Chess solved?

[mwyoung]

You do not need to guess about future speed. There is a limit to how fast you can make a computer. Using Moore's law that limit will be reached in 75 years. Just use the theoretical limit.

Moore's law is not about the speed of computers. Koomey's Law is not either but it's more relevant, since as was mentioned, the power use matters most at our current technological level.

I will not argue every point with you. Just use the theoretical limit.

Moore's Law states that we can expect the speed and capability of our computers to increase every couple of years...
And by then the computers will be almost free.

[mwyoung]

One method that seems interesting to me is an AND/OR proof search using move generators on an array of GPUs using the internet.
Since you only need to know won/lost/drawn and a move generator can tell you all three of those things, you do not even need an eval function.
Ankan has already written an obscenely fast move generator:
https://github.com/ankan-ban/perft_gpu
Imagine if you had a million GPUs cooperating in an AND/OR proof search.
Sounds like a lot but I imagine it is less than 1/1000th of the GPUs on the planet, and the quality of the GPUs continues to rise exponentially.
A cooperative effort might say that Chess is a mate in 3,827 for white. Or some other such interesting nonsense.
Of course, we would want some way to record the solution. That is the hard part.

Interesting! Looks as though a single GPU can get 10^9 positions per second. With a million of them, and assuming "perfect efficiency", that would be 10^9 * 10^6 = 10^15 positions per second. If white does have a forced win, that might be enough - but if, as seems likely, chess is a draw, surely you won't be able to prove that? The chess tree is just too big.

31,622,400,000,000,000,000,000 Position per year

3.1623153207852661404573972879984e+97 Years for your computer to solve chess to the lower bound.

Age of the Universe
13.787±0.020 billion years

I will not be waiting for your results...

[Dann Corbit]

You do not need to guess about future speed. There is a limit to how fast you can make a computer. Using Moore's law that limit will be reached in 75 years. Just use the theoretical limit.

Moore's law is not about the speed of computers. Koomey's Law is not either but it's more relevant, since as was mentioned, the power use matters most at our current technological level.

I get several letters a month from the power company with graphs.
See this little bar? That's your energy saving neighbors.
See this medium sized bar? That's the average customer.
See this gigantic, hog-sized bar? That's you.
Do you want us to show you have to save electricity?

[Dann Corbit]

I don't know how to tell them, "My house is a place where we turn electricity into chess."
I am not sure they would understand, even if I explained it very carefully

[mwyoung]

I don't know how to tell them, "My house is a place where we turn electricity into chess."
I am not sure they would understand, even if I explained it very carefully

WIth all this Covid chaos. I needed a good laugh. I relate. THANK YOU!

I can not even explain it to my wife and kids.....

[Angrim]

Imagine if you had a million GPUs cooperating in an AND/OR proof search.

You could generate 1 million openings from the starting position for which evals of SF, LC0, and Komodo are between -1 and 1 at the leaf nodes. Choose a few at random and try to solve them using this method. If you can solve them all, it would be worth it to investigate further. My guess is that even at 1 trillion openings, it won't be possible.

I think that starting with balanced positions would give few(if any) solutions, but to really see how hard it is, try solving early game positions that are between -4 and -5 according to strong engines. I expect that it will be rare and difficult to prove a win even in these positions that we are fairly sure that there is a win to be proven.
I have wasted a fair amount of cpu time trying to prove that giving queen odds is a forced loss.

[Dann Corbit]

According to my calculations, once you have an advantage of 444 centipanwns or more, you are almost certainly going to win.
It might be hard to prove it, but I guess new technology will make it easier in about 5 years

[duncan]

I have wasted a fair amount of cpu time trying to prove that giving queen odds is a forced loss.

So what can you prove is a forced loss, Queen + rook, Queen + 2 rooks ?

[duncan]

Does Stockfish 12 evaluate opening position differently than Stockfish 11?

[syzygy]

I accept that there's no hard proof that solving chess like algebra is possible, but I think that the balance of evidence is that it can be: people have written theorem proving software, so why wouldn't chess theorem proving software be possible?

Do you believe chess to be special, or do you believe that any two-player zero-sum game with full information can be solved "like algebra"? After all, all the evidence you have is based on games that are totally unrelated to chess.

(As discussed earlier, it is trivially true that chess has a solution and that an algorithm exists to find it. Apparently "like algebra" means that constructing, storing and verifying the proof can be done with limited computational resources, let's say one year of a TOP 10 super computer.)