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Let $X_n$ the outcome of the $n^{th}$ coin. Its value is $1$ if it is heads, $0$ otherwise. Let $G_n$ the value of your portfolio after the $n^{th}$ round. If $X_n=1$, I have to check the outcome of $X_{n+1}$. If $X_{n+1}=1$, I make one dollar, if $X_{n+1}=0$, I lose one dollar. If $X_n=0$, I have to check the outcome of $X_{n+1}$. If $X_{n+1}=1$, I make ...


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