Estimating Responses to the Dice Question

[redietz]

I think the 1/11 folks are trying to sidestep this one, so let me start up a new thread. My questions are very simple.

1) What percent of a general population, reading the original dice question for the first time, would answer 1/6?

2) What percent of a general population, reading the original dice question for the first time, would answer 1/11?

3) Would the 1/11ers be able to prove their case beyond a reasonable doubt in a US court with a jury of their peers?

Let's put those formidable IQs to work and see what people think. You know, the scary thing is, since this question has been around for decades, someone may have actually done a study (published or not) regarding this very question.

[regnis]

We can't find a jury of the peers of the 1/11ers. Where would we be able to find enough geniuses to form a jury?

Our standard jurors can barely read or write.

[redietz]

Regnis, I edited many a paper of math majors and engineers. My ex-girlfriend edited many, many more, including dissertations. If there's one thing math geniuses and our jury pools have in common, it's that they don't read or write very well.

[OneHitWonder]

If there's one thing math geniuses and our jury pools have in common, it's that they don't read or write very well.

I wouldn't call them math geniuses either. Ninety-nine percent of gambling forum people are not math geniuses. The other one percent takes a little "weeding out".

It never ceases to amaze me that people think the Wizard is a math genius. He's insulted when others don't think this. The uni-bomber was a math genius. There aren't many people with an extraordinary iq who can also create something original of staggering profundity. Googe "math genius".

What you are describing is likely a relative observation, redietz.

http://www.livescience.com/16897-mat...scalculia.html

[Alan Mendelson]

I asked the "original question" on my Facebook page. All but TWO people said the answer was 1/6. There were more than 300 responses with many of the 1/6 "friends" arguing with the two 1/11 friends.

There was a third 1/11 respondent who switched to 1/6 when she realized that with real, physical dice the answer could not be 1/11.

[redietz]

Wow -- that is quite a sample. That suggests a lot of things, but how about some others chime in here? C'mon, 1/11ers -- take a stab at answering the questions.

[arcimede$]

All we need is Alan to back his views with some real money.

[redietz]

I've never known arci to duck a question. The silence from the 1/11ers is deafening.

[arcimede$]

The questions are meaningless. Science is not a democracy. Just the fact you ask such silly questions is kind of amusing. We know the vast majority of people are poor at math. Exactly what do you think asking these questions would accomplish?

[Alan Mendelson]

What it accomplishes Arc is not scientific, but shows the misunderstanding of common English.

Look what we just saw today: Kewl telling us that probability must be determined before the throw of the two dice -- in effect admitting that he is ignoring the conditions presented in the problem which is that the dice have been thrown, and one is showing a 2.

And look at the further "evidence" of what the Wizard did in his video: rotating and changing the die that came to rest as a two, further altering the conditions of the original problem.

The fact is, you don't have to be a math expert to understand what the problem asks for and what conditions are presented. In fact, it is the math experts who ignore the facts and the conditions presented in the problem.

And when this is pointed out to the math experts they disregard the errors of their ways and continue to make the same bad calls and maintain that their changes fit what is the established norm for figuring probability.

Unfortunately, the original problem isn't the "textbook question" that fits the "textbook answer."

And while the "math experts" will stick to their "textbook answer" it's pretty clear to the rest of the world that this isn't the "textbook question."

[arcimede$]

Alan, your comment is pure nonsense. Probabilities are determined by understanding the problem. It has nothing to do with any actual dice throw. For example, we know the probability of a head in a fair coin toss is 1/2. No one needs to toss a coin to understand the probability.

[Zedd]

I’m quoting Wikipedia’s page on the Boy or Girl paradox…

One scientific study showed that when identical information was conveyed, but with different partially ambiguous wordings that emphasized different points, that the percentage of MBA students who answered 1/2 changed from 85% to 39%.

The Boy or Girl paradox is the same problem but uses gender of children instead of dice. So ½ is analogous to the 1/6 answer for the dice problem (and 1/3 is analogous to the 1/11 answer).

OneHitWonder recently yelled at me for using Wikipedia when I never did—so I can’t imagine how nuts this would make him. But here’s the link to the actual study. Unfortunately it’s not free, so I haven’t read it. It might be a good read though. http://psycnet.apa.org/?&fa=main.doi...3445.133.4.626

Anyways, asking the original question to the general public would most likely get a majority of 1/6 answers.
But if asking the question with the ambiguity cleared up (so the bet as described in the other thread), then I would suspect more 1/11 answers.

If in a US court, I believe it would be a hung jury. But I do think the 1/11ers would have a much better shot in court than the 1/6ers.

It should be noted that the 300 responses on Alan’s Facebook were among only about a dozen different people.

It should also be noted that the general population is not the idea group to answer a conditional probability question such as this. You may say it’s a English question all you want...but the bottom line is some understanding of probability is needed to comprehend and answer this problem correctly (which the general population and the 1/6ers on this forum lacks).

Now, bring this question (again with the ambiguity cleared) to a group of people with probability experience...then I'm sure the 1/11 answer would prevail.

[Alan Mendelson]

Now, bring this question (again with the ambiguity cleared) to a group of people with probability experience...then I'm sure the 1/11 answer would prevail.

But would the probability people make the same mistake you are making?

[Zedd]

But would the probability people make the same mistake you are making?

Again, the original question does have ambiguity. Since it is opened to interpretation, your “it’s an English question” argument does have some grounds. But once the ambiguity is killed, the English argument is slaughtered along with it.

If you ask; “two dice are rolled until at least one shows a deuce, what is the probability that both show a deuce?”…then there are no mistakes, it is 1/11.

[Alan Mendelson]

If you ask; “two dice are rolled until at least one shows a deuce, what is the probability that both show a deuce?”…then there are no mistakes, it is 1/11.

That's fine until you have to make a video showing it: one die with a 2 and the 11 faces you are presenting in your answer.

[redietz]

Ah, arci asked, what can we learn by asking such questions? Science, he says, is not a democracy. What are we to infer from such a statement, other than arci's superiority to the mere mortals who arrive at 1/6?

It's not that the 1/11ers argue their answer that's of interest; it's how they argue their answer. And what they choose to ignore both about the question and about their self presentation and about the public in which they seem to find themselves distastefully immersed.

Arci, care to answer the questions, or are they beneath you?

[arcimede$]

Ah, arci asked, what can we learn by asking such questions? Science, he says, is not a democracy. What are we to infer from such a statement, other than arci's superiority to the mere mortals who arrive at 1/6?

It's not that the 1/11ers argue their answer that's of interest; it's how they argue their answer. And what they choose to ignore both about the question and about their self presentation and about the public in which they seem to find themselves distastefully immersed.

Arci, care to answer the questions, or are they beneath you?

My answers would be as meaningless as the questions. I'd be guessing. What is real interesting is that anyone would think the questions are useful. You've backed yourself into a corner by trying to claim this problem is not clearly mathematical. Now you appear to be trying to justify that position.

[Alan Mendelson]

My answers would be as meaningless as the questions. I'd be guessing. What is real interesting is that anyone would think the questions are useful. You've backed yourself into a corner by trying to claim this problem is not clearly mathematical. Now you appear to be trying to justify that position.

It is mathematical. Unfortunately for you, Arc, you are not using the correct math because you can't understand -- or won't understand -- the actual question being asked.

This is very sad.

[arcimede$]

It is mathematical. Unfortunately for you, Arc, you are not using the correct math because you can't understand -- or won't understand -- the actual question being asked.

This is very sad.

LOL. I understand the question perfectly. That is why I proposed a test and you refuse to run a test and see what happens. I am 100% confident of the result. You obviously are not.

[Alan Mendelson]

LOL. I understand the question perfectly. That is why I proposed a test and you refuse to run a test and see what happens. I am 100% confident of the result. You obviously are not.

You do mine first: have two dice, with one showing a 2, and show me the 11 faces in your answer.