Shuffle mode?

I think there may be some bias in the "random" selection, depending on the program

I noticed on my iPod Classic that if I didn't skip songs from a particular artist, I'd be more likely get more played from the same artist... Just as an example...

Never really compared it to iTunes's shuffle because I avoided using it, but I'd presume it's somewhat similar

I was thinking the exact same thing a while ago and I looked up how they came at these supposedly "random" numbers.
Turns out most devices don't generate real random numbers.

They're known as Pseudorandom number generators or deterministic random bit generators.
It uses an algorithm for generating a sequence of numbers that approximates the properties of random numbers. The sequence is not truly random in that it is completely determined by a relatively small set of initial values.

So technically it isn't random, but it's random enough for the purposes such as shuffling songs.

One does not just simply pick a random song.