Quote:
Originally Posted by Didace
Can you walk through this equation with words? Something doesn't seem quite right to me.
Because it's not. In the post I made after that I fixed it:
Quote:
Originally Posted by heehaww
E(50) = 1 + (.5-.0025)*E(50) + .5*E(49)
There will be at least 1 play no matter what. There will be
only 1 play .0025 of the time.
.5-.0025 of the time, a song >10 (but not 50) is chosen, so we're right back where we started.
.5 of the time, a song <11 is chosen and the song bumps up to #49.
Quote:
Originally Posted by Didace
Songs are discrete units; there is no such thing as half a song. If the final answer was something like 47.2568745 songs, you would round up so the answer was 48 songs heard before the favorite plays again.
I wouldn't, because an EV doesn't have to be a possible outcome. If would round up if I were answering the question, "How many plays do I need for at least an X% chance of this happening?" But for the question of the weighted average, rounding would be wrong. So no, rounding doesn't come up anywhere in the calculation I outlined.