...when i wanna run a quick check w/ say less than 1000 samples i use excel. and function out say the 'randarray' w/ its arguments. tests out every time. for this one i also strung in the 'unique' operative (ridding ea black ball along the way). i ran it like 10x's and it tada'ed...goodbye.
Chess will never be solved, here's why
so the probability of not drawing a white ball 50 times in succession is .99^50. 1-(.99^50) is 39.4993...%
try 1/100 + 1/99 + ... >> ...+ 1/52 + 1/51. ~69%. and s/t else. it reaches 100% at abt 37 left (63 pulls). or 1/ln e. eulers #.
math hasta come to u. u cant go gettit. ppl like einstein & squawking tried to bend it to how they wanted it. doesnt work. and if u cant figure out s/t as simple as black ball-white ball then u dont have it. iows dont be a meggy.
The discussion was about drawing with replacement. Your original post was vague on that point.
Interesting that you think you're certain to have pulled the white ball when there are still 37 left in the bag if you do it without replacement. You might want to check that.
I agree with your last sentiment.
(Btw wouldn't it be simpler to just write 1 rather than 1/ln e?)
...when i wanna run a quick check w/ say less than 1000 samples i use excel. and function out say the 'randarray' w/ its arguments. tests out every time. for this one i also strung in the 'unique' operative (ridding ea black ball along the way). i ran it like 10x's and it tada'ed...goodbye.
Better to understand what you're doing. The software and the formulae don't absolve you from that.

so the probability of not drawing a white ball 50 times in succession is .99^50. 1-(.99^50) is 39.4993...%
try 1/100 + 1/99 + ... >> ...+ 1/52 + 1/51. ~69%. and s/t else. it reaches 100% at abt 37 left (63 pulls). or 1/ln e. eulers #.
Reaching 100% after drawing 63 balls should tell you that you have made a mistake! Obviously, it is not certain you have the black ball by that point.
If you want to work it out the hard way, the probability is:
1/100 + (99/100) * (1/99) + (99/100) * (98/99) * (1/98) + ...
This is because you stop if you get the black ball, so the next probability has a factor to say how often you _haven't_ stopped.
You will see this is easier than it seems if you start to work it out. It is:
1/100 + 1/100 + 1/100 ...
The way I did it is to observe that drawing up to k times is the same as splitting the balls into two subsets, one with k balls and one with (100 - k) balls. The probability that the black ball is in the first subset is simply k/100.
math hasta come to u. u cant go gettit. ppl like einstein & squawking tried to bend it to how they wanted it. doesnt work. and if u cant figure out s/t as simple as black ball-white ball then u dont have it. iows dont be a meggy.
Do you think Einstein and Hawking would have got that right?

Anyway I have to go. Stay well and happy. Eat more turnips or something.
O is already 'gone'. Even when he's 'here'.
Yes Dio is well and happy. Somehow O got that one right.
But didn't mean to. He slipped up with the word 'stay'.
In O's world - honesty from him is always a mistake.
Odd but there it is. A kind of self-inflicted pit he shouts from the bottom of.
Its for others to have the main conversations and forum topic conversations.
O isn't competent to do so.
Long Covid because of vaxx denial? Yes that would fit in his case.
And he would have phobias regarding the main science community that is so much more capable than him.
Analagous to flat-earthism.
@13673
...
If chess is no draw, then 112 draws would mean all 112 games must contain an odd number of errors, e.g. error distribution 0-112-0-0. That is not plausible: all 17 finalist would have to collude to make exactly 1 error. ...
If you take a large bunch of people who have never played chess before, teach them the rules then get them to play 112 games from a winning KBNvK position, you'll almost certainly get 112 draws. Do you seriously think that's because they'll all collude to make an odd number of half point blunders?

If chess is no draw, then 112 draws would mean all 112 games must contain an odd number of errors, e.g. error distribution 0-112-0-0. That is not plausible: all 17 finalist would have to collude to make exactly 1 error. ...
If you take a large bunch of people who have never played chess before, teach them the rules then get them to play 112 games from a winning KBNvK position, you'll almost certainly get 112 draws. Do you seriously think that's because they'll all collude to make an odd number of half point blunders?
This point is a good one, but beyond him. He's incapable of realizing that engines are only on a slowly moving plateau that is not the exhaustive end of chess play. This is due to his emotional belief system...he wants Sveshnikov to be right at any cost, and he also desperately wants for humans to still be having a role in ICCF play, but they really don't. What we are seeing is engines hitting a plateau, and human beings already having hit their maximum threshold in terms of being able to make engine play better. ICCF participants are just shuffling results between engines, nothing more. Their "input" in terms of which lines to follow is guided by engines, and when it is not, it is detrimental.

It can't be solved Now.
That's known.
For two reasons.
First - it isn't.
Second - the computers aren't fast enough.
------------------------------------------------------
If you massed a whole bunch of computers - with different rooms full of computers attacking different aspects of the project - could it then be solved?
No.
Because if you had a thousand such rooms - that only knocks three zeros off the GiNormous number of positions.
And that's not nearly a big enough Dent.
if you add "Now" to the argument it becomes a different argument, and is true
as for solving it in the future:
- you do not know that a new logical technique to make the solution exponentially more efficient will not be discovered. no one could "solve" pi, and could only bruteforce it, until Leibniz discovered calculus. it was a problem that could not be solved without infinity work, and then...
and now it's solved.
- Moore's law still holds
target is some very large number. current number doubles every 2 years. target will be hit as a function of time, even without unpredictable emergence of new logical technique
/thread
Hi onedream !
That nice equation you posted wouldn't copy in the quote function.
I'm going to see if it'll copy/paste but I doubt it.
It might post as an 'image' somehow.
No. No go. Neither with paste nor ctrl V nor Win V nor image insertion.
It seemed to rightclick 'copy' though.
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Anyway regarding Moore's Law I believe it will run into fundamental limits eventually.
But at issue is - when?
To discuss that properly we'd need to have more basics here about 'transistors' in the modern usage of the word and how computer circuitry is laid down in the 'substrate' and so on.
--------------------------------------------
Regarding the forum topic and 'solved' there's an interpretation availble.
That is that the forum topic actually pertains to all of chess - not just an obscure idea within it.
Yes its not a direct connection but there are many indirect connections.
We can discuss the limitations of computer hardware ...
But we can also discuss the nature of chess as relevant too.
I have some 'difference' with Elroch as to legitimate shortcuts in 'solving' chess.
None of tygxc's 'shortcuts' appear to be legitimate.
But I think many positions can be 'logically solved' including by the computers - with neither gametree 'brute forcing' (much too slow) nor tablebase 'brute-forcing' (only available up to 7 pieces on board anyway)
--------------------------------------------
One only needs reach positions where it becomes too obvious that one side has no path to drawing its therefore Lost position.
Elroch has argued that computers can't 'think' that way.
Martin has rightly pointed out how even the strongest computers make astounding obvious blunders in assigning wins or draws to positions that are obviously the opposite.
But also being commented about throughout the two year thread is software -
usually with the word 'algorithm'.
------------------------------------
If you're going to have legitimate shortcuts -
they would have to be software shortcuts.
Algorithms that make logical conclusions.
Is there no such thing? No such artificial intelligence?
---------------------
Computers can't assign a win to K+R versus King where there's no stalemate - without referring to a tablebase or 'brute-forcing' through to checkmate?
If there's to be real shortcuts - that's where they're to be found - in that 'without' ...
along with 'logical' algorithms to quickly identify and dismiss 'legally unreachable' positions.
I'm confident by the way - that both are being worked on - but I think the first one hasn't been much discussed here if at all.
------------------------------
In the astounding positions posted by Martin where Stockfish erroneously assigns a win or draw where a human can quickly see its wrong -
do other engines make the same mistake if presented with the same positions?
Do they 'catch' Stockfish's errors?

@onedreamingeye
How did you paste that equation here?
It copies fine to my clipboard - I can even see it there using Windows key + V ...
but it refuses to paste.
What is the trick?
I'm hoping to add this option - without adding Word or Excel or any gigantic software of any kind to my computer.
Just tried the chrome extension 'fx'. No go.
@13686
"any distribution is plausible" ++ No. It is not plausible to have 62 games with 0 error, 50 with 2 errors and none with 1 error. It would need all errors to come in pairs.
"It could be extremely likely that errors come in pairs"
++ In previous years ICCF WC Finals had decisive games, i.e. unpaired errors.
The likelihood of them coming in pairs was the same as it is now.
"It's fundamentally wrong trying to calculate odds for a series of events (errors) that are all different and dependant of each other in a way we cannot predict accurately."
++ We can predict from previous ICCF WC finals, which had decisive games, each year fewer.
Now we have reached 0 decisive games, 0 error/game.
Taking a bad analogy: assume you toss a coin 112 times and get 112 heads.
It is disrespectful to compare a 2 year engine assisted WC Finals chess game to a coin toss.
You could say it is a random fluctuation likely to occur with probability 0.5^112 = 2*10^-34.
A better explanation is the coin is loaded and the probability it is not is 2*10^-34.
@13698
"If you take a large bunch of people who have never played chess before, teach them the rules then get them to play 112 games from a winning KBNvK position, you'll almost certainly get 112 draws." ++ Here are 2 crucial elements:
- You take people who have never played chess before. The ICCF WC Finals has 17 Finalists who qualified through Preliminaries, Semifinals, Candidates and who use top engines on top hardware (the 4 Russians less so) and 5 days per move. If your bunch of people were jailed and those who win get out, then at 5 days/move some might figure out how to win.
- You give them a won position to start with, while the initial position of Chess is a draw.
I proposed you a relevant KRPP vs. KRP position: it is a draw, despite the pawn advantage and despite endgame books prior to the 7-men endgame table base giving it as a white win.
@13699
"engines are only on a slowly moving plateau"
++ But now 0 error/game has been reached at 5 days/move, 2*90 million positions/second.
"he wants Sveshnikov to be right" ++ He was right, whether we want or not.
"humans to still be having a role in ICCF play"
++ The humans are decisive, that is how they qualified for the Finals.
4 of the 17 Finalists are Russian, despite inferior hardware due to sanctions.
@13698
"If you take a large bunch of people who have never played chess before, teach them the rules then get them to play 112 games from a winning KBNvK position, you'll almost certainly get 112 draws." ++ Here are 2 crucial elements:
- You take people who have never played chess before. The ICCF WC Finals has 17 Finalists who qualified through Preliminaries, Semifinals, Candidates and who use top engines on top hardware (the 4 Russians less so) and 5 days per move. If your bunch of people were jailed and those who win get out, then at 5 days/move some might figure out how to win.
- You give them a won position to start with, while the initial position of Chess is a draw.
I proposed you a relevant KRPP vs. KRP position: it is a draw, despite the pawn advantage and despite endgame books prior to the 7-men endgame table base giving it as a white win.
The question was, " Do you seriously think that's because they'll all collude to make an odd number of half point blunders?".
You've snipped it off the end and made no attempt to answer. Have you got an answer?

tygxc with the cope posting, and continuing to ignore mathematical rigor.
""any distribution is plausible" ++ No. It is not plausible to have 62 games with 0 error, 50 with 2 errors and none with 1 error. It would need all errors to come in pairs."
And you cant prove that errors cant come in pairs, so its perfectly plausible. you just dont like it and it doesnt make sense to you intuitively so to you it cant exist. but just because there isnt an apparent explanation for an unusual phenomenon doesnt mean an explanation cant exist, until you prove it rigorously.
"4 of the 17 Finalists are Russian, despite inferior hardware due to sanctions." heres something you are missing tygxc. the russians dont necessarily have inferior hardware anymore. the interview you cited only covered a specific time period, during which russians played CONSIDERABLY worse.
"Taking a bad analogy: assume you toss a coin 112 times and get 112 heads."
"A better explanation is the coin is loaded and the probability it is not is 2*10^-34."
actually it doesnt prove anything. it just says that it is PROBABLY the case.
argument by high probability isnt a mathematical proof.
but the coin could be perfectly fair but the flipping method was heavily biased. or any other number of tertiary explanations

tygxc only needs to get one detail wrong and then all his other details are wrong too.
Constantly happens in his posts.
But its predictable. And for two years now.
Its kind of 'innocent' in a way though.
Its kind of like somebody who wouldn't want to know what a chemical element is.
Another way to say it is:
Nobody really has an option to supervise an adult's intellectual spare time 'thinking and nonthinking'.
In professional situations yes.
Or in some family situations.
Or in educational situations.
But this situation here is about as 'unprofessional' at tygxc's end as could be.
And in the situation of tygxc 'relating' to others here and others relating to him.
He has zero 'obligation' to get rid of his disdain for mathematical objectivity.
----------------
This could be understood better if we consider flat-earthism in the public forums here.
I believe its allowed.
Flat-earthism seems less forgivable though. Much less forgivable.
Kotshmot remember when i told you that tygxc fundamentally rejects the principles of mathematical logic and proof? (at least im pretty sure i did, i try to tell everyone who starts an interaction with tygxc this so they dont waste their time on tygxc's fantasy).
I think you are starting to see what i mean.