Chess will never be solved, here's why

Corrected my typo in the other post.
To Lesser air pressure on the top of the airfoil.

That Bernoulli was one smart cookie.

Even simpler is the probability of drawing the white ball is 1 - the probability of not drawing the white ball 50 times. On each draw with replacement the probability of not drawing a white ball is .99 and the probabilties on different draws are independent, so the probability of not drawing a white ball 50 times in succession is .99^50. 1-(.99^50) is 39.4993...% on my calculator.

Not sure why you bothered responding, since that poster is gone. My philosophy on alts is simple...I don't really care if somebody is attacking me on an alt. If they are trolls and do not know what they are talking about, then I will dismantle them, and the username doesn't matter. That doesn't mean I don't keep my eyes open, but I don't have a driving need to find out some hidden "truth" ala somebody who believes in cartels/cabals.

In fact, it is often helpful is somebody starts creates trolling accounts, because if a mod notices the same IP or VPN keeps popping up with similar trolling posts, they might get muted or banned.

This is both simpler and incorrect.

This is because .99^50 is not the probability of drawing a white ball 50 times

I didn't say it was - I said it's the probability of not drawing the white ball 50 times.

The probability of any number of independent events all occurring is the product of the individual probabilities of occurrence.

As I said. Put away your formula book.

That's in fact one of the reasons I responded.
Because that poster is gone. With O returned.
Unfortunately VPN's can be changed.
In other words a person with a single IP address can apparently dodge the mods by using VPN's.
No fancy computer knowledge needed it seems.
I've never tried that myself. No need for alts.
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Another reason to respond:
O constantly making accusations of 'alt accounts'.
He fails to be annoying doing so.
But could be himself doing so.
The more he talks about alts - we don't have to imitate ... but ibrust definitely looks like a candidate. Especially the way ibrust was obsessing over 'intelligence levels'.
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As for 'caring' well what is really 'cared' about?
Real 'caring' is usually kind of visceral.
People 'care' about not being in accidents so they stop at red lights.

The trials follow a binomial distribution since the probability of success and failure differ. Hence, to find the probability of 1 success in 50 trials, you have to multiply the factor by the appropriate binomial coefficient.

The figure .99^50 doesn't represent 1 success in 50 trials, it represents zero successes.

As you'll see, if you plug in k=0 successes in the formula I gave you, you'll get .99^50

This is an intuitive mistake people that people that haven't studied probability and statistics make.

But at least it gives the right answers.

Just plug in k=0 successes into the formula and you'll know why I'm right and you're wrong

Exactly. The probability of nonzero successes is therefore 1 - that figure. Just think about it; it isn't a hard problem.

You're not looking for the probability that the white ball is drawn exactly once if that's what you've been doing.

btw yall the confusion between the different numbers is this: whether we are checking the probability for EXACTLY ONE success over the 50 replaced attempts, or whether we are checking the probability for AT LEAST ONE success.

for EXACTLY ONE success, the bernoulli formula is used (although with something like that the formula is a bit overbearing)

for AT LEAST ONE success, the double negative formula is used (the 1-(99/100)^50 formula). Both resulting numbers provided in discussion are correct in what they are evaluating.

edit: welp i guess u guys kinda figured it out already. actually no u didnt lol.

the previous discussion that lead to the requested probability was based around the AT LEAST ONE success probability, which punch didnt see, and therefore jumped to the conclusion that it was EXACTLY ONE.

Except, "if u put 99 bl balls and 1 wh ball in a rabbits hat ?...the chance of pulling the wh ball out in the first 50 tries is ~69%...maybe.", says nothing about exactly once, so @Elroch was perfectly correct. @punchdrunkpatzer is plugging his balls into the wrong formula.

imagine pulling the balls out one by one and labeling them 1 to 100. The probability that the white ball is labeled with a number less than or equal to 50 is 50%.

Works without replacement.

But will there be enough time to solve it?
And money?
Remember the forum topic.
its not 'can it be solved?' its 'will never be solved'.
Depends. Will there be enough time?
We don't know.
It can't be solved Now.
That's known.
For two reasons.
First - it isn't.
Second - the computers aren't fast enough.
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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.

I doubt Optimissed knows what a VPN is...but regardless, each VPN, like any other provider, only has so many Class C IP addresses, etc. So you can't identify the end users, but you could confirm the same troll's alts are all using some regional VPN server. It takes a dedicated sleuth, but you can nail it down somewhat. If they are using a VPN that has some option to send their traffic all over the world, then their online chess play will suffer the consequences...either way, it's a pain the butt for the VPN user. and that is all that is required.

Making new Emails is also a chore...sadly, the mods here do not have leeway to ban repeat trolls on sight. When I ran my own boards, I would ban them so fast (without even a message/acknowledgement to mark their passing) that it took longer for them to recreate a new account than it took me to ban them...that's the sweet spot. Trolls will get frustrated an fade away if you make things onerous for them. Chess.com is hopelessly lax, though, so it will always take 5-10 minutes to make a troll account and takes the mods weeks or months to ban just one alt at a time for cause...

bro are u sure u write textbooks because k=0 literally equates to (99/100)^50, which is exactly what they wrote. this can be calculated mentally and confirmed by whatever calculator you have. the probability of k≠0, (what is being asked) is thus 1- (99/100)^50, which is again exactly what they wrote.

Dio you know a zillion times more about computers and the internet than I do.
And I agree it often take the mods a while to ban an alt account and other trolling accounts.
Sometimes its fast though.
O will try to take advantage of 'green' mods who don't know about him and his history - but when those new mods check with the more established and higher ranked moderators and staff they find out that O has a history going way back.
Its something that its better new members know about and are informed about from time to time too.