Chess will never be solved, here's why

‘Would you say that a ticket in a 1 in a quadrillion lottery could not win? If you answer that it could not, you need a refresher in epistemiology.’

this analogy is faulty because in the lottery, the possibility of winning is slim yet absolute, while the possibility of white winning or even drawing after blundering its bishop is absurd. or iow, the possibility may not exist at all.

That's true

Show us against SF16.1.

(If you win as Black I can post you an example that doesn't - two if you like.)

express what as a probability? the possibility or our state of knowledge about it?

you make no sense. i’m talking solely about the possibility.

The probability about our state of knowledge about it is know:0 don't know:1.

But re making no sense, I can show you that not winning as Black after 2.a6 is definitely possible. You seemed to claim otherwise.

maybe i wasn’t clear enough, so i asked gpt to rephrase..

Probability vs. Possibility:
• Lottery: In a lottery with odds of 1 in a quadrillion, each ticket still has a non-zero probability of winning. The event of winning, while highly unlikely, is still within the realm of possibility.
• Chess Game: When White blunders a bishop, the chances of White winning or even drawing can be effectively zero if the blunder is decisive and assuming perfect play from the opponent. The possibility of White winning may not exist at all if the position is completely lost.

All Black has to do is resign, so the possibility obviously exists.

If you're asking if Black has a forced mate then it can be a matter of probability if the timeout rules, for example, are in force.

interesting. please show me..

are you being funny?

Not very.

He's never done this. do you have reading comprehension isseus?

" 1 e4 e5 2 Ba6? is a white loss, ultra-weakly solved."

objectively false.

a mathematical solution requires the game tree or formal proof.

you obviously dont have the game tree, so where's the proof?

tygxc why do you continue to cite definitions that you have no understanding of?

And shouldnt you take the fact that everyone else could understand what elroch was saying while you couldnt as a sign of your own incompetence? not understanding the arguments made by others is literally the first sign that you don't know what you are talking about.

Thanks for this observation (which resembles one by @tygxc where he justified his conclusion about the optimal result of chess by saying that was a definite thing with no uncertainty in it. But clearly his thinking was wrong - the fact that a theorem is definitely either true or false does not excuse lack of rigor in a proof).

I hope I can clarify this point by drawing attention to the Bayesian viewpoint. It can be proven that Bayesian probability theory is the only consistent way to quantiify BELIEF about propositions (given some very mild assumptions based on how beliefs need to behave). Not everyone will be familiar with this application of probability theory, which is separate to the more familiar one that has the much narrower scope of "repeatable random events")

In the case of the lottery ticket, viewed from the future, whether the ticket is a winner or not is a definite thing with no uncertainty. But in the past, whether it won was uncertain. The appropriate belief state in the past was one embodying the 1 in a quadrillion chance of winning.

Likewise, for the optimal value of chess, despite what people who inappropriately conflate strong confidence based on empirical evidence and inductive reasoning with certainty say, at the moment the appropriate belief state is an uncertain one. Exactly what probabilities you allocate to a black or white win is a matter of subjective modelling (just like the probability one would allocate to a given very large number being prime, for example), but the probabilities for all three results should be non-zero. With most of the probability on a draw, IMHO!

Likewise for the position 1. e4 e5 2. Ba6, until this position is solved. It may seem absurd to suggest that we don't even know that white is not winning - this is very unlikely - but my logical self demands that I allocate this possibility some tiny probability (for the specific reason that my logical self CANNOT deduce the opposite, and nothing can be truly certain without being deduced. Of course, no-one is ever going to have a problem ignoring really tiny probabilities - in a lifetime it is the difference between zero and tiny is unlikely to have any effect, but the philosophical difference is huge.

Intuitively, it may help to think in terms of log odds. The reason is that the log odds scale extends from -infinity to +infinity, with certain falsehood (0 on the probability scale) being minus infinity on the log odds scale and certain truth (1 on the probability scale) being plus infinity on the log odds scale. I feel this better indicates the very big difference between certainty and high confidence. Big numbers are not infinity!

AIs and neutral networks in general typically work with log odds as raw output (or something similar when there are more than 2 possibilities).

i didn’t say that white lose by force. just think of it for a moment. for you it should be a brief to recognize the subtle nuance. not sure about some others..

@Sillver1, I see now you asked the question that I have just tried to answer (whether rhetorical or not, I can't be sure!).

The thing which we express as a probability is our belief state. That is what Bayesian probability is about.

‘Thanks for this observation’

you welcome.