Problem #120

Alice and Bob play the following game. Alice chooses a sequence of heads and tails of length 3 then Bob chooses a different sequence of length 3. A fair coin is tossed repeatedly and a record is made of the results. The first person whose sequence appears (consecutively and in order) is the winner. For example, if Alice chooses HTH and Bob chooses THT and the sequence of tosses is TTHHTH..., then Alice wins.

• If Alice chooses HHT and Bob chooses THH, who is more likely to win and with what odds?
• If Alice chooses HHT and Bob chooses HTH, who is more likely to win and with what odds?
• What happens in general?

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