Expected duration of a fair game

In a fair gambler's ruin you start at $3 with absorbing barriers at $0 and $10. What is the expected number of $1 bets until you stop?

Show hints (2)+
  1. Fair-walk absorption time is i(N−i)i(N-i).
  2. 3⋅(10−3)3\cdot(10-3).

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