Chess will never be solved, here's why

@8692

"And every theorem in the mathematical sciences (including computer science and game theory) has NO uncertainty."
++ Many have, like Shannon's theorem, the Uncertainty principle and many more.

@8675

"these engines are just reallly strong"
++ ICCF (grand)master + engines at average 5 days/move
are much stronger than engines running unjockeyed,
and these are much stronger than the strongest humans at 3 minutes/move.

As for the latter, consider the 2024 Toronto Candidates' Tournament.
Out of 56 games there were 25 decisive games.
Fitting a Poisson distribution of the errors/game leads to a distribution:

• 0 error: 18 games
• 1 error: 21 games
• 2 errors: 12 games
• 3 errors: 4 games
• 4 errors: 1 game
  The average is 1.1 error/game.

But why are you fitting a Poisson distribution in particular?

You also have a choice of fitting a Bernoulli distribution, a Rademacher distribution, a beta-binomial distribution, a degenerate distribution, a discrete uniform distribution, a hypergeometric distribution, a negative hypergeometric distribution, a Fisher's noncentral hypergeometric distribution, a Wallenius' noncentral hypergeometric distribution, a soliton distribution. a power-law distribution, a Zipf distribution, a beta negative binomial distribution, a Boltzmann distribution, a Gibbs distribution, a Maxwell–Boltzmann distribution, a Borel distribution, a discrete phase-type distribution, an extended negative binomial distribution, a Gauss–Kuzmin distribution, a geometric distribution, a Hermite distribution, a logarithmic (series) distribution, a mixed Poisson distribution, a negative binomial distribution, a discrete compound Poisson distribution, a parabolic fractal distribution, a displaced Poisson distribution, a Conway–Maxwell–Poisson distribution, a zero-truncated Poisson distribution, a Polya–Eggenberger distribution, a Skellam distribution, a skew elliptical distribution, a Yule–Simon distribution, a zeta distribution, a Hardy distribution, a Beta distribution, a four-parameter Beta distribution, an arcsine distribution, a PERT distribution, a uniform distribution, an Irwin–Hall distribution, a Bates distribution, a logit-normal distribution, a Kent distribution, a Kumaraswamy distribution, a logit metalog distribution, a Marchenko–Pastur distribution, a bounded quantile-parameterized distribution, a raised cosine distribution, a reciprocal distribution, a triangular distribution, a trapezoidal distribution, a truncated normal distribution, a U-quadratic distribution, a von Mises–Fisher distribution, a Bingham distribution, a Wigner semicircle distribution, a continuous Bernoulli distribution, a Henyey–Greenstein phase function, a Mie phase function, a von Mises distribution, a wrapped normal distribution, a wrapped exponential distribution, a wrapped Lévy distribution, a wrapped Cauchy distribution, a wrapped Laplace distribution, a wrapped asymmetric Laplace distribution, a Dirac comb of period 2π, a Beta prime distribution, a chi distribution, a noncentral chi distribution, a chi-squared distribution, an inverse-chi-squared distribution, a noncentral chi-squared distribution, a scaled inverse chi-squared distribution, a Dagum distribution, an exponential distribution, an exponential-logarithmic distribution, an F-distribution, a noncentral F-distribution, a folded normal distribution, a Fréchet distribution, a Gamma distribution, an Erlang distribution, an inverse-gamma distribution, a generalized gamma distribution, a generalized Pareto distribution, a Gamma/Gompertz distribution, a Gompertz distribution, a half-normal distribution, a Hotelling's T-squared distribution, an inverse Gaussian distribution, a Lévy distribution, a log-Cauchy distribution, a log-Laplace distribution, a log-logistic distribution, a log-metalog distribution, a log-normal distribution, a Lomax distribution, a Mittag-Leffler distribution, a Nakagami distribution, a Pareto distribution, a Pearson Type III distribution, a phase-type distribution, a phased bi-exponential distribution, a phased bi-Weibull distribution, a semi-bounded quantile-parameterized distribution, a Rayleigh distribution, a Rayleigh mixture distribution, a Rice distribution, a shifted Gompertz distribution, a type-2 Gumbel distribution, a Weibull distribution, a modified half-normal distribution, a Polya-Gamma distribution, a modified Polya-gamma distribution, a Behrens–Fisher distribution, a Cauchy distribution, a centralized inverse-Fano distribution, a Chernoff's distribution, an exponentially modified Gaussian distribution, an expectile distribution, a Fisher–Tippet extreme value distribution, a Fisher's z-distribution, a skewed generalized t distribution, a gamma-difference distribution, a generalized logistic distribution, a generalized normal distribution, a geometric stable distribution, a Gumbel distribution, a Holtsmark distribution, a hyperbolic distribution, a hyperbolic secant distribution, a Johnson SU distribution, a Landau distribution, a Laplace distribution, a Lévy skew alpha-stable distribution, a Linnik distribution, a logistic distribution, a map-Airy distribution, a metalog distribution, a normal distribution, a normal-exponential-gamma distribution, a normal-inverse Gaussian distribution, a Pearson Type IV distribution, a Quantile-parameterized distribution, a skew normal distribution, a Student's t-distribution, a noncentral t-distribution, a skew t distribution, a Champernowne distribution, a type-1 Gumbel distribution, a Tracy–Widom distribution, a Voigt distribution, a Chen distribution, a Magnum Extra Large Size Silicone Lubricated Condom, and a host of other things that would be equally likely to impress the uninformed.

In fact, given that it's a chess site, something like Fisher's z-distribution might be more persuasive to your intended audience.

The problem with quoting a Poisson distribution is that the first sentence in the link you give for it is 

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event.

Not only is that a patently stupid assumption (even to the uninformed) to make of the moves by either player in a chess game, but if you do assume that the moves have an independent fixed probabilty of losing half a point it's easy to prove that chess is a Black win. (The game shown is valid in FIDE basic and competition rules and ICCF chess.)

But it's also obvious that choosing a different game that ends in a provable White win in the link would prove that chess is a White win from the same assumption. Which proves the assumption false, because both cannot be true.

Given that ICCF (grand)master + engines at 5 days / move >> human at 3 min / move
this makes it plausible that 106 draws out of 106 games indeed means 0 error / drawn game,
i.e. an error distribution of 106 - 0 - 0 - 0.

@8695

"computers will continue to draw in the future" ++ ICCF is not computers, it is a human with computers. Here is an interview with the reigning ICCF World Champion ICCF GM Jon Edwards. It gives some insight in how ICCF correspondence chess is now played at top level and what is the role of the human and his computers.

That makes no difference. Equally matched humans draw in exactly the same way as computers when they're out of their depth. I've posted you many examples of that using Stockfish and you've posted us many examples with Stockfish+human.

"chess being a draw" ++ Yes

"the ICCF doesnt change it" ++ It does: it shows how to draw.
It also shows there are several ways to draw.

I can show you much quicker ways, but none are relevant to the topic of the thread.

@8693

"I could draw again a gm anyday" ++ You are rated < 2000 chess.com...

@8696

....

"you still havent given your math education" ++ More than any here and much more than you.

@8696

"proof is direct deduction using only axioms" ++ No. Inductive proofs are valid too.

Here you reveal you are not aware there are two unconnected uses of the word "induction".

Mathematical induction is a form of deduction that has no connection with inductive reasoning which never constitutes a proof.

I understand that some people have difficulty coping with the fact that a word can be used in two unconnected ways, but that does not affect the relevance of this.

Note that mathematical induction ALWAYS reaches a definite conclusion without uncertainty (like all deductive proofs) and inductive reasoning NEVER reaches a definite conclusion - it always has uncertainty. While mathematical induction is a form of proof, inductive reasoning is about forming an uncertain belief about a population based on an incomplete sample of its members.

This alone is enough to see that not only are the concepts different, they do not even overlap.

"you still havent given your math education" ++ More than any here and much more than you.

Now you need to fill in the gap in your education that meant I had to explain the above.

@8711

"There is no evidence that Stockfish 16 "assisted" by Jon Edwards can beat Stockfish 16 on its own." ++ There is: he qualified for the World Championship Finals, defeating other candidates with Stockfish, maybe some who are stupid enough to just play what Stockfish indicated.

Second, you cannot go below zero error per game.