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From: HenHanna <HenHanna@dev.null>
Newsgroups: rec.puzzles
Subject: Re: Repeated digits in Pi -- the Feynman point
Date: Mon, 23 Jun 2025 19:58:59 +0000
Organization: novaBBS
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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.