I think expecting Radio Paradise to have a playlist of 8 billion songs, or even 8 million songs, is quite a bit of lack of perspective. Do you ever come out in the real world? Even in my country where FM radio doesn't suck as hard as in the US, you'll hear the same song multiple times a day unless you'd go working, shopping and dining while wearing industrial ear protection. Because you seem to like numbers, here's some mathematics. Suppose a station has a playlist of 10000 songs. I have no idea how many songs the active playlist of RP has, but this seems reasonable, especially in the light of the following assumption. Suppose this station is run by DJ Random, who gives every song a number between 1 to 10000 and uses a perfect random number generator to pick the next song. Suppose you listen to 120 songs this way (at an average of 4 minutes per song, that would take 8 hours). The birthday paradox says that in this case (see simulation below), there's a 50% chance that you'll hear the same song twice in this time span! 

For a playlist of 50000 songs, the 50% chance of repetition is already reached at approx. 250 picks, not the expected 600. Of course, while many radio streams work this way, on RP this is not how it's done — luckily. First of all, Bill avoids the horrible transitions that DJ Random would produce, by combining songs that actually belong together. This reduces the amount of randomness, but of course Bill has a memory and will try to avoid repeating the same song often. To minimize repetition, he would need to create an ideal sequence of all songs once, and repeat this eternally. But that would become boring too, so as a compromise and to keep managing RP tractable, Bill recycles 'stretches' of playlist, slowly mutating them and discarding them after a while. And Bill is only human, so he'll play the songs that he likes a little bit more often than others. I wasted some of my time telling this story to show that things can be a whole lot worse, and I believe RP comes damn close to an ideal radio station. You just have to accept the fact that ideality doesn't exist and that some of the songs you don't like will be played, and repeated after a while.