Understanding “randomness”

Question

I can\'t get my head around this, which is more random?

rand()

OR:

rand() * rand()

I´m f

Answer 1

The concept you're looking for is "entropy," the "degree" of disorder of a string of bits. The idea is easiest to understand in terms of the concept of "maximum entropy".

An approximate definition of a string of bits with maximum entropy is that it cannot be expressed exactly in terms of a shorter string of bits (ie. using some algorithm to expand the smaller string back to the original string).

The relevance of maximum entropy to randomness stems from the fact that if you pick a number "at random", you will almost certainly pick a number whose bit string is close to having maximum entropy, that is, it can't be compressed. This is our best understanding of what characterizes a "random" number.

So, if you want to make a random number out of two random samples which is "twice" as random, you'd concatenate the two bit strings together. Practically, you'd just stuff the samples into the high and low halves of a double length word.

On a more practical note, if you find yourself saddled with a crappy rand(), it can sometimes help to xor a couple of samples together --- although, if its truly broken even that procedure won't help.