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Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:12 pm
by Flannel Jesus
Right, glad we got that cleared up, now you know what everybody else means by over and under estimation, and you can disagree with it meaningfully without derailing the conversation into your own interpretation of those words.

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:17 pm
by Skepdick
Flannel Jesus wrote: Sun Jul 17, 2022 10:12 pm Right, glad we got that cleared up, now you know what everybody else means by over and under estimation, and you can disagree with it meaningfully without derailing the conversation into your own interpretation of those words.
And when are we going to clear up your habbit of speaking on behalf of everyone else?

Almost as if you are committing a bandwagon fallacy.

If you want to discuss whose interpretation is better - I will be happy to convince you of your error.

Mine is grounded and relevant to the real world.
Yours isn't (your own words).

So you'll have to forgive me if I don't find judgments of "correctness" and "incorrectness" about thought experiments.... interesting.

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:26 pm
by Flannel Jesus
It's not about better or worse, it's about the fact that you don't even realize when you're having a different conversation than other people in the conversation. You're not very good at detecting when that has happened or disambiguating it when it has happened.

I know he meant overestimating in the way I said, because I continued my discussion with him and it was clear, between the posts we made to each other, that he was referring to the 50% position as "overestimating for the 1+100 box", and I know that for 2 reasons:

That's the common sense most likely thing for him to have meant, and he later literally said that that's the position he's referring to as an overestimation. I'm qualified to speak for him, because I have a better intuitive understanding of these types of discussions than you apparently have, AND I read what he was posting and listened to him.

You have a unique approach and a unique way with words, and those things aren't bad in themselves, but in the absence of skills to detect when you're stuck in a conversation where you're not even talking about the same thing, and the absence of skills to disambiguate the conversation when you do detect that, you're going to run into problems. I can see that that happens to you a lot. If you have that unique approach and a unique way with words, you need those skills.

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:30 pm
by Skepdick
Flannel Jesus wrote: Sun Jul 17, 2022 10:26 pm It's not about better or worse, it's about the fact that you don't even realize when you're having a different conversation than other people in the conversation. You're not very good at detecting when that has happened or disambiguating it when it has happened.

I know he meant overestimating in the way I said, because I continued my discussion with him and it was clear, between the posts we made to each other, that he was referring to the 50% position as "overestimating for the 1+100 box", and I know that for 2 reasons:

That's the common sense most likely thing for him to have meant, and he later literally said that that's the position he's referring to as an overestimation. I'm qualified to speak for him, because I have a better intuitive understanding of these types of discussions than you apparently have, AND I read what he was posting and listened to him.

You have a unique approach and a unique way with words, and those things aren't bad in themselves, but in the absence of skills to detect when you're stuck in a conversation where you're not even talking about the same thing, and the absence of skills to disambiguate the conversation when you do detect that, you're going to run into problems. I can see that that happens to you a lot. If you have that unique approach and a unique way with words, you need those skills.
I think you are misunderstanding what's going on here.

I am perfectly aware of the ambiguity.

And I am perfectly aware that you both continued to converse using uninteresting, and unrelaed to real life uses of the words "correct", "incorrect"; "underestimating" and "overestimating".

The confusion comes from the fact that you said you want to talk about ideas.

I proceeded to do that and you didn't. You wanted to talk about meaningless, uninteresting and inconsequential thought experiments.

Of course, in the absence of skills to say what you mean and mean what you say, this is going to keep happening to you when you interact with people who say they want to talk about ideas and actually mean it.

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:32 pm
by Flannel Jesus
So you knew about the ambiguity and chose to increase it rather than to make an effort to disambiguate?

You sound like a troll if that's the case. How the fuck can you have a productive conversation when you know the people you're talking to aren't even talking about the same shit as you?

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:34 pm
by Skepdick
Flannel Jesus wrote: Sun Jul 17, 2022 10:32 pm So you knew about the ambiguity and chose to increase it rather than to make an effort to disambiguate?
I am disambiguating.

I gave you the correct interpretation. The one which relates to the real world - the one which relates to ideas.

You ignored it.
Flannel Jesus wrote: Sun Jul 17, 2022 10:32 pm You sound like a troll if that's the case.
The feeling is mutual.
Flannel Jesus wrote: Sun Jul 17, 2022 10:32 pm How the fuck can you have a productive conversation when you know the people you're talking to aren't even talking about the same shit as you?
Normally, I go about explaining to people why my use of words is better than theirs. And if they realise their mistake (and they actually want to do what they say they want to do - e.g talk about ideas) they tend to switch gears.

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:35 pm
by Flannel Jesus
How's that working for you? Be honest

Re: A fun little probability puzzle for you.

Posted: Sun Jul 17, 2022 10:36 pm
by Skepdick
Flannel Jesus wrote: Sun Jul 17, 2022 10:35 pm How's that working for you? Be honest
100% success rate.

Either people realise they want to talk about ideas; or they figure out they were lying to themselves all along.

But it takes a while to navigate the mess when people tell lies.

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 1:03 am
by Age
Flannel Jesus wrote: Sun Jul 17, 2022 5:00 pm but... it's not 50% probability anymore. We've selected the first bill. It's a $100. It started out as 50% probability, before we picked the first bill out of it. It's 66%, by your own logic, by your own code that experimentally proves it, after we select the first bill and find that it's $100. After that moment, we know we have a 66% chance that we've selected the box with 2x $100.
You are both getting confused here, and this is just because of the choice of words and the presumption being used in the example. There are only TWO boxes, so the chance here, IS 50%, and can only be 50%. The same applies when ONE bill is picked out of the ONE chosen box, the choice left is STILL 50%, and NOT 66% at all.

This can NOT be refuted.

There, OBVIOUSLY, can ONLY be a $100 or a $1 dollar bill in there.

Now, if ANY one would like some more CLARITY and/or (more) PROOF here, then just let me know.
Flannel Jesus wrote: Sun Jul 17, 2022 5:00 pm It's not a silly tautology, it's probabilities mate.
Having chosen any box gives me incomplete/imperfect/probabilistic information about which box I have initially selected.
No, I still don't think you're getting it. Choosing the box doesn't give you any information AT ALL about which box you've selected. The moment after you've chosen the box, you don't know which box you've chosen. Selecting the first bill - that's what we're talking about. That's what gives you information, probabilistic information, about which box you've selected.

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 5:32 am
by bobmax
What intrigues me is that the random event is never absolutely random...

If, for example, I only have a box with a $ 100 bill and a $ 1 bill, every time I select a bill the probability that it is the 100 bill is always 1/2.
This regardless of the results of the previous draws.

However, if after many draws I always find myself with a bill of 100 I would be amazed.
And I would expect the next selection to end up with the 1.
That is, the probability of drawing 1 would be considered to be higher than 1/2.

While this is not the case at all.
If the event is truly random.

We thus have the paradox that with true randomness we would have the extraction of the bill from 100 an infinite number of times.

The lack of any manifestation of randomness is true randomness!

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 6:09 am
by Age
bobmax wrote: Mon Jul 18, 2022 5:32 am What intrigues me is that the random event is never absolutely random...

If, for example, I only have a box with a $ 100 bill and a $ 1 bill, every time I select a bill the probability that it is the 100 bill is always 1/2.
This regardless of the results of the previous draws.

However, if after many draws I always find myself with a bill of 100 I would be amazed.
What 'amazes' or 'does not amaze' you has absolutely NO bearing on randomness.
bobmax wrote: Mon Jul 18, 2022 5:32 am And I would expect the next selection to end up with the 1.
That is, the probability of drawing 1 would be considered to be higher than 1/2.
But what you 'expect' or 'do not expect' ALSO has absolutely NO bearing AT ALL on randomness, itself.
bobmax wrote: Mon Jul 18, 2022 5:32 am While this is not the case at all.
If the event is truly random.

We thus have the paradox that with true randomness we would have the extraction of the bill from 100 an infinite number of times.
This is possible.
bobmax wrote: Mon Jul 18, 2022 5:32 am The lack of any manifestation of randomness is true randomness!

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 7:23 am
by Flannel Jesus
Age wrote: Mon Jul 18, 2022 1:03 am
Flannel Jesus wrote: Sun Jul 17, 2022 5:00 pm but... it's not 50% probability anymore. We've selected the first bill. It's a $100. It started out as 50% probability, before we picked the first bill out of it. It's 66%, by your own logic, by your own code that experimentally proves it, after we select the first bill and find that it's $100. After that moment, we know we have a 66% chance that we've selected the box with 2x $100.
You are both getting confused here, and this is just because of the choice of words and the presumption being used in the example. There are only TWO boxes, so the chance here, IS 50%, and can only be 50%. The same applies when ONE bill is picked out of the ONE chosen box, the choice left is STILL 50%, and NOT 66% at all.

This can NOT be refuted.

But it has been refuted. It's been refuted in numerous ways. Before you get any information about what's inside the box, it's 50/50. Once you've picked the first bill and see that it's $100, it isn't.

It's been refuted with Bayes theorem, it's been shown experimentally, and seeing the $100 has been shown to be information about what box you're likely to have picked by way of analogy

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 8:38 am
by Age
Flannel Jesus wrote: Mon Jul 18, 2022 7:23 am
Age wrote: Mon Jul 18, 2022 1:03 am
Flannel Jesus wrote: Sun Jul 17, 2022 5:00 pm but... it's not 50% probability anymore. We've selected the first bill. It's a $100. It started out as 50% probability, before we picked the first bill out of it. It's 66%, by your own logic, by your own code that experimentally proves it, after we select the first bill and find that it's $100. After that moment, we know we have a 66% chance that we've selected the box with 2x $100.
You are both getting confused here, and this is just because of the choice of words and the presumption being used in the example. There are only TWO boxes, so the chance here, IS 50%, and can only be 50%. The same applies when ONE bill is picked out of the ONE chosen box, the choice left is STILL 50%, and NOT 66% at all.

This can NOT be refuted.

But it has been refuted. It's been refuted in numerous ways.
What does your 'it' refer to here, EXACTLY?
Flannel Jesus wrote: Mon Jul 18, 2022 7:23 am Before you get any information about what's inside the box, it's 50/50. Once you've picked the first bill and see that it's $100, it isn't.
You are MISSING the OBVIOUS.

Once you have picked the first bill and see that it is a $100 dollar bill, then it IS 50/50 that the other bill inside the box is either a $100 dollar bill or a $1 dollar bill. There are NO other options.
Flannel Jesus wrote: Mon Jul 18, 2022 7:23 am It's been refuted with Bayes theorem, it's been shown experimentally, and seeing the $100 has been shown to be information about what box you're likely to have picked by way of analogy
1. The 50/50 conclusion has NOT (YET) been refuted.

2. "Bayes theorem" does NOT refute what I have CLAIMED here. (Unless, OF COURSE, you can PROVE otherwise.)

3. What is the 'it', which has SUPPOSEDLY "been shown"?

4. And, how EXACTLY does just seeing the $100 dollar bill SUPPOSEDLY inform you about what box you likely picked? Which box are you CLAIMING that you have likely picked when you see the $100 dollar bill?

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 9:26 am
by Flannel Jesus
The idea that it's still 50/50 after seeing the $100 - empirically, it can be shown to hover around 66.66...% likelihood of being the box with 100+100. Analytically, it can be shown to be 2/3, through various means but my preferred means is Bayes theorem.

In a thread with all of these avenues that have been laid out, you're just asserting that their false without looking at them.

In fact, I made this post to you here laying out bayes theorem and the code that runs the experiments:

viewtopic.php?p=583923#p583923

And your reply was "that's too complex for me". If it's too complex for you, fine, no shame in that, but then you don't really stand on very solid ground when you say that the standard position can't be proven. It can't be proven because the proofs are too complex for you?

Re: A fun little probability puzzle for you.

Posted: Mon Jul 18, 2022 9:42 am
by Flannel Jesus
Let's go into more detail on my Bayes theorem layout. This is what I initially said:
Bayes theorem is

P(A|B) = P(B|A) * P(A) / P(B)

A = I picked the box with 2 100$
B = I chose a $100

we want to find P(A|B), probability of A given B

P(B|A) = probability of B given A, which is 1
P(A) is 0.5
P(B) is 3/4

1 * 0.5 / (0.75)
2/3
P(B|A) = probability of B given A, which is 1
Do you agree that the probability that the bill I chose is a $100, IF I chose the box with 2x100, is 1? If not, why not?

P(A) is 0.5
Do you agree that the initial probability that I chose the box with 2x100 is 0.5? If not why not?

P(B) is 3/4
Do you agree that my first bill selection is 3/4 likely to be a $100? If not, why not?

Bayes theorem is formulated as
P(A|B) = P(B|A) * P(A) / P(B)
Do you agree with that? If not why not?

And when you plug in the above values into that formula, you get
1 * 0.5 / (0.75)
Do you agree with that? If not, why not?