Chess will never be solved, here's why

Re: Ba6?! is a win for black.

Is there a good reference for this? It's hard to search 329 pages.

As to other solved games reaffirming conventional wisdom about said games, sure, that's exactly what you would expect... most of the time.

But surely it is possible to conceive of (or perhaps even construct) a game where this does not hold true. One where a deep enough exhaustive search of a conventionally weak opening will reveal some tactical advantage to that opening that is not otherwise apparent and actually allows for player 1 to win when otherwise the game is a draw from all of the conventionally good openings with perfect play.

So the question is, do we know that chess is not such a game, or do we think that chess is not such a game? I would say we think it's not such a game, but that we do not actually know. As such a game wouldn't necessarily produce evidence that the optimal line was not reachable by gradient descent on some heuristic evaluation but involved very deep tactical play.

Ok but someone in this thread was saying there's a forced line of 52 moves. That bishop odds is a huge advantage is categorically different from saying we have proof that it's a win in however many moves at most.

This is an unfortunate example of ego inverting the correct comparison.

People who have a profound understanding of uncertainty, based on a large amount of experience of simpler examples where the probabilities are not so extreme can see that the nature of the evidence involved and the reasoning available means that we cannot justify CERTAINTY about this result. The epistemiologically correct state of belief is that of slight uncertainty.

The error that the proverbial "man in the street" would surely make is one that is pragmatically fine for all normal purposes. This is to treat all small probabilities as zero. It's perfectly reasonable to (literally) bet your life on something with very low probability not happening. But some of us understand that it is quantitatively enormously wrong (in a way that those familiar how to quantify how wrong a belief is can see).

To illustrate that last point, suppose someone takes the view that an event that happens 1 in a trillion times is literally impossible. This would imply that they would be willing to stake an unlimited amount against any return on this being so. And they would be willing to do this an unlimited number of times. That is what certainty means quantitatively.

Suppose in this case they happen to have the power to bet a trillion dollars on the event for a return of 1 cent when they are proven right. A great bet, to this person.

Unfortunately, there are plenty of examples of events more unlikely than this that happen all the time in the quantum world. It's just a matter of numbers. So this person would lose trillions after trillions by treating a low probability as zero.

I feel a non-lazy person should be able to understand the above.

I will separate the part of my attempt at enlightenment that deals explicitly with the specific chess example for clarity.

The key is to recognise the nature of the evidence for the belief and the reasoning that leads to it.

The nature of the evidence is examples of possible chess play from the position. But not an exhaustive calculation, like that necessary to verify a chess problem. It's the sort of thing Sveshnikov imagined - good old fashioned chess analysis, incomplete but enough for high confidence.   In addition, there is weaker evidence from a large number of not so closely related positions with real play, where a material advantage leads to a win.

All of the reasoning from this evidence to the specific question - does a specific lousy opening position lose? - is INDUCTIVE.  For example, suppose you find a line with what appears to be sensible moves by each player to a finish and one side wins, this is weak evidence the position is winning. It is not actually more certain in itself than a game from 1. d4 winning for black with moves we thought were sensible is to support the view that 1. d4 loses.

Every additional step of inductive reasoning increases confidence in the result. But the distance between probability p> 0 and probability 0 is infinite on a logarithmic scale, and this is related to the fact that inductive reasoning steps never turn uncertainty into certainty. All they can do is reduce the uncertainty by a finite amount.

It's a really good bet that a lousy position that we cannot exhaustively analyse is losing, but it is not IMPOSSIBLE that it is not, just very unlikely (a phrase which incorporates an infinite range of levels of confidence short of certainty.

It's only really the somewhat more intuitively difficult nature of quantifying belief that makes this non-trivial. It's really no more complicated than the idea that you can never get to infinity by a finite number of steps of multiplying finite numbers together. This is true even when the numbers are really very big!

Regarding @Optimissed's reference to engines, they are of no significance to the key point. The recognition that inductive reasoning does not lead to certainty, and the quantification of belief by Bayesian probability (and the proof that this is in a definable sense the only consistent way to quantify belief) predates chess computers. All chess computers can do is exploratory analysis - where this is exhaustive it has analogous significance as an exhaustive analysis by a human (or a proof engine for mathematical theorems), and where it is not exhaustive it has analogous significance to the same by a human, and is merely inductive evidence.

Please don't advertise here.

Forget about the ego bit, which merely obstructs your self-improvement.

Mathematics is what is used to represent quantitative knowledge about the real world. This is the case for all of the models of physics. It is also true for, say, informational theory and computer science, which are comfortably included in the broad subject of mathematics as they deal with abstractions that are perfect for dealing with the underlying nature of many applications. It is also true of the quantification of belief - this just happens to be less familiar to many people.

"it loses. It doesn't probably lose"

There are two senses a position can lose, empirically and analytically.

Empirically, Ba6 loses (or... probably loses? it's the same thing). You could run billions of high level engine games and you probably wouldn't even get one draw. The reason anyone wins or draws with Ba6 is if their opponent makes serious blunders. Mostly at very low ELO.

Analytically, we don't know. Nobody has convincingly solved chess for Ba6. No amount of empirical evidence will show that Ba6 is losing unless it constitutes an exhaustive search. In all likelihood it is losing. But we do not have certainty either way.

Given the title of the thread is about solving chess, the context here is that we are talking about whether a position is an analytical loss, and not an empirical one.

@6559

"The first move advantage is enough to force a win."
++ No, it is not. You cannot queen a tempo.
The first move advantage diminishes with each move made. Engine-wise it starts at +0.33 reflecting the extra tempo and then gradually evaporates to 0.00.
A tempo is not enough to win. A pawn is. A bishop is.
It is curious that some people refuse to accept that a tempo is not enough to win,
and some people refuse to accept that a pawn, or a bishop is enough to win.

"some forced checkmates are many hundreds of moves long"
++ Yes, but those positions where there is such a forced checkmate cannot be reached from the initial position by optimal play from both sides.
In ICCF players are allowed to claim a 7-men table base win that exceeds 50 moves without pawn move or capture. Such claims never occur. No 7-men table base win claims occur at all, all decided games are by resignation after a human error. 22% of draws are by 7-men endgame table base draw claims.
All ICCF games are over long before the 50-moves rule would be triggered, the longest game was a draw in 119 moves. 50-moves draw claims do not occur in ICCF.

@6581

"There are two senses a position can lose, empirically and analytically."
++ We are only concerned about analytically here in this context of game solving.
From the AlphaZero paper we know that 1 g4? is the worst of the 20 possible moves.
Empirically white wins 29%, draws 22% and loses 48%.
The late IM Basman played it with success at IM level.
Analytically 1 g4? loses by force.

Steinitz "knew" he could give God pawn and move and still win.

Do you know what "loses by force" means? I don't think you do.

@6586
I know, you do not. I provided analysis.
Try to find an improvement for white. You will fail.

Oh, so you analyzed 1.g4 to a forced loss...

I haven't been following this topic so I didn't realize this line of argument would bring up more of your "proofs." I'll just quietly go away now.

It is very likely that 1. e4 e5 2. Ba6 loses by force. It is not impossible that it does not.

Some people have difficulty understanding very low probability possibilities when they are more than trivial.

For example, I would say you would understand that tossing N fair coins and getting N heads is possible for any number N. When N is, say 1,000,000, this probability is so tiny that it is for all practical purposes zero. But it is still a small positive number and anyone who claimed it was impossible to have a million heads from a million coin tosses (or that the probability of this event is zero) is easily refuted.

If you were to study the process of Bayesian inference, and to understand that inductive learning cannot do better than this the fact that an inductive conclusion never reaches certainty would be as obvious as that N heads has a strictly positive probability.

Hello

@6590
"understanding very low probability possibilities"
++ There are no probabilities, this is deterministic. A position is either drawn, won, or lost.

Sigh.

Any unfamiliar position has a deterministic result. Your faulty reasoning implies that this means the only belief states about it are certainty about one of the possible results.

Your reasoning is (obviously) wrong.

@6593

1 e4 e5 2 Ba6? loses by force for white. That is not 'very likely', there are no coin flips involved.
1 g4? loses by force for white. Anybody who doubts that, find an improvement for white @6584.
The initial position is a draw. Evidence has been provided above,  inductively from ICCF and deductively from 1 pawn = 3 tempi, and 1 pawn needed to queen.
Those are facts we know.

I do not know if 1 e4 c5 draws as well as 1 e4 e5. Probably both draw.
I cannot put a percentage on it. They either draw or not.
I do not know if 1 e4 e6 or 1 e4 c6 draw or not, probably not.
I cannot put a percentage on it. They either draw or not.
I do not know if 1 f3 loses for white or not, probably not.
I cannot put a percentage on it. It either loses or not.