There's maybe some counterintuitive math going on here.

If you have 100 songs and listen to 1 song per day (which is 1% of the library), on any given day your odds of hearing the same song as yesterday are 1 in a 100.

If you have 1000 songs and listen to 10 per day (still 1%), the odds of hearing a song that was also played yesterday are a little less than 1 in 10, right?

So what matters is not only what fraction of your library's play time you sample daily, but also how finely subdivided the time is into individual tracks for sampling.