h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Doesn't this work only work when repeating the experiment with a varied upper limit?

Suppose the upper limit was 29. Wouldn't the chances of the first digit being one or two be the same (33.3%)?

With a random upper limit the mentioned distribution pattern applies:

1. Pick any number greater than 10. Call it x.
2. Pick any number between 1 and x. Call it y. Do this 800 times, recording all values for y.
3. Go back to 1 and keep repeating until you get really bored, then do it 799 more times for good measure.

Without step 3, you will get a distribution pattern where one has the best chance of being the first digit, but the chances might be the same for two, if the x is greater than 29. I'm sure that would come up with some interesting patterns though, based on the value of x.

It is a curious little law. Do you know of any specific applications?

One application is the detection of fraud.
We run the following SQL across a database table of payments:

select count(*), userid_cd, right(reverse(convert(varchar(100), o_act_trans_amt)),1)
from tclmtrxn
group by userid_cd, right(reverse(convert(varchar(100), o_act_trans_amt)),1)

and then graph it using Excel.

Now if an employee is commiting a fraud they will tend to put in payments near the upper range of their authority limit (i.e. a not random distribution) so there will be a spike on the digit just below their payment authority limit...not cast iron proof, but indicative of a need to look in more detail at their schedule.

I believe that the SETI program also uses this to look for non-random radio signals i.e. intelligent ones, but have no hard and fast proof of this.