Re: Repeated digits in Pi -- the Feynman point

On Mon, 23 Jun 2025 16:14:19 +0000, David Entwistle wrote:

On Sun, 22 Jun 2025 19:15:32 +0000, HenHanna wrote:
>

          The Feynman point refers to the sequence of six consecutive
nines (999999) that appears in the decimal expansion of pi (π), starting
at the 762nd digit after the decimal point. This point is notable
because such a long run of identical digits is statistically rare so
early in the sequence, leading to its fame as a mathematical curiosity.

>
>
I didn't immediately see anything surprising about the six consecutive
nines, but I've thought about it...
>
If the following isn't right, could you put me straight?

  I hope you don't mean  ME...

>
With a number system including ten single-digit integers, zero to nine,
for a base ten number system, if the sequence of numbers is random
(which
pi isn't),

         Really?   i thought  Pi was random.

 then there is a one in ten probability that any given digit
will be followed by the same digit. There is a nine tenths probability
that the subsequent digit will be different. The probability of three
identical digits is one in ten multiplied by by one in ten, or a
probability of one in one hundred of three identical digits following
each
other. If the sequence of identical digits is n digits long, then the
probability of it happening in a random sequence of digits is one in
10^(n-1).
>
So, the probability of six nines occurring together, in a random
sequence,
would be one in one hundred thousand. If 999999 occurs after the 762nd
digit after the decimal point of pi, I now recognize that is surprising.
>
Thanks I feel better for that.

_______________________
Almost every day....  i get briefed   from my fav AI.
     I just  got tutored by AI  on the following....
When flipping a fair coin repeatedly, the expected number of tosses
needed to see 6 consecutive heads is:     Expected tosses = 126
When randomly selecting digits from 0 to 9, the expected number of
digits you need to draw before seeing 6 consecutive 9’s is:
Expected digits = 1,111,110
      So how unusual or UNexpected is that?
      (the Actual  Feynmann  point )
Is that the T-test?   p-value?   I'll ask my AI maybe tomorrow.