The Wizard will bank this bet: 1/6 vs 1/11

[Alan Mendelson]

The single event is just describing the situation (just like I did in my VP example). It is not asking a question. How can one ask a question without some descriptive information?

Wow. You 1/11ers have to twist words just like rotating dice to prove your point.

[Alan Mendelson]

The answer to that question is not 1/47.

It's 1/235.

I love this. With a 52 card deck the answer is 1/235.

(By the way, regnis pointed out the answer is 1/48 since only four cards were dropped, not 5.)

[OneHitWonder]

If you're using Wikipedia as your reference in a serious discussion, you're in trouble.

People look stuff up on the internet instead of thinking it through from first principles themselves.

I think that the Wizard's "autobiography" is in there too. Funny, how it comes off when you do it for, by, and of, yourself.

[Zedd]

I love this. With a 52 card deck the answer is 1/235.

(By the way, regnis pointed out the answer is 1/48 since only four cards were dropped, not 5.)

Yes, the correct answer to his question is 1/48.

I proceed to make a similar mistake with my question—the answer should be 1/236.

And yea, that might seem ridiculous to you. But it is true nevertheless. That’s why this dice/coin/child/card/whatever problem is referred as a veridical paradox.

But if you can’t grasp the 1/11 for the dice problem, I wouldn’t go near this card/Royal Flush variant.

[OneHitWonder]

That’s why this dice/coin/child/card/whatever problem is referred as a veridical paradox.

Why is the "dice problem" as written here any sort of a paradox? Is it listed as written in Wikipedia under veridical paradox? How so?

[Zedd]

Why is the "dice problem" as written here any sort of a paradox? Is it listed as written in Wikipedia under veridical paradox? How so?

Again, the problem as written is ambiguous. The problem as written to produce the 1/11 answer is a veridical paradox because the 1/11 answer is very counterintuitive, yet it’s true.

[arcimede$]

Wow. You 1/11ers have to twist words just like rotating dice to prove your point.

No twisting at all. Just silly denial on your part. BTW, why didn't you respond to the VP example? Maybe because it makes your position ridiculous?

[Alan Mendelson]

No twisting at all. Just silly denial on your part. BTW, why didn't you respond to the VP example? Maybe because it makes your position ridiculous?

Do you mean this question?

Here's the same type of question ... You are dealt 5 cards on a VP machine. A friend covers the screen so you can't see the cards. He tells you that the hand contains at least a one deuce. What is the probability you have at least two deuces?

Sorry. I ignored it.

[arcimede$]

Do you mean this question?

"Here's the same type of question ... You are dealt 5 cards on a VP machine. A friend covers the screen so you can't see the cards. He tells you that the hand contains at least a one deuce. What is the probability you have at least two deuces?"

Sorry. I ignored it.

Of course you did. It destroys any possibility you are right.

[Alan Mendelson]

No, I ignored it because I wanted to.

[OneHitWonder]

The problem as written to produce the 1/11 answer is a veridical paradox because the 1/11 answer is very counterintuitive, yet it’s true.

I didn't ask you for your definition of veridical paradox. I asked about how the problem as written is a paradox of any sort. Ie, what is the counter intuitive other aspect here which isn't part of working the problem one way? The reason that I asked for even a Wikipedia certification from you.

Saying that "1/6 seems to be the answer because one die is a 2", would merely be not considering the other column or row of the dice-chart given the proper question with the 1/11 chance answer. No paradox to that.

Clearly, you aren't "up to" discussing this. There is a reason that the Wizard failed the Mensa test. And, that no one with degrees in pure math endorses him, let alone the casinos of the companies for which he works, or has worked. Sorry, but Jacobson and Collins aren't independent entities. They have gambling books to sell, or similar web-pages of their own; as well as perennial involvement with the Wizard's.

Indeed, there is a bit of a paradox to the dice questions in general, but you are nowhere near this yet(?). Please don't re-post the Wikipedia conditional lingo on that which AceTwo posted up at the Wizard's. Nobody responded to it there either.
______________________________________________

And again, no, the problem as written is not ambiguous in your way, or even ambiguous enough. You have to be intelligent enough to work with what you are given, and realize what information is necessary to which answer.

Even were it ambiguous, one would have a bad bet that the first roll just happened to be of 2, and just what the "peeker" was looking for.

[OneHitWonder]

No, I ignored it because I wanted to.

Me too. People with the right answers don't have to "change the channel".

[Zedd]

I didn't ask you for your definition of veridical paradox. I asked about how the problem as written is a paradox of any sort. Ie, what is the counter intuitive other aspect here which isn't part of working the problem one way? The reason that I asked for even a Wikipedia certification from you.

Saying that "1/6 seems to be the answer because one die is a 2", would merely be not considering the other column or row of the dice-chart given the proper question with the 1/11 chance answer. No paradox to that.

Clearly, you aren't "up to" discussing this. There is a reason that the Wizard failed the Mensa test. And, that no one with degrees in pure math endorses him, let alone the casinos of the companies for which he works, or has worked. Sorry, but Jacobson and Collins aren't independent entities. They have gambling books to sell, or similar web-pages of their own; as well as perennial involvement with the Wizard's.

Indeed, there is a bit of a paradox to the dice questions in general, but you are nowhere near this yet(?). Please don't re-post the Wikipedia conditional lingo on that which AceTwo posted up at the Wizard's. Nobody responded to it there either.
______________________________________________

And again, no, the problem as written is not ambiguous in your way, or even ambiguous enough. You have to be intelligent enough to work with what you are given, and realize what information is necessary to which answer.

Even were it ambiguous, one would have a bad bet that the first roll just happened to be of 2, and just what the "peeker" was looking for.

It’s not me giving it the 'paradox' label. I have a strong background in mathematics, so the question is not counterintuitive to me—and is not a paradox in my opinion. But for most people, the question is counterintuitive and therefore it is considered a paradox.

If you google “Boy Girl Problem” (which is the same problem as this dice question), nearly all the top searches refer to it as a paradox.

But I am unsure why we are debating whether this is a paradox or not…why does it even matter?

And I’m sorry, but your third and fourth paragraphs read as gibberish to me. I have no clue who those people are. And what does any of that have to do with the problem at hand?

The original question is open to multiple interpretations—that’s the definition of being ambiguous. You seem more interested in arguing semantics than mathematics.

[champ724]

if the dice were thrown one at a time the odds would be 1/11 against 2 2 idk if the peeking is the same as them being thrown one at a time but once the first dice is on 2 then its a 1/6. so once both dice are sitting there and one is on 2 the chance of the other die being on 2 is 1/6.

[RS__]

if the dice were thrown one at a time the odds would be 1/11 against 2 2 idk if the peeking is the same as them being thrown one at a time but once the first dice is on 2 then its a 1/6. so once both dice are sitting there and one is on 2 the chance of the other die being on 2 is 1/6.

What happens when the first die lands on 6? Chance of getting a 2-2 is 0. But you can still get "at least one die is a 2". Or did you not think that far ahead?

[arcimede$]

No, I ignored it because I wanted to.

Yup, it's called denial. Common human condition when faced with uncomfortable information.

[OneHitWonder]

What happens when the first die lands on 6? Chance of getting a 2-2 is 0. But you can still get "at least one die is a 2". Or did you not think that far ahead?

No, there is no longer the "or more is a 2" part about the specific roll in question then. Here, the roll of 6-X.

You must ask for a roll which is an element of the set of rolls which contain the number 2. The only specific roll which can satisfy "at least one die is a 2" is when only the first die is seen, and it's a 2. This allows for the roll to satisfy "at least one die is a 2". The other die could still be another or the more 2.

[OneHitWonder]

The question is not counterintuitive to me—and is not a paradox in my opinion.

But I am unsure why we are debating whether this is a paradox or not…why does it even matter?

You brought the word paradox into this!

I asked you a couple of specific questions. No answer.

But for most people, the question is counterintuitive and therefore it is considered a paradox.

If you google “Boy Girl Problem” (which is the same problem as this dice question), nearly all the top searches refer to it as a paradox.

The reason Wikipedia isn't considered any sort of a scientific standard. Lol.

I have a strong background in mathematics. You seem more interested in arguing semantics than mathematics.

I don't know in which branch of mathematics you believe you have any background, but arguing semantics is fundamental to all.

[Zedd]

You brought the word paradox into this!

All I said was that the problem is referred as a paradox.

I asked you a couple of specific questions. No answer.

What were the couple of specific questions that you had asked in which I did not give an answer?

The reason Wikipedia isn't considered any sort of a scientific standard. Lol.

Did I say anything about Wikipedia?
I simply said to google the problem. Just look at the top searches—on the first page (top 9 results…and yes, one of them is Wikipedia but go ahead and ignore it if you wish). I’m seeing 7 of them with the word ‘paradox’ in the main tagline (despite leaving the word out of the search). So I was correct in saying ‘the problem is referred as a paradox’. But again, paradox or not, this has much to do about nothing.

I don't know in which branch of mathematics you believe you have any background, but arguing semantics is fundamental to all.

My background is strong enough to be able to answer this simple probability problem. For someone who just wants to argue semantics…you’re not being great at it.

[Rob.Singer]

Zedd's dead.