This problem comes from a TED talk by Peter Donnelly
Alice and Bob are flipping fair coins (in a fair manner). They each flip once per second. Alice flips until she gets two consecutive heads, then stops. Bob flips until he gets a heads followed by a tails, then stops.
Who is more likely to stop first? What is Alice’s expected number of tosses before she stops? What is Bob’s? What are the full probability distributions of coin tosses before stopping for Alice and Bob? What is the probability that they tie?
Can you generalize this scenario to longer patterns?