On Sat, 28 Jun 2014 19:53:08 -0500 Canek Peláez Valdés <can...@gmail.com> wrote:
> On Sat, Jun 28, 2014 at 7:37 PM, <gottl...@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.
