Chess will never be solved, here's why

slippery slope fallacy. cmon bro

tygxc making wild predictions that dont match reality as per usual.

the original question was to name even a single math proof class he'd taken, which he refused to do.

you assume the games are coin tosses to begin with lmfao thats such an obvious fallacy

@12576

"ESTIMATES reached are UNCERTAIN"
++ Monte Carlo methods allow to calculate nearly all mathematical problems e.g. calculate pi to any precision, no more or less than series expansions.
Labelle used a Monte Carlo method to calculate a lower bound of 10^29241 for the number of possible chess games.

No, they allow estimation WITH UNCERTAINTY. They do not prove anything. In fact the estimates for pi you describe would have a finite probability of being wrong even for the first digit (if we didn't know that digit was correct by actual calculations, such as Ramanujan's formula for pi. THIS is a calculation:

The thing that makes it so is being able to achieve any absolute bound on the error. Monte Carlo methods can achieve a given error with a given probability that is less than 1. That means a finite probability of any given error. For example, a Monte Carlo method can get an estimate for pi with a probability of 1e-12 that it is more than 0.1 wrong. Or a probability of 1e-24 that it is more than 0.1 wrong. But never a probability of 0 that it is more than 0.1 wrong.

That being said, I would respect a valid statistical result relating to the solution of chess. It would not be a solution, but it would be something. We have not seen a single such result: you keep repeating a result that is absurdly flawed.

wow, citing the use of an estimation function in an estimation, such proof of it being not just an estimation. wow tygxc. you're really convincing everybody.

id like to add that the equivalent statement to the chess games is only that it is likely that future iccf games are drawn.

you assign cause to WHY the games are drawn off of only claims that the games are likely to be drawn.

@12601

"they allow calculation WITH UNCERTAINTY"
++ So what. They answer questions and yield results. How many chess positions are legal?
(4.82 +- 0.03) * 10^44 that is certainly more useful than an agnostic 'we do not know'.

"They do not prove anything." ++ They can prove pi = 3.141592654... to any precision.

"a valid statistical result relating to the solution of chess"
++ These are facts: 116 games strongest chess on the planet, human + engines, 5 days/move
Conclusions:

1. Chess is a draw, confirming the white initiative, an advantage of +1 tempo = +1/3 pawn is not enough to win, also as each further move dilutes the advantage.
2. The 116 games are perfect games with optimal play by both sides.
   Certainty 1 - 1/117² = 99.992%.
3. The games are part of a weak solution of Chess. As they show not 1, but 5 different strategies to achieve the draw, even if a few (1-2-3) games had a pair of errors, error (?) + missed win (?), then these games could be removed and still a strategy to achieve the draw remains.

@12601

The Ramanujan series and other series sum up to infinity. Infinite Monte Carlo steps reach the same precision. I am not arguing that Monte Carlo methods are better or worse than other methods. I argue that Monte Carlo methods, which are inductive, are part of mathematics, and thus that mathematics are not confined to deduction.

strawman fallacy. nobody is claiming that estimation methods arent part of mathematics. the distinction is whether they count as mathematical proof, which as they are not direct deduction, do not count as mathematical proof.

literally first result on google btw

"A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion"

It seems that @tygxc does not understand the distinction between a Monte Carlo method and a calculation. In computer science, the latter is made precise by the concept of a computable number.

A computable number is one where there is an algorithm that gives the digits of its decimal expansion one by one, each one with absolute certainty. Ramanujan's formula can very easily be used to do this.

No Monte Carlo method can ever do this. In fact, if the first decimal place of the number is not certain before you start, it will never become so!

Based on recent posts, I infer this is one of those concepts forever beyond @tygxc.

[An explicit example would be the following Monte Carlo estimation of the value of pi. You have a way to generate numbers that are uniformly distributed in the range [0, 1].

Repeat the following two steps N times:

1 . generate 2 random numbers x and y in [0, 1]

2. if x^2 + y^2 <= 1, count 1 hit.

When complete, your estimate for pi is:

4 * (number of hits) / N

It is easy to see that regardless what N is, there is a finite probability that you have, say, zero hits. This empirical result will make your estimate for pi also zero, which is quite inaccurate.

The probability of this (and less extreme inaccuracies) goes down as N increases, but it never becomes zero.]

@12609

Your Ramanujan series, or 4*arctan(1), or the Wallis product also only approximate pi for any finite number of steps.

Do you agree that the number of possible chess games is at least 10^29241 according to a Monte Carlo simulation is a proof?

@tygxc, you act like you are playing casual chess whenever discussing anything. Try to read and understand what has been said rather than acting as if it is all the enemy!

Ramanujan's series, or even 4 * (1 - 1/3 + 1/5 - 1/7 + ...), permits you to find, say, the 1000,000th decimal digit of pi, with no uncertainty. A Monte Carlo estimation does not even achieve this, even for the first decimal digit.

That's a difference.

In the case of solving chess, a valid mathematical method will conclude the value of chess is some value from the set {0, 1/2, 1} with no uncertainty.

A hypothetical Monte Carlo method (none has been suggested) could only conclude that the value of chess is some value from the set {0, 1/2, 1} with probability p, where p is some value that is strictly less than 1.

Monte Carlo techniques can be the best tool when high confidence suffices (rather than certainty). When certainty is required, they are useless.

A Monte Carlo simulation can sometimes give answers with very high confidence. People are often willing to ignore a low probability of being wrong. Mathematical proofs are not one of those purposes: they require certainty.

I won't ask for pictorial proofs of your mathematics credentials, but you might mention what they are. Otherwise your "more than anyone here" claims just seem like comical boasting.

i betcha tygxc is pretty close tho...if not really-REALLY close. so I could see where that'd bother summa u math cheek-palmers.

plz u dorks...have some self-respect ? (as ur not getting any from me lol !).

that's funny - we're not getting any 'self-respect' from Lola.
You got that 'self-respect' all locked up in the medicine cabinet Dear?
Reminds me of 'the Caine Mutiny' and the strawberries ...
yes I'll post the vid if I can find it.
s