Hard · Probability & Combinatorics · Numerical · ~12 min · #2

Expected Flips Until HTH

A fair coin is flipped until the pattern HTH appears in three consecutive flips. What is the expected number of flips?

Follow-up to think about: why is the answer different from the expected wait for HTT, even though both patterns have probability $\tfrac18$ at any given position?

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First-step analysisPattern overlapMartingale (gambler) method

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Expected Flips Until HTH

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