A person plays a game, where they are given a single card in the first round. In each round, they take each of the cards they have and has a 1/4 chance of getting 2 extra cards for the next round, and 1-(1/4)=3/4 chance of getting nothing. (Note that the cards do not otherwise carry over). What is the expected number of rounds they play until they have no more cards?
I have ran some simulations, and came up with a value of roughly 1.46, but I don't know what is the exact value supposed to be.
Here is my code: https://ideone.com/MbP5B9