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Benford's Law

Topic closed. 5 replies. Last post 10 years ago by Thoth.

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tntea's avatar - Lottery-059.jpg

United States
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Posted: January 10, 2007, 11:11 pm - IP Logged
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    NY
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    October 16, 2005
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    Posted: January 11, 2007, 12:36 pm - IP Logged

    Benford's law definitely points to some interesting stuff, but the simple form of it is really just that numbers that aren't random don't have a random distribution, and the interesting conclusion is that a lot of numbers we might think would be random aren't.

      alsports2000's avatar - 23606770150900
      Pharr, Texas
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      Posted: January 11, 2007, 10:10 pm - IP Logged

      Read the article on Benford's Law and learned the the number one is a more probable number to come out from one to nine more often. How does that fit in to the Texas pick three's midday and evenings???? Thanks. AL. What?

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        NY
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        Posted: January 12, 2007, 2:08 am - IP Logged

        Read the article on Benford's Law and learned the the number one is a more probable number to come out from one to nine more often. How does that fit in to the Texas pick three's midday and evenings???? Thanks. AL. What?

        It doesn't. Lottery results are random and don't  follow Benford's law.

          Thoth's avatar - binary
          Findlay, Ohio
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          Posted: January 12, 2007, 11:39 am - IP Logged

          It doesn't. Lottery results are random and don't  follow Benford's law.

          The digits on the balls themselves (or electronically selected digits/combos in an RNG drawing) do not follow benfords law.  We will not find the digit one being drawn in a significantly higher amount than any of the other digits in the game.  However, the skips of the digits and/or combos follow Benford's Law very closely. 

          If you do some reading into Benford's Law you will see that it has been attributed to the effect of the probability of probability.  I have found (and shown) that the skips of digits and combos do follow Benford's law quite closely in the Pick 3 game.  Skips are random events, just like the digits and combos being drawn are random events.  However, some skips are much more probable than others and that is why we see them more often.

          ~Probability=Odds in Motion~

            Thoth's avatar - binary
            Findlay, Ohio
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            Posted: January 12, 2007, 12:26 pm - IP Logged

            Take a look at the performance of the following two skips ranges:

             The 1,s Range
            1, 10:19, 100:199

            The 2,s Range
            2, 20:29, 200:299

            Both the ranges include 111 possible points for skips to end in.  I intentionally left out 1000:1999 from the 1,s range and 2000:2999 from the 2,s range.  This shows that a bias does exist even without including that vast stretch of skips from 1000 to 1999 games later.  In every instance, hits in the 1,s range occured more often.

            STATE1's2's%
            OH1135101110.93%
            PA122411119.23%
            NJ1338114314.57%
            MD1529130314.78%
            NH105093011.43%

            ~Probability=Odds in Motion~