On: Scrambling eggs for Spotify with Knuth's Fibonacci hashing

[nemetroid]

The odds of hearing a specific song that was played yesterday is ~1%, the odds of hearing any song that was played yesterday is ~10%.

[_teyd → nemetroid]

What are the chances of hearing the same three or four every day for a week though out of a set of a thousand? Certainly that must be quite unlikely.

[crazygringo → nemetroid]

No it's not. That's already accounted for by the "10*".

It's 1%. Any specific song is 0.1%.

[nemetroid → crazygringo]

That's not quite right. You need one 10 for the fact that you listened to ten songs yesterday, and another 10 for the fact that you're listening to ten songs today.

Assume that you got 10 unique songs yesterday, which is the case ~96% of the time. Then there are 990 songs you didn't hear yesterday, and for every song you listen to today, there is a 990/1000 chance that it's one of those songs. Hence the chance of only hearing new songs today is (990/1000)^10 = 90.4%.