Which numbers have digits that are random or nearly so? I was told that the digits of $\pi$ are random (or at least nearly so). Would $\pi$/2 etc. also have that property? Which other numbers have that property? In case there are a vast number of them, do they have some common properties such that one could computationally randomly pick one out of a class of such numbers for use? If one combines two such numbers digitwise $\mod 10$, is it always true that the result can only be better random and never worse?
 A: $\pi$ is conjectured to be a normal number, which means that all digits and all combinations of digits appear just as often as you'd expect if you were choosing digits randomly, at least asymptotically. Almost all numbers share this property, though it's hard to prove that a given number has it. Numbers known to be non-normal include rational numbers.
A: On your final question

If one combines two such numbers digitwise mod 10, is it always true that the result can only be better random and never worse?

the answer is no if combining digitwise means interleaving:  if $\pi$ has random digits then so too does $10-\pi \approx 6.858407\ldots$, but their combination is decidely not random in that you can predict half the digitis from the previous digits.
A: The digits of $\pi$ are, of course, deterministic and so not random. But looking only at the digits, they are nonrandom in an important sense: they have low Kolmogorov complexity. There are short algorithms that can (given enough time) generate as many digits of $\pi$ as desired, and so the digits of $\pi$ are highly compressible: instead of writing out the first billion digits, taking on the order of a billion bytes, you can write a program for generating pi to a given number of digits (taking a few kilobytes) and then the number one billion, taking a few additional bytes. Truly random numbers cannot be compressed in this fashion.
