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MediumStochastic Processes
Flips Until Two Heads in a Row
Jane StreetCitadel
What is the expected number of fair-coin flips to get two heads in a row (HH)?
Approach
Track states: 0 heads so far vs. 1 head so far.
A tail always sends you back to the start state.
Related problems
Gambler’s RuinMediumExpected Flips for HTHHardRandom Walk — Expected StepsHardExpectation of GBMHardVariance of Brownian MotionEasyCovariance of Brownian MotionMedium
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