[gentoo-user] Re: OT: Mapping random numbers (PRNG)

[»Q« <boxcars@gmx.net>]

On Sat, 28 Jun 2014 19:53:08 -0500
Canek Peláez Valdés <caneko@gmail.com> wrote:

> On Sat, Jun 28, 2014 at 7:37 PM,  <gottlieb@nyu.edu> wrote:
> > On Sat, Jun 28 2014, Canek Peláez Valdés wrote:
> >
> >> That doesn't matter. Take a non-negative integer N; if you flip a
> >> coin an infinite number of times, then the probability of the coin
> >> landing on the same face N times in a row is 1.
> >
> > This is certainly true.
> >
> >> This means that it is *guaranteed* to happen
> >
> > That is not as clear.
> 
> Let me be more precise (and please correct me if I'm wrong): It is
> guaranteed to happen at some point in the infinite sequence of random
> flip coins, but we cannot know when it will happen, only that it will
> happen.
> 
> That's the way I got it when I took my probability courses, admittedly
> many years ago.

The probability is 1 in the sense that the as the number of flips M
increases, so does the probability of getting N heads (or tails) in a
row also increases, and the upper bound for the sequence of
probabilities is 1.  It's not a probability about something which
actually happens;  no one so far has been able to flip a coin an
infinite number of times, not even a computer.

> In any way, even if I'm wrong and it is not guaranteed, the main point
> remains true: the probability of getting a large sequence of the same
> number from a RNG is 1 for every true random RNG, and therefore seeing
> a large sequence of the same number form a RNG doesn't (technically)
> means that it is broken.

It's true that that wouldn't *prove* the generator is broken.  But it
might be a good reason to take another look at the algorithm.
> 
> Regards.