Life Not So Random

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Jack Ricci:

Here is an interesting read which is making its' rounds in a lot of email boxes recently. I'm not certain of its' accuracy, but it appears to be useful and applicable data for Lotto play! Should we use this type of information and try to formulate a plan or process based on Benford's Law that may aid us in better predicting our next " rational " pick of numbers in lottery play? Is there any software out there that already makes use of these kinds of data, ideas, or concepts? Take a gander... LottoHackJack
All in life is not so random..
Original Message

To: (Email Removed)
Sent: Thursday, August 05, 2004 3:26 PM
Subject: Interesting read...
...if you are fascinated by numbers and mathematical/statistical stuff.

Here is something that you may already be aware of, but if you have not heard of Benford's Law before, you will find this of interest (and hard to believe!!!)
Intuitively, most people assume that in a string of numbers sampled randomly from some body of data, the first non-zero digit could be any number from
1 through 9. All nine numbers would be regarded as equally probable.But, as Dr. Benford discovered, this is not so.
Given a string of numbers, the chance that the first digit will be 1 is not one in
nine, as you would imagine; according to Benford's Law, it is 30.1 percent, or
nearly one in three. The chance that the first number in the string will be
2 isonly 17.6 percent, and the probabilities that successive numbers will be the first
digit decline smoothly up to 9, which has only a 4.6 percent chance.

So what I hear you say, well the income tax agencies of several nations and several US states, large companies and accounting businesses are using detection software based on Benford's Law as a powerful and relatively simple
tool for pointing suspicion at frauds, embezzlers, tax evaders, sloppy accountants
and even computer bugs.
So what are the probabilities of the first digits. Well it follows the following
formula : the probability of any number "d" from 1 through 9 being the first digit
is log to the base 10 of (1 + 1/d). i.e.
Digit Probability

1 30.10%
2 17.61%
3 12.49%
4 9.69%
5 7.92%
6 6.69%
7 5.80%
8 5.12%
9 4.58%

Hard to believe but true. We (some friends and I) have tested it on a sample size
of 8,000, 55,000 and 65,000 numbers, and it all closely matches the above.

Further reading
http://www.rexswain.com/benford.html
http://www.math.yorku.ca/Who/Faculty/Brettler/bc 98/benford.html http://www.mathpages.com/home/kmath302/kmath302.htm

best regards,
Sanjay
e-mail: (Email Removed)
Cell: +27 (83) 449-6848
Tel: +27 (11) 234-9321
Fax: +27 (11) 234-9329
"Don't dwell on the past. Live the Moment. Embrace the future."

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John:

In a 6/49 draw the digit *1* should appear as a first digit 22.5% of the time i.e. 1, 10,11..19 = 11 numbers and 11/49 = 22.5% Same for 2,3 & 4
The other numbers 5,6,7,8, & 9 make up the balance i.e. 2% of appearances each.
I did a check of the SA main lottery with 386 draws to date and I included the bonus number.
Results:-

1 23.0%
2 22.1%
3 21.3%
4 22.8%
5 1.8%
6 2.0%
7 2.4%
8 2.3%
9 2.1%

Any thoughts?
John

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EdH:

[nq:1]Here is an interesting read which is making its' rounds in a lot of email boxes recently. I'm not certain of its' accuracy, but it appears to be useful and applicable data for Lotto play![/nq]
Very accurate from what I have read in a scientific publication a while ago. Unfortunately, Benford's Law is not applicable to lottery play. That is to say using Benford's Law as a strategy to select numbers to bet on.
Benford's Law may be useful in deciding what NOT to choose as numbers as it may reflect what joe public may select and hence increase the likelihood of a shared prize and much reduced winnings.
[nq:1]Should we use this type of information and try to formulate a plan or process based on Benford's Law that may aid us in better predicting our next " rational " pick of numbers in lottery play?[/nq]
No
[nq:1]Is there any software out there that already makes use of these kinds of data, ideas, or concepts? Take a gander... LottoHackJack All in life is not so random..[/nq]
Huge Snip
[nq:1]Further reading http://www.rexswain.com/benford.html [/nq]
From the above article:
The fit of number sets with Benford's Law is not infallible.

"You can't use it to improve your chances in a lottery," Dr. Nigrini said. "In a lottery someone simply pulls a series of balls out of a jar, or something like that. The balls are not really numbers; they are labeled with numbers, but they could just as easily be labeled with the names of animals. The numbers they represent are uniformly distributed, every number has an equal chance, and Benford's Law does not apply to uniform distributions."
EdH

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EdH:

[nq:1]In a 6/49 draw the digit *1* should appear as a first digit 22.5% of the time i.e. 1, ... with 386 draws to date and I included the bonus number. Results:- 1 23.0% 2 22.1% 3 21.3% 4 22.8%[/nq]
A Big difference in percentages because the ball numbers only go up to
49.
[nq:1]5 1.8% 6 2.0% 7 2.4% 8 2.3% 9 2.1% Any thoughts? John[/nq]
No predictive value.
Which horses (1,2,3,4,5,6,7,8,9) are going to come in and in which order?
Not sure how you did your calculations John
[nq:1]In a 6/49 draw the digit *1* should appear as a first digit 22.5% of the time[/nq]
How can 5,6,7,8,9 crop up as the first digit?
EdH

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Dave:

The draw numbers are from 1 to 49 ; therefore numbers 5,6,7,8 & 9 have those numbers as first (and only) digit hence the +/- 2% ( 1/49) probability of being drawn.
Dave

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gARY :

Hi ya Ed,
Nice to see you bunging a post or two in here.
[nq:1]The draw numbers are from 1 to 49 ; therefore numbers 5,6,7,8 & 9 have those numbers as first (and only) digit hence the +/- 2% ( 1/49) probability of being drawn. Dave[/nq]
Hello Dave,
Taking just the focus at this point . . ."first (and only) digit".

Have you looked at least "last (and only) digit*" as in a zero, 4 only (10 ,20 ,30 ,40) ?
Good luck to you's both,
gARY

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Dave:

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EdH:

[nq:1]Hi ya Ed, Nice to see you bunging a post or two in here.[/nq]
[nq:2]The draw numbers are from 1 to 49 ; therefore ... the +/- 2% ( 1/49) probability of being drawn. Dave[/nq]
[nq:1]Hello Dave, Taking just the focus at this point . . ."first (and only) digit*". Have you looked at least "last (and only) digit" as in a zero, 4 only (10 ,20 ,30 ,40) ? Good luck to you's both, gARY[/nq]
Hi gARY,
I've got some free time on me hands so have stuck my head over the castle walls to try and help out on this Benford's Law thing.

The law seems to hold for many real world applications. The reason why IMHO is very simple but the math is complicated. Logarithms - yuch.
Benford's law works because people normally use number 1 before they use number 2 and then use number 3 before number 4 and so on. Fundamentally, there is some form of human involvement. For example, it would be reasonable to suppose that most house numbers will start with a number 1 then a 2 then a 3 etc.
[nq:1]Results:- 1 23.0% 2 22.1% 3 21.3% 4 22.8% 5 1.8% 6 2.0% 7 2.4% 8 2.3% 9 2.1% Any thoughts? John[/nq]
It is unclear, to me, without doing some 'numerology' is the how John obtained the results above. The data is laid out as digits 1 to 9 in one column implying that all numbers are treated equally. eg all are 'first digits'.
This is not correct and I questioned that in my initial response - not really wanting to jump in unless I knew more about the methods used to obtain the Benford-like data.
Dave responded:
[nq:1]The draw numbers are from 1 to 49 ; therefore numbers 5,6,7,8 & 9 have those numbers as first (and only) digit hence the +/- 2% ( 1/49) probability of being drawn.[/nq]
I'm not sure what 'those numbers' means:
I think this means that 5,6,7,8,9 are not 'first digits' but are 'linked' somehow to the 'first digits'. In which case a fatal error has been made in putting the numbers 1 to 9 in order and implying that there is something significant there. In other words Jack inadvertanly made the data look Benford-like.
The data is fatally flawed because the numbers 1 to 4 are 'first digits' and 5 to 9 are not 'first digits'.
This is an example of what I would call 'numerology'. The misuse of numbers - in this case - by listing entities that are not alike into a group that appears alike then trying to make judgements from this flawed data.
The method used is flawed. Unlike items should not normally be listed with like items when analysing data. It is clear, to me, that there are two subsets of data combined together into one larger set.

If 1 to 4 are oranges and 5 to 9 are apples then anyone for juggling ?

Benford's Law cannot be used for lottery predictions because the law requires some human involvement whereas lottery balls do not require human involvement in their random selection.
Benford's law 'may' be useful in helping to ascertain which numbers are commonly selected by people. Here there is human involvement. Thus helping us to avoid particular popular sequences. eg 1,2,3,4,5,6 because of the reduced prize money due to sharing the spoils with too many punters.
A bit wordy but I hope this helps to explain my reasoning.

Regards
EdH

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gARY :

Looks like you will learn, as you will not even look at the other side of the coin (excuse the phase)?
To get ahead (if there is such a thing) whilst playing lotto, you must study everything 'on it's head' also.
As such, ya learn.
Good luck,
gARY

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gARY :

[nq:1]Hi gARY, I've got some free time on me hands so have stuck my head over the castle walls to ... reasonable to suppose that most house numbers will start with a number 1 then a 2 then a 3 etc.[/nq]
"Numbers" are but valid marks recognized World Wide in monetary terms but not in lotto machine language. In lotto the "Numbers" are marks on a ball, in no particular order. . .
EXCEPT machine placement before the draw, because a human/s was involved!

This is the key (1-49) and where we focus I'm sure, too spot on really!

[nq:1]A bit wordy but I hope this helps to explain my reasoning. Regards EdH[/nq]
We rowing the same boat Ed? Emotion: wink

Nice one,
gARY
BTW. New RedCar users are plenty etc. Please mail me (your new address?) Ed, Thanx.

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Life Not So Random

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