A fun little probability puzzle for you.

[Flannel Jesus]

Still don't know what you're on about matey, you're off on one again. Started a conversation with yourself it seems.

[Skepdick]

Still don't know what you're on about matey, you're off on one again. Started a conversation with yourself it seems.

OK... I'll spell it out for you.

In so far I as you are accusing me of using words rather "uniquely" - that doesn't actually preclude me from being the only one who's using the word "idea" correctly.

Language devoid of actionables is devoid of ideas. So just about most of the language on this forum contains no ideas.

What hinders communication between me and most people is that they aren't action-oriented. And if you are not action-oriented - you are not idea oriented.

[Flannel Jesus]

Why are we talking about who is using the word "idea" correctly? I don't recall disputing that, and I don't know why you are.

[Skepdick]

Why are we talking about who is using the word "idea" correctly? I don't recall disputing that, and I don't know why you are.

I interpret language the way I interpret language.
You interpret language the way you interpret language.

You might try to pass it off as a "everyone goes through this" type scenario, but I think you have a uniquely strong problem with this one.

And here you are confused about my correct interpretation of having ideas.

It's almost like the problem is not me

[Flannel Jesus]

I really have no clue what you are going on about still.

[uwot]

Language devoid of actionables is devoid of ideas.

What is actionable about that piece of language?

[Skepdick]

I really have no clue what you are going on about still.

How could you possbly understand?

You are not idea-driven

[Skepdick]

Language devoid of actionables is devoid of ideas.

What is actionable about that piece of language?

Nothing! There's no idea in there. It's just a statement of fact.

[bobmax]

It seems to me that there is a tendency to overestimate the probability that the chosen box is the one that contains 100 and 1.

Why does this overestimate?

In my opinion, because the $ 100 bill is thought to say more than it actually does.
That is, we think as if that extracted bill is uniquely identified.

While it is not.

If there is another 100 bill in the box it was taken from, these two bills are indistinguishable, one is worth the other.

[Flannel Jesus]

It seems to me that there is a tendency to overestimate the probability that the chosen box is the one that contains 100 and 1.

Why does this overestimate?

In my opinion, because the $ 100 bill is thought to say more than it actually does.
That is, we think as if that extracted bill is uniquely identified.

While it is not.

If there is another 100 bill in the box it was taken from, these two bills are indistinguishable, one is worth the other.

You're saying the mistake is treating the two $100s as different is the mistake, but wouldn't that cause someone to overestimate the probability that the chosen box is the one that contains 2x 100, and not the one that contains 100 and 1?

In fact, I think it's the reverse of what you're saying - the problem is that people AREN'T treating the two 100s as different, when they are.

[Skepdick]

It seems to me that there is a tendency to overestimate the probability that the chosen box is the one that contains 100 and 1.

If the first 100 says there is a 66% probability the next bill will be a 100 (66%) we are actually over-estimating that we are in the 100/100 box, and under-estimating that we are in the 100/1 box.

We are agreeing on the fact that we are making an over-estimation and disagreeing on the reasoning as to why it's happening.

The fact of the matter is that Bayesian estimates are just that - estimates.

Whatever the reasons - the very next draw resolves all over or under-estimations we've made so far. It's an iterative/convergent process.

[Flannel Jesus]

It seems to me that there is a tendency to overestimate the probability that the chosen box is the one that contains 100 and 1.

If the first 100 says there is a 66% probability the next bill will be a 100 (66%) we are actually over-estimating that we are in the 100/100 box, and under-estimating that we are in the 100/1 box.

We are agreeing on the fact that we are making an over-estimation and disagreeing on the reasoning as to why it's happening.

The fact of the matter is that Bayesian estimates are just that - estimates.

Whatever the reasons - the very next draw resolves all over or under-estimations.

In what sense is it an overestimation? You ran the experiments yourself. You know there really is a 66% chance, once you've pulled the first 100, that we're in the box with 2 100s. You've done the experiment. By what metric have you decided that it's an overestimation, if it matches your experimental results?

[Skepdick]

In what sense is it an overestimation? You ran the experiments yourself. You know there really is a 66% chance, once you've pulled the first 100, that we're in the box with 2 100s. You've done the experiment. By what metric have you decided that it's an overestimation, if it matches your experimental results?

By the existence of two possible futures.

Future 1: I draw a 1 next. Which would re-calibrate my over-estimated 0.666... into a 0.
Future 1: I draw a 100 next. Which would re-calibrate my under-estimated 0.666... into a 1.

[Flannel Jesus]

I don't think you understood the question. I'm not sure you understand what it means to over or underestimate something either.

[Skepdick]

I don't think you understood the question. I'm not sure you understand what it means to over or underestimate something either.

I don't think you understood the answer.

What do you call the delta between your estimate and the true value?

if the true value is 0 my 0.666... is an over-estimate.
If the true value is 1 my 0.666... is an under-estimate.