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Yes but why is Bob's harder? Answer without enumerating the full list of possible flip sequences

If they both fail to get what they need on their second tosses, it's possible for Alice to win on the next flip, but Bob needs two flips to win!

If Alice has failed to win on her second toss, her flip sequence was "HH", so she can win on the next toss, by flipping a T!

If Bob has failed to win on his second toss, his flip sequence was "HT", so he needs two more flips to win!