A person starting with $$$$64$and making$6$ bets, wins three times and loses three times,
the wins and losses occurring in random order. The chance for a win is equal to the chance for a loss.
If each wager is for half the money remaining at the time of the bet, then the final result is:
$\textbf{(A)}\text{ a loss of }$ 27 \qquad \textbf{(B)}\text{ a gain of }$27 \qquad \textbf{(C)}\text{ a loss of }$ 37 \qquad \\ \textbf{(D)}\text{ neither a gain nor a loss}\qquad \\ \textbf{(E)}\text{ a gain or a loss depending upon the order in which the wins and losses occur}$