After their last game, Alice and Bob decide to have a bit more fun with their fair coin. Bob proposes the following game: considering a flip can come out as heads or tails, they will both predict one sequence of three consecutive flips each (both sequences must be distinct). Alice picks her sequence first. Bob will then start repeatedly flipping the coin, until the last three flips match one of the predicted sequences, and the predictor will be declared the winner.
Alice doesn't have enough time to calculate all of the probabilities, so you probably shouldn't do that in the answer either. She just wants you to convince her of which moves are good enough. What sequences can she pick so she has at least a 50% chance of winning?