IKMC 2027 - Grades 11-12 - Self-study SET 9 - Thematic Batch 3 Question 4

Alice and Bob play a dice game. First they draw lots to choose who starts. They then take turns rolling a die until someone rolls a 3 or a 6; that player wins. What is the probability that Alice wins in at most two of her rolls?

Editorial clarification: The limit is two rolls by Alice herself; the die and the initial draw are fair.