanding shows it to be impossible.

It isn't really a debate, since we don't have the tools to achieve it. It's nothing to do with money, because resources which don't exist would be necessary.

Yes. So we can only guess at when the 5 year point would start. I say at least 200 years, probably at least 300 years from now. For the reason you said, it would take resources that don't exist right now. 

But no matter when it starts, there will be a lot of PatriotGames posterity telling Optimissed posterity "told ya so". 

lfPatriotGames

Well 5 years, starting now, 2 years ago, or even 5 years from now does seem a little unreasonable. 

Yoyostrng

Maybe my logic is flawed, but I would think that if tik tak toe can be solved then so can chess. 🤔

tygxc

@4073
"I feel there are slightly more attractive investments."
++ Of course solving Chess is not an attractive investment.
Solving Checkers or Losing Chess did not give any return on investment either.
Sending men to the Moon did not give real payback either.
Sending humans to Mars will not give payback either.

"ask the question "is chess a draw?"
++ No, that is not the question.
In the pre-engine are chess games were adjourned after move 40 and resumed next day after overnight analysis. The players tried to answer 2 questions:
1) Is the position a draw, a win, or a loss?
2) How?

Ultra-weakly solving chess is answering question 1) for the initial position.
Weakly solving chess is answering question 2) for the initial position.

White tries to win, black tries to draw.
White fails, black succeeds
Then Chess is weakly solved.

tygxc

@4075
"If the starting point is when resources become available."
++ The engines exist that calculate a billion positions per second. They cost money to rent.

"Which is probably at least 200 years from now."
++ We do not know when somebody opens his wallet. It might as well be tomorrow.

"But even then my guess is it wont be solved"
++ If the engine exhausts the 100 million billion legal, sensible, reachable, relevant positions then chess is weakly solved, then it is proven just like Checkers or Losing Chess, no speculation. We will then know for sure how black can draw.