Chess solved?

[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

What calculations are these? It sounds like you've just made a statistical observation, which just forms a rule of thumb.

I used a parabolic curve fit of wins, losses and draws to form points from actual data.
Obviously, there are extremely rare reversals larger than 444 centipawns.
That is why I said "almost certainly".
Howerver, I suspect that with perfect play, that size of an advantage would not be reversible.
So not even a rule of thumb. More of a hunch.

[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

Alternatively, you could place your computers all over your house, so that they substitute regular heating. Electricity based heating is inefficient, so the graph would be quite normal then. Granted, you lose a few months in summer, but at least you got them off your back.

I used to put them downstairs for that reason.
And my industrial computers are shut down for the summer.
Today's notice:

[syzygy]

As for the polynomials, from what you write you seem to be thinking of fitting a polynomial evaluation function to a number of "solved" positions and hoping that the resulting function will give meaningful values for all positions. And it seems the polynomial evaluation function will have to be constructed by trial and error.

How do you want to formally verify that a particular polynomial evluation function that you have constructed indeed does give the correct value for all positions? Perhaps by testing it on a million positions (comparing their polynomial evaluation with SF's evaluation?) and then arguing that the evidence suggests that you have found the solution to chess?

Well, how to 'solve' chess via an evaluation function?

We tried the computation method of splitting the chess position into features, applying weights and adding them up. Works up to a point but nowhere near solving (without AB and a lot of time).

We tried a lookup function, but didn't yet get beyond 7 or 8 pieces, because the address space is impossibly large.

We tried a mix of a lookup and a computation, neural network, which can be seen as stacked layers of spreadsheets, or stacked polynomials, and we were quite surprised when this gave ply one 'lookup' results which can arguably be seen as approaching GM strength, or arguably may approach GM strength given a few years.

If we're prepared to overlook the inexact nature of NN output, it looks already that we managed to short-circuit the impossibly large address space and/or impossibly large search time by using/training stacked polynomials (at the cost of inexactitude). For some reason, towforce wants to reduce the stack to one layer and apply some sort of pre-processing of terms (psq) that finds the necessary non-linearities beforehand. he doesn't call it that, preferring a wide range of mixed word salads, 'Fitting polynomials to the multi-dimensional space of chess", or theorem proving, or finding emergent properties or whatever. Essentially, he's arguing to take the non-linearity finder of the hidden layers of an NN, work out how to apply those non-linearites to pre-process the inputs, et voila, add them all up in a weighted polynomial. Since 'Fitting polynomials to the multi-dimensional space of chess" is currently the function of the hidden layers of NN, with his 'polynomial' being the final layer, our best technology is already doing it, with, as we know, inexactitude being the price paid for shrinking the address space from impossibly large to tractable. His 'Fitting polynomials to the multi-dimensional space of chess" means essentially unravelling the hidden layers of the NN and still doesn't constitute a solve or "proof" of chess (inexact output result).

Exactly.

A near-perfect evaluation function would be great for building an engine but doesn't help much if the goal is to solve chess. You would still have to construct and verify a proof tree for chess, and it is pretty certain that verifying a minimal proof tree is still too big a task for current technology (even if you could use the evaluation function to pick the best move at each non-losing node).

[Ozymandias]

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

Alternatively, you could place your computers all over your house, so that they substitute regular heating. Electricity based heating is inefficient, so the graph would be quite normal then. Granted, you lose a few months in summer, but at least you got them off your back.

I used to put them downstairs for that reason.
And my industrial computers are shut down for the summer.
Today's notice:

My last bill was for 156kWh in 30 days, all computers off. In the worst of winter I barely do over half what you're showing there, although with Lc0 entering the fray, it'll be somewhat higher this time around. I'm guessing you don't stop completely come summer?

[towforce]

A near-perfect evaluation function would be great for building an engine but doesn't help much if the goal is to solve chess. You would still have to construct and verify a proof tree for chess, and it is pretty certain that verifying a minimal proof tree is still too big a task for current technology (even if you could use the evaluation function to pick the best move at each non-losing node).

* A near-perfect evaluation function would be a good outcome

* Can you prove that chess cannot be be solved without a proof tree?

[Dann Corbit]

My commercial systems have enormous power draw. One system has 4x1400 watt power supplies, and one has 4x1200 watts, for example.
Now, there is redundancy in the power supplies so we are not drawing 5600 and 4800 watts, but they do pull more power than my 3970x. I have several smaller systems that pull a few hundred watts and I don't turn them off. But the 64 amd 128 core commercial systems take a nap starting in July and come back on line in October.

The commercial systems are also very loud. You have to buy sound proof boxes for them to use them in a house (unless you were to build your own dedicated server room, which I am considering -- I would also want to wire the room for 220V and add special dedicated air conditioning).

[syzygy]

Since I see no reason to think that chess is special, I see no empirical evidence that supports the belief that chess can be solved with current technology (let alone "with polynomials").

I think you have "special" the wrong way around - "special" systems are the ones that don't have emergent patterns:

* most systems have emergent patterns

I'm sorry but "emergent' is just a meaningless term in this ill-defined context.

* most mathematical conjectures can be proved or disproved

Luckily we don't need to go into this statement, since it is absolutely certain that chess can be solved. We even know how to do it: just run mini-max or alpha-beta.

The question is how many computational steps and what kind of storage is needed to construct and verify a proof that chess is a (pick your preferred option) win for white/draw/win for black.

It is quite clear that your "polynomial evaluation function" is not going to be of any help here. Just like an NN-based evaluation function or a handcrafted evaluation function is not going to do the job.

But I get it, it would be surprising if you do not succeed...

[Dann Corbit]

A near-perfect evaluation function would be great for building an engine but doesn't help much if the goal is to solve chess. You would still have to construct and verify a proof tree for chess, and it is pretty certain that verifying a minimal proof tree is still too big a task for current technology (even if you could use the evaluation function to pick the best move at each non-losing node).

* A near-perfect evaluation function would be a good outcome

* Can you prove that chess cannot be be solved without a proof tree?

It is possible that the proof tree is not a worst case size. Suppose, for instance, from the root position there is a checkmate in 42 that nobody has ever found that is forced from the root position. Once the mate was verified, chess would be weakly solved.
Now, the chances of this happening are somewhere very, very close to zero, but the same idea could apply in less favorable circumstances.

[syzygy]

A near-perfect evaluation function would be great for building an engine but doesn't help much if the goal is to solve chess. You would still have to construct and verify a proof tree for chess, and it is pretty certain that verifying a minimal proof tree is still too big a task for current technology (even if you could use the evaluation function to pick the best move at each non-losing node).

* A near-perfect evaluation function would be a good outcome

* Can you prove that chess cannot be be solved without a proof tree?

I asked you what idea you have for doing what is commonly regarded as impossible. If you have no good idea to begin with, it is safe to dimiss your claims.

The only somewhat concrete idea I have so far been able to discern is constructing an evaluation function.

Since an evaluation function is not going to help much, I can conclude that you have no good idea to begin with, and I can dismiss your claims.

That ends it for me. I have better things to do. If you are still thinking that tic-tac-toe having been solved is "evidence" that chess can be solved with current technology, then what can I do more...

[towforce]

It is possible that the proof tree is not a worst case size. Suppose, for instance, from the root position there is a checkmate in 42 that nobody has ever found that is forced from the root position. Once the mate was verified, chess would be weakly solved.

Unfortunately, it is likely that the opposite is true - that it's not possible for either side to be able to force any material gain in the first 30 moves. Or any number of moves.