How do you interpret the "dice problem"?

[arcimede$]

Alan, no one is double counting. They are looking at multiple possible results. That is how probabilities are computed. Not unlike VP where all possible draws for a hold are examined to determine the value of any hold.

[Alan Mendelson]

Alan, no one is double counting. They are looking at multiple possible results. That is how probabilities are computed. Not unlike VP where all possible draws for a hold are examined to determine the value of any hold.

You can't have multiple results with two dice. Only one face on each counts. Stop.

[arcimede$]

You can't have multiple results with two dice. Only one face on each counts. Stop.

You're saying you can't get two different results on two throws of the dice? Quite a strange position you are taking.

[Alan Mendelson]

You're saying you can't get two different results on two throws of the dice? Quite a strange position you are taking.

It's not two throws of the dice. It's ONE THROW.

[arcimede$]

It's not two throws of the dice. It's ONE THROW.

Nope, that's your problem. You keep ignoring what the question is asking and inserting your own misguided opinion. If you ever took the time to read what people are telling you, you might have figured it out a long time ago.

[1in11]

It's not two throws of the dice. It's ONE THROW.

If we want to consider only the outcome of that ONE THROW with the outcome known by the peeker (as he has seen both dice), then here's the probability: If the peeker saw 2-2, then the probability is 1 in 1 that the throw was 2-2. If the peeker saw anything else, then the probability is 0 in 1 that the throw was 2-2.

[OneHitWonder]

If the peeker saw anything else, then the probability is 0 in 1 that the throw was 2-2.

... 0/10, or 2 X (0/5).

[redietz]

Arci, God knows you have been patient beyond my means when discussing mathematics here, so let me try this again. The context is not clear. Is this primarily a description of a single event or a hypothetical question regarding multiple events? The author of the question starts IN PRESENT TENSE with a description of a SINGLE EVENT. This conjures up a particular minds' eye picture for most people. The author of the question then tries to subvert/reverse/override that mind's eye picture with the insertion of the single word, "probability," at the end. For you, this turns it into a multiple event, math question. For many, if not most people, it does not.

The piece of writing is at odds with itself, and probably purposefully so. It starts off with a single event in present tense. The piece of writing establishes itself as being about that single event. The addition of the word "probability" after the fact doesn't - and shouldn't necessarily - make this about multiple events. The author undoubtedly did this on purpose. It's either a really bad piece of writing or a deliberately manipulative piece of writing designed to divide the readers into two at-odds groups. If you look at this as a piece of writing, which it is, rather than as a math problem, there is no reason for the use of the word "probability" to override the present tense description of a single event. If you look at this as a math problem, which it probably also is (but not absolutely necessarily due to "probability" having a non-math primary definition), then the use of the "probability" at the very end frames it as a multiple event problem.

So, the context is not crystal clear. The beginning of the question frames it as one thing. The use of "probability" at the end frames it as something else at odds (for many, if not most readers) with its own beginning. Arci chooses to have the end of the question, with "probability," frame the beginning. Many people choose to have the beginning of the question, with a single event, frame the end. To add to the layers of this, "probability" has its own multiple definitions, and the present-tense, single-event opening could be defined as hypothetical, even though there is no clear reason to do so.

This question is not a math equation. It is a piece of writing. It should foremost be analyzed as a piece of writing before being analyzed as a math equation.

[OneHitWonder]

This question is not a math equation. It is a piece of writing. It should foremost be analyzed as a piece of writing before being analyzed as a math equation.

Agreed, with one proviso.

Ultimately, we can not be on "the right track" once we have found analytical clarity in the writing or the math. Such commitment is about no possible further wondering or "no more track".

"It took the madmen of yesterday for us to be able to act with extreme clarity today. I want to be one of those madmen. We must dare to invent the future." - Thomas Sankara

"Although our intellect always longs for clarity and certainty, our nature often finds uncertainty fascinating. - Carl von Clausewitz

[regnis]

"what the eff are you talking about"-Regnis

[OneHitWonder]

"what the eff are you talking about"-Regnis

Only that no one can completely clarify anything. And, to take this into consideration with what clarifications can be made. Ie, after a point, it is better to look at the thing from other directions.

As far as your own quote goes, were you a famous army general or other military officer? When they said that the internet was to be the equalizer for the masses, I don't think they - Bill Gates and the others - meant that everyone was to be an instant authority on everything. Other posters ought to be respected as persons at all times, same as in person. At least, their known sources or references. Please ask before you "shoot your..." . (You came off as someone sitting somewhere in his underwear with nothing better to do.)

[regnis]

No offense, but you come off as a quasi-intellectual who thinks he is impressing some mope sitting here in his underwear with quotes that have no relevance to the issue at hand.

I actually said it in jest--but you obviously have such a high regard for your great intellect, that you have no sense of humor.

[OneHitWonder]

I already noted that there are still two key, and very interesting, elements which have yet to be introduced for discussion to the dice problem. Not to be anyone's quasi-intellectual, I will leave those to the one who sought his own clarity above.

And, my point exactly. Do we feel better now that we have such clarity. Will it lead us somewhere? No. Merely a guy who claims no offense but goes on with more of the same in the same breath to try to dig himself out of a just joking bit of parody replete with quote.

His not being a "famous army general or other military officer" must make me a quasi-intellectual. Got it.

[Rob.Singer]

What? Who?....Where's the famous military general on the forum??
Happy Memorial Day!

[Alan Mendelson]

I tried to "read" the posts above but I got lost. I would like to say that while I was at Caesars during Memorial Weekend I read the original question to as many craps dealers as I was able to and they all said the answer was 1/6.

When I mentioned the 1/11 answer I got several "looks" and "eye rolls." And one dealer said he reads the Wizard of Vegas forum.

[redietz]

And that's why I said what I did elsewhere -- namely, that if you tried to prove the answer was 1/11 in a US court, you would fail. That doesn't mean the 1/11 answer is "wrong" so much as it demonstrates that the question as written, for most people, leads them to a 1/6 answer. So, to the 1/11 backers, I say that if 1/6 is where the question leads the majority of readers, and you think they are wrong, then the fault lies with the author, not the readers. Don't argue with the readers or make fun of them; argue with the idiot who wrote the question. Or argue with the idiots who posted the question as is without fixing it. They wanted to be clever and look clever and wax eloquent about how clever they are because they "understand" the question.

The question is not, as I have said, an equation. It is a piece of writing. If it is interpreted as having a particular meaning by most people (1/6 being that meaning), then that is its meaning.

[arcimede$]

Arci, God knows you have been patient beyond my means when discussing mathematics here, so let me try this again. The context is not clear. Is this primarily a description of a single event or a hypothetical question regarding multiple events? The author of the question starts IN PRESENT TENSE with a description of a SINGLE EVENT. This conjures up a particular minds' eye picture for most people. The author of the question then tries to subvert/reverse/override that mind's eye picture with the insertion of the single word, "probability," at the end. For you, this turns it into a multiple event, math question. For many, if not most people, it does not.

Yes, I understand that many (if not most) people will get this wrong. That doesn't change what the correct answer is.

The piece of writing is at odds with itself, and probably purposefully so. It starts off with a single event in present tense. The piece of writing establishes itself as being about that single event. The addition of the word "probability" after the fact doesn't - and shouldn't necessarily - make this about multiple events. The author undoubtedly did this on purpose. It's either a really bad piece of writing or a deliberately manipulative piece of writing designed to divide the readers into two at-odds groups. If you look at this as a piece of writing, which it is, rather than as a math problem, there is no reason for the use of the word "probability" to override the present tense description of a single event. If you look at this as a math problem, which it probably also is (but not absolutely necessarily due to "probability" having a non-math primary definition), then the use of the "probability" at the very end frames it as a multiple event problem.

You are over analyzing.

So, the context is not crystal clear. The beginning of the question frames it as one thing. The use of "probability" at the end frames it as something else at odds (for many, if not most readers) with its own beginning. Arci chooses to have the end of the question, with "probability," frame the beginning. Many people choose to have the beginning of the question, with a single event, frame the end. To add to the layers of this, "probability" has its own multiple definitions, and the present-tense, single-event opening could be defined as hypothetical, even though there is no clear reason to do so.

The initial part is just framing the problem. It is not asking a single question. You are trying to read into it far more than was intended or reasonable.

This question is not a math equation. It is a piece of writing. It should foremost be analyzed as a piece of writing before being analyzed as a math equation.

Sorry, asking for a "probability " is clearly a math question. Framing the situation as dice clearly shows this is a typical probability question.

[arcimede$]

I tried to "read" the posts above but I got lost. I would like to say that while I was at Caesars during Memorial Weekend I read the original question to as many craps dealers as I was able to and they all said the answer was 1/6.

Did you explain to them why the correct answer is 1/11? I suspect most of them would have said something like "Ah, yes I can see that is the right answer".

[Rob.Singer]

I know arci has trouble sleeping when he doesn't have the last word. It's what people like him have a need to do. But based on his less-than-certain and rather elementary line item veto of everything redietz said, one cannot help coming to the conclusion that red very effectively broke down then entire context of the original question--clearly on an irritating level for the 1in11ers, and from reading arci's response, well above their heads. Red most definitely has no need to come back and win this one twice.

[Alan Mendelson]

Excellent line redietz: "the question ... is not an equation."