Estimating Responses to the Dice Question

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.

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.

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.

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.

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.

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Originally Posted by redietz

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.

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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

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

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

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?

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."

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.

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?

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Originally Posted by 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?

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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.

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

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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%.

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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.

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Originally Posted by arcimede$

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.

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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.

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Originally Posted by Zedd

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.

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

Arci, you seem to have trouble grasping the fact that it's writing, not an equation. I've told you this a dozen times, and you ignore it, which tells me something about you. Second, if most people reading it respond one way, but if it's reformulated into an equation, then they respond another way, then clearly there is a real issue with the original question, which you also choose to ignore. Third, if the question leads an audience to what to you is an incorrect response, then one would think you would lay blame at the author of the question, which you refuse to do.

I encountered this question many, many years ago, and it annoyed the living hell out me then and it annoys the hell out of me now because it's designed to be an "aha!" question that divides an audience into two camps. This whole attitude by people that there is a "great unwashed" that is incapable of understanding basic math and science is unbelievably arrogant. Propping up this attitude with poorly written trick questions that "prove" the gap between math-haves and math-have-nots is despicable.

Any reasonable person knows the probability for an event occurring is the same for one single event or for multiple events.

A reasonable person who doesn't know how to figure out the probability of an event occurring would know that doing the event many times (many trials) would be an indicator of what the probability of the event occurring.

In other words, a reasonable person would not dismiss a simulation.


FYI, I wrote a simulation where it checks for at least one die to be a 2. If at least one die is a 2, then it records the frequency of the other die. Yes, it was looking specifically at "the other die"....not both dice or anything. Just " other" die.

The frequency I got was about 9.08%.

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Originally Posted by Alan Mendelson

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

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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.

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Originally Posted by Alan Mendelson

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.

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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.

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Originally Posted by Zedd

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.

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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.

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Originally Posted by arcimede$

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.

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

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Originally Posted by Alan Mendelson

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.

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That's like trying to show a coin has 2 faces using a potato....

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Originally Posted by RS__

That's like trying to show a coin has 2 faces using a potato....

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Exactly. You cannot show 11 faces with a total of two dice when one die is frozen showing a 2. This is why the answer of 1/11 does not answer this question.

In order to facilitate your answer of 1/11 you must use both dice -- and the question has already given you the condition that one die is a 2.

As soon as one die is identified as a 2 -- there are only six faces on the second die to be considered.

It is every bit the same as the "spinner" problem on a craps table with the first die coming to rest as a 2.

I'll go on record as guessing that somewhere around 82-88% of the US general population would say 1/6 as the answer.

Here's a tell. When confronted with the statistics from Alan's Facebook page regarding this question, the 1/11ers responded with comments regarding how poorly the general population does with basic math and statistics. Nobody made the comment that the author of the question must be an example of how badly math guys write because he/she led people to a "wrong" conclusion. The 1/11ers who responded criticized the readers as a group and judged them, which seems harsh considering how many readers there were. They did not criticize the author, even though the likelihood of there being one really bad author seems (if probability principles are used here) more likely than a couple hundred really bad readers.

Maybe the proper conclusion isn't "general population bad in math," but "math guys really bad at writing and evaluating others' writing."

Redietz, after a while you might convince RS__ that he doesn't do so well in the reading comprehension arena. One look at how he sometimes gets laughed at on WoV for his head-scratching comments probably tells that tale. But if you think you're ever gonna get arci to confess to anything other than having mensa-level reading skills, don't stay on the toilet waiting. A more apropos comment for him might be "imagine living with that". Oh....that's a moot point.

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Originally Posted by Rob.Singer

Redietz, after a while you might convince RS__ that he doesn't do so well in the reading comprehension arena. One look at how he sometimes gets laughed at on WoV for his head-scratching comments probably tells that tale.

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Like which ones?


It's not the readers who have poor reading comprehension....I think most people don't use the proper logic when trying to determine the answer. ie: Month Hall problem.

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Originally Posted by Alan Mendelson

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

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Sorry Alan, but that has nothing to do with the original question. The original question is about probability. The only way to test the probability is through multiple events. The correct answer should converge rather quickly given the low number of possible combinations. Why are you unwilling to run the test which should take no more than 10-15 minutes (a half hour if you are methodical).

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Originally Posted by Alan Mendelson

Exactly. You cannot show 11 faces with a total of two dice when one die is frozen showing a 2. This is why the answer of 1/11 does not answer this question.

In order to facilitate your answer of 1/11 you must use both dice -- and the question has already given you the condition that one die is a 2.

As soon as one die is identified as a 2 -- there are only six faces on the second die to be considered.

It is every bit the same as the "spinner" problem on a craps table with the first die coming to rest as a 2.

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One problem Alan, that is not the question that was asked. The only way you'll be convinced is to run the test and see what answer you get. Hey, do it yourself at your own desk. All you need is a pair of dice and a piece of paper. The fact you won't do the test tells me you know you are wrong.

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Originally Posted by redietz

Maybe the proper conclusion isn't "general population bad in math," but "math guys really bad at writing and evaluating others' writing."

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Do you know if a ’math guy’ wrote this question? What if an English author wrote it? Anybody can write it. Then you’re back to “general population bad in math”.

You're absolutely correct, Zedd. That's why I put "at evaluating others' writing" at the end. If an English guy wrote it (odds against, I'd say, given the placement in a math forum and all, but point taken), that still doesn't excuse the evaluations -- or rather, lack of evaluations -- from the math-oriented folks.

I went through the same thought process when writing it, so all I can say to you is that I appreciate you reading carefully and asking the absolutely correct questions. I've learned quite a bit from this exercise, and hopefully the WoVers have, too. I have doubts about the latter.

P.S. I realize now that "or" rather than "and" should have been in that final sentence, but I'm trying to avoid "or" at this point, mainly because I'm still recovering from trying to figure out inclusive "or" versus non-inclusive. I hereby reinstate my use of "or" in normal conversation.

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Originally Posted by redietz

I have doubts about the latter.

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I'll make it easy for you. They exist only to feed the online casinos.

The administrators are the ones who have the time to waste for the online casinos' sponsorship. We aren't getting paid to do this, let alone to try to straighten people who don't want that to begin with.

They are fairly honest over there about nobody of note really doing the AP thing, or about very few trying it for any stretch of time. But like every other gambling forum, the topics mask the gambling addictions of many.

I would bet my last dollar that 99% of them continue to lose their last dollar gambling. Just the way it is. Those people simply do not want to learn. The reason that not a single one of them has achieved anything of not. Least of all the Wizard. Talk about persons who say idiotic mundane things.

The reason that we have to discuss this over here.

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Originally Posted by arcimede$

Sorry Alan, but that has nothing to do with the original question. The original question is about probability. The only way to test the probability is through multiple events. The correct answer should converge rather quickly given the low number of possible combinations. Why are you unwilling to run the test which should take no more than 10-15 minutes (a half hour if you are methodical).

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Arc, I did use two dice and rolled them according to the original question. And each time at least one die was a 2 the other die had a 1/6 chance of also showing a 2. And with at least one die showing a 2 I was unable to find 11 faces to consider for your 1/11 answer.

Really it amazes me how I couldn't find 11 faces. Why?

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Originally Posted by Alan Mendelson

Arc, I did use two dice and rolled them according to the original question. And each time at least one die was a 2 the other die had a 1/6 chance of also showing a 2. And with at least one die showing a 2 I was unable to find 11 faces to consider for your 1/11 answer.

Really it amazes me how I couldn't find 11 faces. Why?

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That's not the original question. There is no mention of "the other die" in the original question. It is getting more than obvious that you know you are wrong. Otherwise, you would do the simple test. Thanks for making it so obvious.

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Originally Posted by arcimede$

That's not the original question. There is no mention of "the other die" in the original question. It is getting more than obvious that you know you are wrong. Otherwise, you would do the simple test. Thanks for making it so obvious.

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You're right Arc. There's no "other die." There are just two of them. And at least one is showing a 2.

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Originally Posted by Alan Mendelson

You're right Arc. There's no "other die." There are just two of them. And at least one is showing a 2.

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Exactly, there are only two conditions to the problem. That's why I proposed the test to match those conditions. You mark one row when you see "at least one 2" and you mark another row when you see "a pair of 2s". You've then met the conditions of the problem. When you are done you divide the second number into the first number and if you are right that should be very close to 6. No more than a half hour of your time (much less probably) and you've proven to yourself that you are right (or wrong).