Infinite Geometric Series and the Geometric Series Test

Alice and Bob play a game!

First, Alice rolls a fair six-sided die. If the number that results is composite, she wins.

If not, she gives the die to Bob and he rolls it. If a prime number comes up, then Bob wins; if not, he gives the die to Alice and she rolls again.

They continue in this manner, with Alice winning if it is composite on her turn, and Bob winning if it is prime on his turn, until the game eventually ends.