KöMaL 2019 B5027

Arthur Dumpling (Hungarian cartoon character: a fat bird who loves chocolate of all kinds) lives at 1 Sweet Street. The chocolate shop is operating at number $n$, the far end of the street. Arthur's daily fitness programme is as follows: he starts in front of number 2. When he stands in front of number $k$ (where $1<k<n$), he tosses a fair chocolate coin. If it shows heads, he moves to number $(k-1)$. If it shows tails, he moves to number $(k+1)$. If he reaches the chocolate shop, he enters and throws a chocolate ball down his throat, and then moves to number $(n-1)$. If he arrives back home, the fitness programme terminates. On average, how many chocolate balls does Arthur throw down his throat per day?