@jon-nyc said in Puzzle time - rolling a die:
But you were on the right track with your logic, I'm not sure where it went wrong.
I thought about this again.
My model computes a subtly different probability. p(13,6) = 0.5138 means that if I roll the dice 13 times, then in 51.38% of the cases I'll hit all 6 numbers. If I do this only 12 times, then in 43.8%. I verified this with a simulation and it is indeed true.
But that's different from "how many times do you need to roll a die before all six different numbers have turned up?". That's an expected value that averages over any number of rolls: Sometimes I need just 6 rolls, and if I'm unlucky I may need 500.
So I have answered a related but different question that would have been a nice follow-up puzzle 🙂