For a logistic map using $f_r(x)=rx(1-x)$, what values of $r$ and starting $x$ are guaranteed (i.e., with an accepted proof) to be chaotic? I mean "chaotic" in the loosest sense: The limiting sequence of $x$ does not tend to a finite number of points.

I am currently using $r=3.8$ and starting $x=0.501234567890123456789$, but have only tested through 10,000 iterations. What is the probability that I am chaotic?