## Sequences of Die Rolls

**Moderators:** mvs_staff, forum_admin, Marilyn

msaintpc wrote:Remember, I'M the one who stated that others write most of her commentary.

Kindly clearly define the expression "her commentary" with examples you do not attribute to Marilyn.

She has said that she has difficulty removing fraudulent material from her website,

The homeopathy site was not "her website". And Marilyn has never mentioned "removing fraudulent material" under any other circumstance to my knowledge.

now here you are, revealing an impersonator,

The "impersonator" has not been revealed; only the impersonation.

thereby actually fortifying my assertion.

Please clearly define your assertion. Is it that you think Marilyn does not write all of her column and blog?

I AM familiar with her writings, actually more familiar with then than most people on this forum

How would you know?

, and this is why I KNOW she isn't behind many comments bearing her name.

Nonsense: you don't "know" anything of the sort. Are you cognizant of the difference between knowledge and speculation?

SHE is always thorough, without lacunae, and concise,

Marilyn has limited column space and rarely meets this criteria, although she does well at brevity.

whereby, many of her imposters/impersonators, haven't the ability to a-priorily, make an incontravertable

Do you mean "incontrovertible" to go along with "furthermore" and your 200+ IQ? Why do you put in three commas?

case as she always does when she's doing the talking.

Talking, as on Channer interviews, or writing?

Even to the novice, it is quite evident that this is far too much work, requiring too much time, and much too divergent for one human being to do.

Are you that novice? Please define the expression and basis of "much too divergent". Your assertion is more nonsense: Marilyn only writes a few lines per day, other than any book she may be working on.

*****

JeffJo wrote:robert 46 wrote: ...

As you can easily see, Robert seldom attempts to understand what other people write, so there isn't much point in replying to him.

Congratulations, JeffJo, this is the most self-contradictory post you have made yet. Why did you bother? And whose burden was it, if he thought I had misinterpreted his circumlocutory post, to clarify himself in plain English; which he has yet to accomplish?

So what is your opinion on msaintpc's thesis?

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

Marilyn's timely column:

(Italics added for emphasis)

Is there anyone who believes that Marilyn did not write the above response?

Parade website wrote:Is Our Language Changing for the Better?

ask marilyn Marilyn vos Savant November 09, 2011

Paula Chamberlain of West Point, Virginia, writes:

Marilyn: You wrote about words with expanded meanings, including the word "impact." (September 25, 2011) I have also noticed how the media and others--especially corporate America--have taken what I learned as nouns and expanded them into verbs. I've compiled a list, and "impact" is at the top: Instead of something having an impact on your life, it "impacts" your life. Rather than getting access to a file, you "access" the file. You don't inquire about the status of a situation; you "status" the situation. It's quicker that way! You don't have a partner; you "partner" with another person. You don't turn the power on; you "power" it on. And you may be a parent, but you also "parent" your children. I have more words on my list, but you get the idea. It seems that the language has been "trending" toward this phenomenon for several years now!

Marilyn responds:

Yes, and I don't mind. The trend is to efficiency and straightforwardness. For example, one need not say, "In order to...," when one can say, "To..." And it seems wordy to say, "on a daily basis," when one can simply say "daily."

(Italics added for emphasis)

Is there anyone who believes that Marilyn did not write the above response?

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

msaintpc wrote:...actually commanded of us in order to survive as a species...

robert 46 wrote:Her blog at the parade.com website, which she writes to daily...

Note that the bold type is wordy...

Marilyn wrote:...one need not say, "In order to...," when one can say, "To..." And it seems wordy to say, "on a daily basis," when one can simply say "daily."

msaintpc wrote:I highly doubt she even sees these articles and comments...

Definitely another faulty opinion.

Now that sounds like Marilyn, the Marilyn I love to read

They all are the Marilyn we love to read.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

### Followup

Parade wrote:ask marilyn Marilyn vos Savant March 19, 2012

Ask Marilyn: Still Not Convinced About the Die-Rolling Answer?

Alan Moger of Waterford, Connecticut, writes:

Marilyn: The math instructor who wrote about your die-rolling answer was correct. You were wrong. (October 23, 2011) I also teach math, and the string of consecutive 1's is equally probable. Try considering each roll separately. One number is as likely as any other number.

Marilyn responds:

I've been swamped with mail from readers who think the same. The question was, "Say you plan to roll a die 20 times. Which result is more likely: a) 11111111111111111111; or b) 66234441536125563152?"

I said they are equally likely and added, "But let‚s say you rolled a die out of my view and then said that the results were one of those series. Which is more likely to be the one you rolled? The answer is (b) because the roll has already occurred. It's far more likely that the roll was a mixed bunch of numbers than a series of ones."

That second statement is freaking out way too many math instructors who should know better! Here‚s another way to explain: The difference is that the first question was about the future; the second question was about the past.

For example, I have just rolled a die 20 times and written down the result. (No kidding.) It is one of these: a) 11111111111111111111; or b) 44132411666623551133. Now say that I offer to pay you $100 if you can guess which one I rolled. Given that you know the roll has already occurred, and it is indeed one of those two strings, wouldn‚t you choose the second one?!

Considering b) as representative of a generic sequence, b) is expected to have been the sequence rolled.

Note for concerned parties: The apostrophe is left of the "enter" key.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Followup

robert 46 wrote:Considering b) as representative of a generic sequence, b) is expected to have been the sequence rolled.

Yes, that is most certainly the question Marilyn is answering. Unfortunately, it is not the one that was asked. To be that question, it must be made explicit that b) is an example, and not a specific sequence that is being compared.

- JeffJo
- Intellectual
**Posts:**2140**Joined:**Tue Mar 10, 2009 11:01 am

### Re: Followup

JeffJo wrote:robert 46 wrote:Considering b) as representative of a generic sequence, b) is expected to have been the sequence rolled.

Yes, that is most certainly the question Marilyn is answering. Unfortunately, it is not the one that was asked. To be that question, it must be made explicit that b) is an example, and not a specific sequence that is being compared.

Given the one-time occurrence, the problem appears to be comparing the specific with the specific. However, whereas statistics proves probability we should consider how the problem repeats:

1. a) and b) both remain the same.

2. a) remains the same, b) changes

3. a) changes, b) remains the same

4. a) and b) both change

If we hypothesize that 2. is the to-be-expected repetition mode then statistically the problem is comparing the specific with the general such that the specific, apparently unlikely, sequence a) is fabricated; and the general, apparently more likely, sequences b) are actual: in each instance.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Followup

robert 46 wrote:Given the one-time occurrence, the problem appears to be comparing the specific with the specific.

Because it is.

However, whereas statistics proves probability

"Statistics" has nothing to do with "proving probability."

we should consider how the problem repeats:

No, we shouldn't; there is no reason to. Besides, "statistics"" has nothing to do with "how the problem repeats" either. This is just jargon you made up to try to convince others you are right, when it is obvious you have no idea what you are talking about.

- JeffJo
- Intellectual
**Posts:**2140**Joined:**Tue Mar 10, 2009 11:01 am

### Re: Followup

JeffJo wrote:robert 46 wrote:...However, whereas statistics proves probability

"Statistics" has nothing to do with "proving probability."

The calculated probability is the asymptote, and if the statistics approaches the asymptote it proves the correctness of the probability.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Followup

robert 46 wrote:The calculated probability is the asymptote, and if the statistics approaches the asymptote it proves the correctness of the probability.

There are no statistics in thought problems. You don't understand what the term means.

But the theorized (not calculated) probability should match what you expect (not achieve) the frequency to be after many repitotions. But it proves nothing; especially if, as you always do, you make the same mistakes in your theorizing as in your expectations.

- JeffJo
- Intellectual
**Posts:**2140**Joined:**Tue Mar 10, 2009 11:01 am

### Re: Followup

JeffJo wrote:robert 46 wrote:The calculated probability is the asymptote, and if the statistics approaches the asymptote it proves the correctness of the probability.

There are no statistics in thought problems. You don't understand what the term means.

But the theorized (not calculated) probability should match what you expect (not achieve) the frequency to be after many repitotions. But it proves nothing; especially if, as you always do, you make the same mistakes in your theorizing as in your expectations.

Marilyn has had the initial column and three followups. In each one she has compared all-1s with a bunch-of-digits. If comparing-the-singular-with-the-singular was correct then in half (two) of those cases all-1s would have been the sequence rolled. Yet I think the bunch-of-digits were the sequences rolled in all four instances; so the problem is, even in the individual case, comparing the specific (fabricated, all-1s) sequence with the general (rolled, bunch-of-digits) sequence.

***** 2012-03-26

Look at all of JeffJo's posts and you will find that he is the "pompous ass" who regulary projects his own failings; is so boorish and unprofessional as to make a mockery of his claim to be an accredited mathematician, which he steadfastly will not prove by refusing to identify himself; apparently has no professional contacts for support; is merely a name-dropper whenever he refers to the mathematical community; and apparently gets all of his information about probability from an on-line textbook, Grinstead & Snell, which saves him the chore of doing any deep thinking.

And, as you will see on the next page, summarily dismisses anything he has no logical rebuttal to by ignoring it.

***** 2012-03-29

As you see, he has a habit of making broad statements without any backing explanation. It is difficult say whether the deterioration in his posts over the years is consequential to senility because we don't know or have any clue as to JeffJo's age, but there has to be some reason for him becoming more and more curmudgeonly.

Last edited by robert 46 on Thu Mar 29, 2012 1:48 pm, edited 2 times in total.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Followup

robert 46 wrote:Marilyn has had the initial column and three followups. In each one she has compared all-1s with a bunch-of-digits.

Yes, she has. But each represents an independent question, despite your attempts to rationalize a solution, and the jargon you make up to do so.

Question: Which is more likely: a) Based on th fact that Robert 46 is the only person in the who subscribes to this logic he keeps insisting on, he is the only person in the world who understands how probability works; or b) Robert 46 is an argumemtative, pompous ass who picks his answers first, and then devises "logic" to support it regardless of any truth.

Based on his own reasoning, b) is much more likely.

- JeffJo
- Intellectual
**Posts:**2140**Joined:**Tue Mar 10, 2009 11:01 am

### Re: Followup

JeffJo wrote:robert 46 wrote:Marilyn has had the initial column and three followups. In each one she has compared all-1s with a bunch-of-digits.

Yes, she has. But each represents an independent question, despite your attempts to rationalize a solution, and the jargon you make up to do so.

If each is an independent question then a) should be as likely to be the actual sequence rolled as b) by your reasoning. But it is impossible to argue this on the awareness that all-1s has a 6^-20 probability of occurrence, but the actual sequence rolled is not specified in advance and can take on any value.

The only way to argue equal probability for a) and b) is repetition method 4.: a) and b) both change. But this is not applicable to the problem-in-question as it has obviously developed.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Followup

robert 46 wrote:If each is an independent question then a) should be as likely to be the actual sequence rolled as b) by your reasoning.

It is.

But it is impossible to argue this

No, it is not "impossible," unless you have accepted your answer first and are trying to rationalize why it is correct.

all-1s has a 6^-20 probability of occurrence, but the actual sequence rolled is not specified in advance and can take on any value.

Every sequences has a 6^-20 probability "in advance." It's called the prior probability for that reason.

The only way to argue equal probability for a) and b) is repetition method

No. Your "repetition method" has no validity, except as a way to understand why (not "prove that") each prior probability is 6^-20. In many (N*6^20, for N>>6^20) repetitions, you expect each sequenece (whether or not it is "specified in advance") to occur about N times, making the probability 6^-20

And the proper way to consider the concept of "picked in advance" is to assess the probability that either sequence was "picked in advance." You don't need an exact value, but if you can accept that the sequences of 1's was more likely to be picked, and not rolled, it is easy to say that it was less likely to be rolled. But then, you've dismissed this trivial argument, prefering your own fabrications to admitting I could be right.

- JeffJo
- Intellectual
**Posts:**2140**Joined:**Tue Mar 10, 2009 11:01 am

If the determiner specifies two sequences in advance (one to be the fabricated, the other to be the rolled) then they each have an equal probability: 6^-20. However, the probability that some other sequence will be the sequence rolled is a near certainty: 1-2/6^20. So we cannot expect to be able to specify the sequence rolled in advance.

This leaves two alternatives:

A) Specifying the fabricated sequence before rolling the die.

B) Rolling the die before specifying the fabricated sequence.

For A) there is a non-zero probability of a collision- that the sequence rolled will be the same as that fabricated, but it is negligible: 6^-20.

For B) there is a zero probability that the sequence rolled is the same as the sequence fabricated because the sequence rolled can be avoided by the determiner when fabricating a sequence.

So assume the fabricated sequence is specified first. Any other sequence has a very much higher probability of being rolled than the fabricated sequence: 1-6^-20. So the sequence fabricated represents the specific, and the sequence rolled represents the general. Most importantly it is impossible for the determiner to bias a fabricated sequence against an as yet unknown rolled sequence except by choosing a definitely less random-appearing sequence.

If the determiner chooses a fabricated sequence after rolling the die then the matter of the determiner's motives comes under consideration. Does the determiner choose a sequence apparently more, or less, random than the sequence rolled? It is nearly always the situation to be able to fabricate a sequence apparently less random, but less often able to fabricate a sequence apparently more random because the sequence rolled is itself a random event. There is no information in the problem to resolve the question, so it cannot be a factor in solving the problem.

As I have pointed out before: a person basically is not a probability agent. Thus arises the fundamental difficulty with some probability problems: How can we have a probability problem where a major factor is not probabilistic but has unknown quirky properties? The only way around this is to simplify those properties by assuming them being either constant or random, lacking any clarifying information.

The problem reduces to deciding which sequence is more specific and which is more general. The heuristic to use is that the sequence which appears less random is assigned to the fabricated/specific, and the sequence which appears more random is assigned to the rolled/general. If we use this heuristic we should be correct in a higher percentage of trials than not.

Why? Because less random-appearing sequences have a lower probability of being rolled than more random-appearing, there being fewer of them. If the determiner tries to choose a more random-appearing sequence as the fabricated sequence then it is more often to look marginally different from the sequence rolled. But if the determiner chooses a less random-appearing sequence as the fabricated sequence then the rolled sequence is more likely to be the more random-appearing.

Whereas we cannot factor in determiner bias consequential to an utter lack of information, we are left with considering a random mix.

Then the over all asymmetry definitely favors the less random-appearing as being the fabricated sequence because in the one case it is an expected toss-up as to which sequence would appear more likely the one fabricated, but in the other case there is a definite favoritism for the less random-appearing sequence being fabricated. Thus if we always choose the less random-appearing as fabricated it is statistically more often to actually be the fabricated sequence, under the conditions outlined.

The circumstance where the above is not expected to work is where the determiner rolls a die to create a fabricated sequence. But this technically is not fabricating a sequence, but merely creating two random sequences through the same random process.

This leaves two alternatives:

A) Specifying the fabricated sequence before rolling the die.

B) Rolling the die before specifying the fabricated sequence.

For A) there is a non-zero probability of a collision- that the sequence rolled will be the same as that fabricated, but it is negligible: 6^-20.

For B) there is a zero probability that the sequence rolled is the same as the sequence fabricated because the sequence rolled can be avoided by the determiner when fabricating a sequence.

So assume the fabricated sequence is specified first. Any other sequence has a very much higher probability of being rolled than the fabricated sequence: 1-6^-20. So the sequence fabricated represents the specific, and the sequence rolled represents the general. Most importantly it is impossible for the determiner to bias a fabricated sequence against an as yet unknown rolled sequence except by choosing a definitely less random-appearing sequence.

If the determiner chooses a fabricated sequence after rolling the die then the matter of the determiner's motives comes under consideration. Does the determiner choose a sequence apparently more, or less, random than the sequence rolled? It is nearly always the situation to be able to fabricate a sequence apparently less random, but less often able to fabricate a sequence apparently more random because the sequence rolled is itself a random event. There is no information in the problem to resolve the question, so it cannot be a factor in solving the problem.

As I have pointed out before: a person basically is not a probability agent. Thus arises the fundamental difficulty with some probability problems: How can we have a probability problem where a major factor is not probabilistic but has unknown quirky properties? The only way around this is to simplify those properties by assuming them being either constant or random, lacking any clarifying information.

The problem reduces to deciding which sequence is more specific and which is more general. The heuristic to use is that the sequence which appears less random is assigned to the fabricated/specific, and the sequence which appears more random is assigned to the rolled/general. If we use this heuristic we should be correct in a higher percentage of trials than not.

Why? Because less random-appearing sequences have a lower probability of being rolled than more random-appearing, there being fewer of them. If the determiner tries to choose a more random-appearing sequence as the fabricated sequence then it is more often to look marginally different from the sequence rolled. But if the determiner chooses a less random-appearing sequence as the fabricated sequence then the rolled sequence is more likely to be the more random-appearing.

Whereas we cannot factor in determiner bias consequential to an utter lack of information, we are left with considering a random mix.

Then the over all asymmetry definitely favors the less random-appearing as being the fabricated sequence because in the one case it is an expected toss-up as to which sequence would appear more likely the one fabricated, but in the other case there is a definite favoritism for the less random-appearing sequence being fabricated. Thus if we always choose the less random-appearing as fabricated it is statistically more often to actually be the fabricated sequence, under the conditions outlined.

The circumstance where the above is not expected to work is where the determiner rolls a die to create a fabricated sequence. But this technically is not fabricating a sequence, but merely creating two random sequences through the same random process.

- robert 46
- Intellectual
**Posts:**2227**Joined:**Mon Jun 18, 2007 9:21 am

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