Expected Winnings Over a Random Number of Bets

A gambler places bets until a random stopping rule halts play; the number of bets $N$ is a stopping time for the i.i.d. bet outcomes with $E[N]=8$. Each bet has an i.i.d. net result $X_i$ with $E[X_i]=-0.05$ (a $5\%$ house edge per unit staked, with unit stakes), and the decision to stop after bet $n$ depends only on outcomes up to bet $n$. Compute the gambler's expected total winnings $E\!\left[\sum_{i=1}^N X_i\right]$, and state whether any stopping rule with $E[N]=8$ can make this positive.