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.
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.