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Benford's Law

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Hi Friends,

  While researching unrelated scientific subject matter I came across an article on Benford's Law.  I decided that LP should/could benefit.  I see that Win D already brought this up on November 25, 2004.

  Of particular interest is how it can be used to determine whether a lottery is being run fairly or not.  You could probably sue the state lottery if Benford's Law proves that they are cheating.

http://www.abc.net.au/science/k2/moments/s116315.htm

 
Hope you enjoy it as much as I did.  I'm doing good, moving into the last rental I will have before I start building my own house.  Scrapped the underground house plan last year to keep Terry and Alex happy.  I have since drawn up plans for a cordwood/strawbale hybrid that uses passive solar.

My new landlord is a co-worker who happens to share my enthusiasm for earth-friendly home design and diy subject material.  Saving a bundle on rent in exchange for labor.  Which means more money going into my own house.

I'm taking the computer down tonight.  I don't know when I'll have my own connection again; so I had to soak up as much research as I could to keep the gears churning.

My latest project deals with Mycology.  I have isolated a strain of Morchella crassipes ("Bigfoot" White Morels) which I harvested from my property this spring.  The mycelium is growing very well in several water cultures and I have succeeded in transferring that to feed corn spawn.  It is growing very well at the moment.

Trying to perfect and patent a commercial technique of cultivation.  There is a patent out there with one company already producing morels in Tennessee.  I'm working on the second.  At the very least I'll start a business around morels.  We have a mushroom festival each year as well as having a market for goods and services related to morel hunting and propagation.  Who knows.....

Anyhoo, enjoy the article....

LANTERN's avatar - kilroy 28_173_reasonably_small.jpg

Glad to have you back again George and good luck.

CARBOB's avatar - ga lottery.png.gif

George,

  Nice to hear from you. Sounds like, you are enjoying yourself and wish you success in the future. I always found your posts on the lottery very informative.

Carbob

SirMetro's avatar - center

" Scrapped the underground house plan last year to keep Terry and Alex happy."

Sounds like a familiar statement...reckon it goes without saying...pick your battles carefully, some you just know you can't win. BTW...an Underground house is my ultimate dream home.

Sir Metro

NemeSys's avatar - Nemesis

Interesting. I'd never heard of Benford's law. If lottery numbers followed it two conclusions could be drawn:

1) The lottery operator is cheating.

2) The draw machine just wasn't designed well enough (the standard statistical tests for randomness would also indicate this).

Badger's avatar - adu50016 NorthAmericanBadger.jpg

Interesting. I'd never heard of Benford's law. If lottery numbers followed it two conclusions could be drawn:

1) The lottery operator is cheating.

2) The draw machine just wasn't designed well enough (the standard statistical tests for randomness would also indicate this).

For the heck of it, I did a backcheck on IN and WI Pick 3, using all drawings that have been picked since the games started. (using Versabet34 software) All ten digits came out in the first position between 9.5% and 10.5% which is what you would think for a random game. Benford's Law didn't apply, so it appears that at least those two states aren't cheating. Smiley

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what about bayes therorem

does it apply and if it does how

NemeSys's avatar - Nemesis

Briefly, Bayes' Theorem states that the probability of A given B times the probability of B equals the probability of both events A and B occurring together and also equals the probability of B given A times the probability of A. As an equation:

            P(B|A) P(A)
P(A|B) = --------------
                  P(B)

Both the law and the equation can be extended in several ways.

Bayesian probability is not the same as frequency probability (which is what most people are talking about when they mention probability). Frequency probability is, as the name suggests, built on observational data from which frequency distributions are derived. In Bayesian statistics hypotheses are derived by inference (or even personal experience), and updated accordingly rather than relying on sets of standard distributions and tables. I've noticed several people here modify their predictions according to past results, so their approach can be said to be Bayesian.

LANTERN's avatar - kilroy 28_173_reasonably_small.jpg

Probability or random that does not take into account pass behavior or past draws, will give fewer right predictions, than probability that does take into account the past draws.

General probability is good in general, but not so good for particular uses like the lottery and even less usefull for a particular lottery like pick 3 than for the lottery in general.

Results is all that counts.

Good luck.

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i think chaos is the best predictor, if one could only predict it.

even if you know the picture is going to be completed, there is no telling when.

 

psykomo's avatar - animal shark.jpg

 

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PSYKOMO 

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