Games and stopping · Subway
Lost on the subway
A lost tourist starts at the first station of a subway line with 11 stations in a row. At every station they board a train in a random direction, each with probability 1/2, and ride exactly one stop. At the first station the only train goes forward. On average, how many rides does it take them to first reach the last station?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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